Abstract
Linear elasticity is one of the more successful theories of mathematical physics. Its pragmatic success in describing the small deformations of many materials is uncontested. The origins of the three-dimensional theory go back to the beginning of the 19th century and the derivation of the basic equations by Cauchy, Navier, and Poisson. The theoretical development of the subject continued at a brisk pace until the early 20th century with the work of Beltrami, Betti, Boussinesq, Kelvin, Kirchhoff, Lamé, Saint-Venant, Somigliana, Stokes, and others. These authors established the basic theorems of the theory, namely compatibility, reciprocity, and uniqueness, and deduced important general solutions of the underlying field equations. In the 20th century the emphasis shifted to the solution of boundary-value problems, and the theory itself remained relatively dormant until the middle of the century when new results appeared concerning, among other things, Saint-Venant’s principle, stress functions, variational principles, and uniqueness.
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1913 Gwyther, R. F.: The specification of the elements of stress. Part II. A simplification of the specification given in Part I. Mem. Manchester Lit. Phil. Soc. 57, No. 5 (4 pp.) (17).
Hellinger, E.: 1914 Die allgemeinen Ansätze der Mechanik der Kontinua. In: Vol. 44 of the Encyklopädie der Mathematischen Wissenschaften, edited by F. Klein and C. Müller. Leipzig: Teubner. (38).
KoLosov, G. V.: 1914 Über einige Eigenschaften des ebenen Problems der Elastizitätstheorie. Z. Math. Phys. 62, 383–409. (47).
Domke, O.: 1915 Über Variationsprinzipien in der Elastizitätslehre nebst Anwendungen auf die technische Statik. Z. Math. Phys. 63, 174–192. (34, 36).
Korn, A.: 1915 Über die beiden bisher zur Lösung der ersten Randwertaufgabe der Elastizitätstheorie eingeschlagenen Wege. Annaes. Acad. Poly. Porto 10, 129–156. (44).
Weyl, H.: 1915 Das asymptotische Verteilungsgesetz der Eigenschwingungen eines beliebig gestalteten elastischen Körpers. Rend. Circ. Mat. Palermo 39, 1–50. (57, 78).
Zaremba, S.: 1915 Sopra un teorema d’unicita relativo alla equazione délie onde sferiche. Atti Accad. Lincei Rend. (5) 24, 904–908. (74).
1916 Prange, G.: Die Variations-und Minimalprinzipe der Statik der Baukonstruktionen. Habilitationsschrift. Tech. Univ. Hannover. (34, 38).
1919 Muskhelishvili, N. I.: Sur l’intégration de l’équation biharmonique. Izv. Akad. Nauk SSSR. 663-686. (47).
Serini, R.: 1919 Deformazioni simmetriche dei corpi elastici. Atti Accad. Lincei Rend. (5) 28, 343–347. (44).
Courant, R.: 1920 Über die Eigenwerte bei den Differentialgleichungen der mathematischen Physik. Math. Z. 7, 1–57. (76, 77).
Rubinowicz, A.: 1920 Herstellung von Lösungen gemischter Randwertprobleme bei hyperbolischen Differentialgleichungen zweiter Ordnung durch Zusammenstückelung aus Lösungen einfacher gemischter Randwertaufgaben. Mon. Math. Phys. 30, 65–79. (74).
Burgatti, P.: 1923 Sopra una soluzione molto generale dell’equazioni dell’equilibrio elastico. Atti Accad. Bologna Rend. (2) 27, 66–73. (44).
Southwell, R.: 1923 On Castigliano’s theorem of least work and the principle of Saint-Venant. Phil. Mag. (6) 45, 193–212. (54).
Lichtenstein, L.: 1924 Über die erste Randwertaufgabe der Elastizitätstheorie. Math. Z. 20, 21–28. (27, 53).
Timpe, A.: 1924 Achsensymmetrische Deformation von Umdrehungskörpern. Z. Angew. Math. Mech. 4, 361–376. (44).
Weber, C.: 1925 Achsensymmetrische Deformation von Umdrehungskörpern. Z. Angew. Math. Mech. 5, 477–468. (44).
Burgatti, P.: 1926 Sopra due utili forme dell’integrale generale dell’equazione per l’equilibrio dei solidi elastici isotropi. Mem. Accad. Sci. Bologna (8) 3, 63–67. (44).
Kotchine, N. E.: 1926 Sur la théorie des ondes de choc dans un fluide. Rend. Cire. Mat. Palermo 50, 305–344. (73).
Auerbach, F.: 1927 Elastizität der Kristalle. Handbuch der Physikalischen und Technischen Mechanik 3, 239–282. Leipzig: Barth. (26).
Korn, A.: 1927 Allgemeine Theorie der Elastizität. Handbuch der Physikalischen und Technischen Mechanik 3, 1–47. Leipzig: Barth. (27, 53).
1927 Love, A. E. H.: A Treatise on the Mathematical Theory of Elasticity, 4th ed. Cambridge. (18, 26, 27, 29, 44, 45, 47, 51, 52, 53, 54, 65, 68, 73).
Friedrichs, K. O., and H. Lewy: 1928 Über die Eindeutigkeit und das Abhängigkeitsgebiet der Lösungen beim Anfangswertproblem linearer hyperbolischer Differentialgleichungen. Math. Ann. 98, 192–204. (74).
Geckeler, J.W.: 1928 Elastizitätstheorie anisotroper Körper (Kristallelastizität). In: Volume VI of the Handbuch der Physik, edited by R. Grammel. Berlin: Springer. (26).
Trefftz, E.: 1928 Mathematische Elastizitätstheorie. In: Volume VI of the Handbuch der Physik, edited by R. Grammel. Berlin: Springer. (34, 44, 47, 51, 53).
Trefftz, E.: 1928 Konvergenz und Fehlerschätzung beim Ritzschen Verfahren. Math. Ann. 100, 503–521. (37).
Kellogg, O. v.: 1929 Foundations of Potential Theory. Berlin: Springer. (5, 6, 8, 52).
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Filon, L. N. G.: 1930 On the relation between corresponding problems in plane stress and in generalized plane stress. Q. J. Appl. Math. 1, 289–299. (45).
1930 Galerkin, B.: On an investigation of stresses and deformations in elastic isotropic solids [in Russian]. Dokl. Akad. Nauk SSSR, 353-358. (44).
Galerkin, B.: 1930 Contribution à 1a solution générale du problème de la théorie de l’élasticité dans le cas de trois dimensions. C. R. Acad. Sci., Paris 190, 1047–1048. (44).
1930 Rellich, F.: Ein Satz über mittlere Konvergenz. Nachr. Ges. Wissen. Göttingen. Math.-Phys. Kl., 30-35. (7).
1931 Burgatti, P.: Teoria Matematica délia Elasticità. Bologna: Zanichelli. (30).
1931 Coker, E. G., and L. N. G. Filon: A Treatise on Photoelasticity. Cambridge. (45).
1931 Galerkin, B.: On the general solution of a problem in the theory of elasticity in three dimensions by means of stress and displacement functions [in Russian]. Dokl. Akad. Nauk SSSR, 281-286. (44).
1931 Hobson, E. W.: The Theory of Spherical and Ellipsoidal Harmonies. Cambridge. (8).
Supino, G.: 1931 Sopra alcune limitazioni per 1a sollecitazione elastica e sopra 1a dimostrazione del principio del De Saint Venant. Ann. Mat. (4) 9, 91–119. (54).
Muskhelishvili, N. I.: 1932 Recherches sur les problèmes aux limites relatifs à l’équation biharmonique et aux équations de l’élasticité à deux dimensions. Math. Ann. 107, 282–312. (47).
Papkovitch, P. F.: 1932 Expressions générales des composantes des tensions, ne renfermant comme fonctions arbitraires que des fonctions harmoniques. C.R. Acad. Sci., Paris 195, 754–756. (44).
Papkovitch, P. F.: 1932 Solution générale des équations différentielles fondamentales d’élasticité, exprimée par trois fonctions harmoniques. C.R. Acad. Sci., Paris 195, 513–515. (44).
Papkovitch, P. F.: 1932 The representation of the general integral of the fundamental equations of the theory of elasticity in terms of harmonic functions [in Russian]. Izv. Akad. Nauk SSSR, Fiz.-Mat. Ser. 10, 1425–1435. (44).
Signorini, A.: 1932 Sollecitazioni iperastatiche. Rend. 1st. Lombardo (2) 65, 1–7. (18).
Marguerre, K.: 1933 Ebenes und achsensymmetrisches Problem der Elastizitätstheorie. Z. Angew. Math. Mech. 13, 437–438. (44).
Muskhelishvili, N. I.: 1933 Recherches sur les problèmes aux limites relatifs à l’équation biharmonique et aux équations de l’élasticité à deux dimensions. Math. Ann. 107, 282–312. (32).
Phillips, H. B.: 1933 Vector Analysis. New York: Wiley. (6).
Signorini, A.: 1933 Sopra alcune questioni di statica dei sistemi continui. Ann. Scuola Norm. Pisa (2) 2, 231–257. (18).
Biezeno, C.: 1934 Über die Marguerresche Spannungsfunktion. Ing.-Arch. 5, 120–124. (44).
Finzi, B.: 1934 Integrazione délie equazioni indefinite délia meccanica dei sistemi continui. Atti Accad. Lincei Rend. (6) 19, 578–584, 620-623. (17).
Muskhelishvili, N. I.: 1934 A new general method of solution of the fundamental boundary problems of the plane theory of elasticity [in Russian]. Dokl. Akad. Nauk SSSR 3, 7–9. (47).
Neuber, H.: 1934 Ein neuer Ansatz zur Lösung räumlicher Probleme der Elastizitätstheorie. Der Hohlkegel unter Einzellast als Beispiel. Z. Angew. Math. Mech. 14, 203–212. (44).
Phillips, H. B.: 1934 Stress functions. J. Math. Phys. 13, 421–425. (47).
Sobrero, L.: 1934 Nuovo metodo per lo studio dei problemi di elasticità con applieazione al problema della piastra forata. Ric. Ingegneria 2, 255–264. (44).
Grodski, G. D.: 1935 The integration of the general equations of equilibrium of an isotropic elastic body by means of the Newtonian potential and harmonic functions [in Russian]. Izv. Akad. Nauk SSSR Otdel Mat. 4, 587–614. (44).
KoLosov, G. V.: 1935 An Application of the Complex Variable in the Theory of Elasticity [in Russian]. Moscow-Leningrad: Gostehizdat. (47).
Marguerre, K.: 1935 Ebenes und achsensymmetrisches Problem der Elastizitätstheorie. Z. Angew. Math. Mech. 13, 437–438. (44).
Neuber, H.: 1935 Der räumliche Spannungszustand in Umdrehungskerben. Ing. Arch. 6, 133–156. (44).
Nielsen, T.: 1935 Elementare Mechanik. Berlin: Springer. (13).
Sobolev, S. L.: 1935 General theory of the diffraction of waves on Riemann surfaces. Trudy Mat. Inst. Steklov 9, 39–105-(42).
Sobrero, L.: 1935 Del significato meccanico della funzione di Airy. Ric. Ingegneria 3, 77–80 = Atti. Accad. Lincei Rend. (6) 21, 264-269. (17).
Sobrero, L.: 1935 Delle funzioni analoghe al potentiate intervenienti nella fisica-matematica. Atti. Accad. Lincei. Rend. (6) 21, 448–454. (44, 47).
Westergaard, H.: 1935 General solution of the problem of elastostatics of an n-dimen-sional homogeneous isotropic solid in an n-dimensional space. Bull. Amer. Math. Soc. 41, 695–699-(44).
Mindlin, R. D.: 1936 Force at a point in the interior of a semi-infinite solid. Phys. 7, 195–202. (51).
Mindlin R.: 1936 Note on the Galerkin and Papkovitch stress functions. Bull. Amer. Math. Soc. 42, 373–376. (44).
1936 Nicolesco, M.: Les fonctions polyharmoniques. Actualités Sci. Ind. No. 331. (8).
Picone, M.: 1936 Nuovi indirizzi di ricerca nella teoria e nel calcolo delle soluzioni di talune equazioni lineari alle derivate parziali della Fisica Matematica. Ann. Scuola Norm. Pisa (2) 5, 213–288 (8).
Southwell, R. V.: 1936 Castigliano’s principle of minimum strain energy. Proc. Roy. Soc. Lond. (A) 154, 4–21. (18, 36).
Zanaboni, O.: 1936 Il problema della funzione delle tensioni in un sistema spaziale isotropo. Bull. Un. Mat. Ital. 15, 71–76. (44).
Goodier, J. N.: 1937 A general proof of Saint-Venant’s principle. Phil. Mag. (7) 23, 607–609. (54).
Goodier, J. N.: 1937 Supplementary note on “A general proof of Saint-Venant’s principle”. Phil. Mag. (7) 24, 325. (54).
Neuber, H.: 1937 Kerbspannungslehre. Berlin: Springer. (44).
Odqvist, F.: 1937 Équations de compatibilité pour un système de coordonnées triples orthogonaux quelconques. C.R. Acad. Sci., Paris 205, 202–204. (14).
Papkovitch, P. F.: 1937 Survey of some general solutions of the fundamental differential equations of equilibrium of an isotropic elastic body [in Russian]. Prikl. Mat. Meh. 1, 117–132. (44).
Zanaboni, O.: 1937 Dimostrazione generate del principio del De Saint-Venant. Atti Accad. Lincei Rend. 25, 117–121. (54, 56a).
Zanaboni, O.: 1937 Valutazione deU’errore massimo cui da luogo l’applicazione del principio del Saint-Venant. Atti Accad. Lincei Rend. 25, 595–601. (54, 56a).
Zanaboni, O.: 1937 Sull’approssimazione dovuta al principio del De Saint-Venant nei solidi prismatici isotropi. Atti Accad. Lincei Rend. 26, 340–345. (54, 55, 56a).
Blinchikov, T. N.: 1938 The differential equations of equilibrium of the theory of elasticity in curvilinear coordinate systems [in Russian]. Prikl. Mat. Meh. 2, 407–413. (14).
1938 Sherman, D. J.: On the distribution of eigenvalues of integral equations in the plane theory of elasticity [in Russian]. Trudy Seismol. Inst. Akad. Nauk SSSR, No. 82. (32).
Slobodyansky, M.: 1938 Expression of the solution of the diferential equations of elasticity by means of one, two, and three functions and proof of the generality of these solutions [in Russian]. Uch. Zap. Mosk. Gos. Univ. 24, 191–202. (44).
Slobodyansky, M.: 1938 Stress functions for spatial problems in the theory of elasticity [in Russian]. Uch. Zap. Mosk. Gos. Univ. 24, 181–190. (44).
1938 Southwell, R. V.: Castigliano’s principle of minimum strain-energy, and the conditions of compatibility for strain. Stephen Timoshenko 60th Aniv. Vol. New York: MacMillan. (18, 36).
Burgers, J. M.: 1939 Some considerations on the fields of stress connected with dislocations in a regular crystal lattice. Proc. Koninkl. Ned. Akad. Wetenschap. 42, 293–325, 378-399. (14).
Friedrichs, K. O.: 1939 On differential operators in Hilbert spaces. Am. J. Math. 61, 523–544. (42).
Graffi, D.: 1939 Sui teoremi di reciprocità nei fenomeni dipendenti dal tempo. Ann. Mat. (4) 18, 173–200. (61).
1939 Papkovitch, P. F.: Theory of Elasticity [in Russian]. Moscow. (44).
Fadle, J.: 1940 Die Selbstspannungs-Eigenwertfunktionen der quadratischen Scheibe. Ing. Arch. 11, 125–149. (56).
Locatelli, P.: 1940 Estensione del principio di St. Venant a corpi non perfettamente elastici. Atti Accad. Sci. Torino 75, 502–510. (54).
Locatelli, P.: 1940 Sul principio di Menabrea. Boll. Un. Nat. Ital. (2) 2, 342–347. (18, 36).
1940 Locatelli, P.: Sulla congruenza delle deformazioni. Rend. 1st. Lombardo 73 =(3) 4 (1939-1940), 457-464. (18, 36).
Platrier, O.: 1941 Sur l’intégration des équations indéfinies de l’équilibre élastique. C. R. Acad. Sci., Paris 212, 749–751. (44).
Sakadi, Z.: 1941 Elastic waves in crystals. Proc. Phys. Math. Soc. Japan (3) 23, 539–547. (70, 71).
1942 Finzi, B.: Propagazione ondosa nei continui anisotropi. Rend. 1st. Lombardo, 75. (3) 6 (1941/42) 630-640. (73).
Goodier, J.N.: 1942 An extension of Saint-Venant’s principle, with applications. J. Appl. Phys. 13, 167–171. (54).
Frank, P., and R. v. Mises: 1943 Die Differential-und Integralgleichungen der Mechanik und Physik, Vol. 1. New York: Rosenberg. (8).
Stevenson, A. C: 1943 Some boundary problems of two-dimensional elasticity. Phil. Mag. (7) 34, 766–793. (47).
Udeschini, P.: 1943 Sull’energia di deformazione. Rend. 1st. Lombardo 76 = (3) 7, 25–34. (24).
Carrier, G. F.: 1944 The thermal stress and body-force problems of the infinite orthotropic solid. Q. Appl. Math. 2, 31–36. (51).
Friedrichs, K. O.: 1944 The identity of weak and strong extensions of differential operators. Trans. Am. Math. Soc. 55, 132–151. (42).
Vlasov, V. Z.: 1944 Equations of compatibility of deformation in curvilinear co-ordinates [in Russian]. Prikl. Mat. Meh. 8, 301–306. (14).
Fox, L., and R. V. Southwell: 1945 Relaxation methods applied to engineering problems. VII A. Biharmonic analysis as applied to the flexure and extension of flat elastic plates. Phil. Trans. Roy. Soc. Lond. Ser. A 239, 419–460. (47).
Kuzmin, R. O.: 1945 On Maxwell’s and Morera’s formulae in the theory of elasticity. Dokl. Akad. Nauk SSSR 49, 326–328. (17).
Locatelli, P.: 1945 Nuove espressioni variazionali nella dinamica elastica. Rend. 1st. Lombardo 78= (3) 9, 247–257. (65).
Locatelli, P.: 1945 Sull’interpretazione di principi variazionali dinamica nella statica elastica. Rend. 1st. Lombardo 78 = (3) 9, 301–306. (65).
Mises, R. v.: 1945 On Saint-Venant’s principle. Bull. Amer. Math. Soc. 51, 555–562. (54).
Rayleigh, J. W. S.: 1945 The Theory of Sound, Vol. 1. New York: Dover. (39).
Stevenson, A. C.: 1945 Complex potentials in two-dimensional elasticity. Proc. Roy. Soc. Lond. (A) 184, 129–179, 218-229. (47).
Butty, E.: 1946 Tratado de elasticidad teorico-technica. Buenos Aires: Centro Estudiantes de Ingenieria. (51, 71).
Hearmon, R. F. S.: 1946 The elastic constants of anisotropic materials. Rev. Mod. Phys. 18, 409–440. (26).
Poritaky, H.: 1946 Application of analytic functions to two-dimensional biharmonic analysis. Trans. Am. Math. Soc. 59, 248–279. (47).
Prager, W.: 1946 On plane elastic strain in doubly-connected domains. Q. Appl. Math. 3, 377–380. (47).
Friedrichs, K. O.: 1947 On the boundary-value problems of the theory of elasticity and Korn’s inequality. Ann. Math. 48, 441–471. (13, 42).
Graffi, D.: 1947 Sul teorema di reciprocità nella dinamica dei corpi elastici. Mem. Accad. Sci. Bologna 18, 103–109. (19, 61).
Gutman, C. G.: 1947 General solution of a problem in the theory of elasticity in generalized cylindrical coordinates [in Russian]. Dokl. Akad. Nauk SSSR 58, 993–996. (44).
Lifshic, I. M., and L. N. Rozencveig: 1947 On the construction of the Green’s tensor for the fundamental equations of the theory of elasticity in the case of an unrestricted anisotropic elastic medium [in Russian]. Akad. Nauk SSSR. Zhurnal Eksper. Teoret. Fiz. 17, 783–791. (51).
Mikhlin, S. G.: 1947 Fundamental solutions of the dynamic equations of the theory of elasticity for inhomogeneous media [in Russian]. Prikl. Mat. Meh. 11, 423–432. (68).
Prager, W., and J. L. Synge: 1947 Approximations in elasticity based on the concept of function space. Q. Appl. Math. 5, 241–269. (34).
Shapiro, G.: 1947 Les fonctions des tensions dans un système arbitraire de coordonnées curvilignes. Dokl. Acad. Sci. URSS 55, 693–695. (44).
1947 Ter-Mkrtychan, L. N.: On general solutions of the problems of the theory of elasticity [in Russian]. Trudy Leningr. Politekhn. Akad. in-ta, No. 4. (44).
Van Hove, L.: 1947 Sur l’extension de la condition de Legendre du calcul des variations aux intégrales multiples à plusieurs fonctions inconnues. Proc. Koninkl. Ned. Akad. Wetenschap. 50, 18–23. (32).
Diaz, J. B., and H. J. Greenberg: 1948 Upper and lower bounds for the solution of the first boundary value problem of elasticity. Q. Appl. Math. 6, 326–331. (52).
Elliot, H.A.: 1948 Three-dimensional stress distributions in hexagonal aeolotropic crystals. Proc. Cambridge Phil. Soc. 44, 522–533. (51).
1948 Erim, K.: Sur le principe de Saint-Venant. Proc. Seventh Int. Cong. Appl. Mech. London. (54).
Flint, E. E.: 1948 A Practical Handbook on Geometrical Crystallography [in Russian]. Moscow: Gosgeolizdat. (21).
Moriguti, S.: 1948 On Castigliano’s theorem in three-dimensional elastostatics [in Japanese]. J. Soc. Appl. Mech. Japan 1, 175–180. (18).
Timpe, A.: 1948 Torsionsfreie achsensymmetrische Deformation von Umdrehungskörpern und ihre Inversion. Z. Angew. Math. Mech. 28, 161–166. (44).
Weber, G.: 1948 Spannungsfunktionen des dreidimensionalen Kontinuums. Z. Angew. Math. Mech. 28, 193–197. (17).
Finzi, B., and M. Pastori: 1949 Calcolo Tensoriale e Applicazioni. Bologna: Zanichelli. (17).
Freiberger, W.: 1949 On the solution of the equilibrium equations of elasticity in general curvilinear coordinates. Australian J. Sci. A 2, 483–492. (44).
Freiberger, W.: 1949 The uniform torsion of an incomplete tore. Australian J. Sci. A 2, 354–375. (44).
Iacovache, M.: 1949 O extindere a metodei lui Galerkin pentru sistemul ecuatiilor elasticitätii. Bul. St. Acad. R. P. Romane 1, 593–596. (44, 67).
Krutkov, Y. A.: 1949 Tensor Stress Functions and General Solutions in the Static Theory of Elasticity [in Russian]. Moscow: Akademkniga. (17, 44).
Moisil, G.: 1949 Asupra formulelor lui Galerkin in teoria elasticitätii. Bui. St. Acad. R. P. Romane 1, 587–592. (44).
Pastori, M.: 1949 Propagazione ondosa nei continui anisotropi e corrispondenti direzioni principali. Nuovo Cimento (9) 6, 187–193. (73).
Peretti, G.: 1949 Significato del tensore arbitrario che interviene nell’integrale generale delle equazioni della statica dei continui. Atti Sem. Mat. Fis. Univ. Modena 3, 77–82. (17).
Aquaro, G.: 1950 Un teorema di media per 1e equazioni dell’elasticità. Riv. Mat. Univ. Parma 1, 419–424. (43).
Arzhanyh, I. S.: 1950 On the theory of integration of the dynamical equations of an isotropic elastic body [in Russian]. Dokl. Akad. Nauk SSSR (N.S.) 73, 41–44. (53, 69).
Blokh, V.: 1950 Stress functions in the theory of elasticity [in Russian]. Prikl. Mat. Meh. 14, 415–422. (17,44).
Fichera, G.: 1950 Sull’esistenza e sul calcolo delle soluzioni dei problemi al contorno, relativi airequilibrio di un corpo elastico. Ann. Scuola Norm. Pisa (3) 4, 35–99. (49, 50).
Fridman, M. M.: 1950 The mathematical theory of elasticity of anisotropic media [in Russian]. Prikl. Mat. Meh. 14, 321–340. (45).
Iacovache, M.: 1950 Asupra relatiilor dintre tensiuni intr’un corp elastic in miscare. Bul. St. Acad. R. P. Romane 2, 699–705. (59).
Ionescu-Cazimir, V.: 1950 Asupra ecuatiilor echilibrului termoelastic. I. Analogul vectorului lui Galerkin. Bul. St. Acad. R. P. Romane 2, 589–595. (44).
Moisil, G.: 1950 Asupra unui vector analog vectorului lui Galerkin pentru echilibrul corpurilor elastice cu isotropie transversa. Bul. St. Acad. R. P. Romane 2, 207–210 (44).
Morinaga, K., and T. Nono: 1950 On stress-functions in general coordinates. J. sci. Hiroshima Univ. Ser. A 14, 181–194. (17).
Reissner, E.: 1950 On a variational theorem in elasticity. J. Math. Phys. 29, 90–95. (38).
Sobolev, S. L.: 1950 Some Applications of Functional Analysis in Mathematical Physics [in Russian]. Leningrad: University Press. (I have seen this work only in the English translation by F. E. Browder, Providence: Am. Math. Soc. 1963.) (42).
Synge, J. L.: 1950 Upper and lower bounds for solutions of problems in elasticity. Proc. Roy. Irish Acad. Sect. A 53, 41–64. (43, 52).
Timpe, A.: 1950 Spannungsfunktionen für die von Kugel-und Kegelflächen begrenzten Körper-und Kuppelprobleme. Z. Angew. Math. Mech. 30, 50–61. (44).
Albrecht, F.: 1951 L’équilibre élastique des cristaux du système cubique. Com. Acad. R. P. Romane 1, 403–408. (27).
Arzhanyh, I. S.: 1951 The integral equations of the dynamics of an elastic body [in Russian]. Dokl. Akad. Nauk SSSR (N.S.) 76, 501–503. (53, 69).
Arzhanyh, I. S.: 1951 Integral equations for the representation of the vector of translation, spatial dilatation, and rotation of an elastic body [in Russian]. Prikl. Mat. Meh. 15, 387–391. (69).
Arzhanyh, I. S.: 1951 The fundamental integral equations of the dynamics of an elastic body [in Russian]. Dokl. Akad. Nauk SSSR (N.S.) 81, 513–516. (69).
Eidus, D. M.: 1951 On the mixed problem of the theory of elasticity [in Russian]. Dokl. Akad. Nauk SSSR. 76, 181–184. (13).
Fichera, G.: 1951 Über eine Möglichkeit zur Kontrolle der physikalischen Widerspruchsfreiheit der Gleichungen der mathematischen Elastizitätstheorie. Z. Angew. Math. Mech. 31, 268–270. (31).
Filonenko-Borodich, M. M.: 1951 The problem of the equilibrium of an elastic parallelepiped subject to assigned loads on its boundaries [in Russian]. Prikl. Mat. Meh. 15, 137–148. (17).
Filonenko-Borodich, M. M.: 1951 Two problems on the equilibrium of an elastic parallelepiped [in Russian]. Prikl. Mat. Meh. 15, 563–574. (17).
Sternberg, E., R. A. Eubanks and M. A. Sadowski: 1951 On the stress function approaches of Boussinesq and Timpe to the axisymmetric problem of elasticity theory. J. Appl. Phys. 22, 1121–1124. (44).
Timoshenko, S., and J. N. Goodier: 1951 Theory of Elasticity, 2nd ed. New York: McGraw Hill. (51).
Timpe, A.: 1951 Spannungsfunktionen achsensymmetrischer Deformationen in Zylinderkoordinaten. Z. Angew. Math. Mech. 31, 220–224. (44).
Valcovici, V.: 1951 Sur les relations entre les tensions. Com. Acad. R. P. Romane 1, 337–339. (59).
Cooperman, P.: 1952 An extension of the method of Trefftz for finding local bounds on the solutions of boundary-value problems, and on their derivatives. Q. Appl. Math. 10, 359–373. (37).
1952 Mikhlin, S. G.: The Problem of the Minimum of a Quadratic Functional [in Russian]. Moscow. (I have seen this work only in the English translation by A. Feinstein, San Francisco: Holden Day 1965.) (13, 43).
Moisil, A.: 1952 Les relations entre les tensions pour les corps élastiques à isotropie transverse. Bul. St. Acad. R. P. Romane 3, 473–480. (27).
Sbrana, F.: 1952 Una proprietà caratteristica delle equazioni dell’elasticità. Atti Accad. Ligure Sci. Lett. 9, 84–88. (43).
Sneddon, I. N.: 1952 The stress produced by a pulse of pressure moving along the surface of a semi-infinite solid. Rend. Circ. Mat. Palermo (2) 1, 57–62. (47).
Tiffen, R.: 1952 Uniqueness theorems of two-dimensional elasticity theory. Q. J. Mech. Appl. Math. 5, 237–252. (50).
1952 Westergaard, H.: Theory of Elasticity and Plasticity. Cambridge. (44).
Arzhanyh, I. S.: 1953 Construction of the integral equations of statics in the theory of elasticity by means of Green’s functions [in Russian]. Akad. Nauk Uzbek. SSR. Trudy Inst. Mat. Meh. 10, 5–25. (53).
Arzhanyh, I. S.: 1953 Stress tensor functions for the dynamics of an elastic body [in Russian]. Dokl. Akad. Nauk Uzbek. SSR., No. 7, 3–4. (17).
Bergman, S., and M. Schiffer: 1953 Kernel functions and elliptic differential equations in mathematical physics. New York: Academic. (53).
Bishop, R. E. D.: 1953 On dynamical problems of plane stress and plane strain. Q. J. Mech. Appl. Math. 6, 250–254. (67).
Bland, D. R.: 1953 Mean displacements on the boundary of an elastic solid. Q. J. Mech. Appl. Math. 6, 379–384. (29).
Brdicka, M.: 1953 The equations of compatibility and stress functions in tensor form [in Russian]. Czech. J. Phys. 3, 36–52. (44).
Churikov, F.: 1953 On a form of the general solution of the equilibrium equations for the displacements in the theory of elasticity [in Russian]. Prikl. Mat. Meh. 17, 751–754. (44).
Courant, R., and D. Hilbert: 1953 Methods of Mathematical Physics, Vol. 1. New York: Interscience. (39, 76, 77, 78).
Dzhanelidze, G. I.: 1953 The general solution of the equations of the theory of elasticity in arbitrary linear coordinates [in Russian]. Dokl. Akad. Nauk SSSR 88, 423–425. (44).
Ericksen, J. L.: 1953 On the propagation of waves in isotropic incompressible perfectly elastic materials. J. Rational Mech. Anal. 2, 329–337. Reprinted in Problems of Non-linear Elasticity. Intl. Sci. Rev. Ser. New York: Gordon and Breach 1965. (73).
Fichera, G.: 1953 Condizioni perché sia compatibile il problema principale délia statica elastica. Atti Accad. Lincei Rend. (8) 14, 397–400. (31).
FöPPL, L.: 1953 Ein Mittelwertsatz der ebenen Elastizitätstheorie. Sitzber. Math.-Naturw. Kl. Bayer Akad. Wiss. München 1952, 215–217. (43).
Hu, H.: 1953 On the three-dimensional problems of the theory of elasticity of a transversely isotropic body. Sci. Sinica (Peking) 2, 145–151. (44).
Kröner, E.: 1953 Das Fundamentalintegral der anisotropen elastischen Differentialgleichungen. Z. Physik 136, 402–410. (51).
1953 Mindlin, R. D.: Force at a point in the interior of a semi-infinite solid. Proc. First Midwestern Conf. Solid Mech. (51).
Misicu, M.: 1953 Echilibrul mediilor continue cu deformäri mari. Stud. Cercet. Mec. Metal. 4, 31–53. (32).
Saenz, A. W.: 1953 Uniformly moving dislocations in anisotropic media. J. Rational Mech. Anal. 2, 83–98. (51, 71).
Schaefer, H.: 1953 Die Spannungsfunktionen des dreidimensionalen Kontinuums und des elastischen Körpers. Z. Angew. Math. Mech. 33, 356–362 (17,18, 44).
Trenin, S.: 1953 On the solutions of the equilibrium equations of an axisymmetrical problem in the theory of elasticity [in Russian]. Vestn. Mosk. Univ. Ser. Fiz., Mat. 8, 7–13. (44).
Washizu, K.: 1953 Bounds for solutions of boundary-value problems in elasticity. J. Math. Phys. 32, 117–128. (52).
Arzhanyh, I. S.: 1954 Dynamical potentials of the theory of elasticity [in Russian]. Akad. Nauk Uzbek. SSR. Trudy Inst. Mat. Meh. 13, 3–17. (69).
1954 Arzhanyh, I. S.: Integral Equations of Basic Problems in the Theory of Vector Fields and in Elasticity [in Russian]. Tashkent: Izdat. Akad. Nauk Uzbek. SSR. (53, 69).
Brdicka, M.: 1954 Covariant form of the general solution of the Galerkin equations of elastic equilibrium [in Russian]. Czech. J. Phys. 4, 246. (44).
Browder, F. E.: 1954 Strongly elliptic systems of differential equations. Contrib. Th. Partial Diff. Eqns. Annals, of Math. Studies No. 33, 15–51. (32).
Eubanks, R., and E. Sternberg: 1954 On the axisymmetric problem of elasticity theory for a medium with transverse isotropy. J. Rational Mech. Anal. 3, 89–101. (44).
Graffi, D.: 1954 Über den Reziprozitätssatz in der Dynamik der elastischen Körper. Ing. Arch. 22, 45–46. (19, 61).
Günther, W.: 1954 Spannungsfunktionen und Verträglichkeitsbedingungen der Kontinuumsmechanik. Abhandl. Braunschweig. Wiss. Ges. 6, 207–219. (17).
Hu, H.: 1954 On the general theory of elasticity for a spherically isotropic medium. Sci. Sinica (Peking) 3, 247–260. (44).
Ionescu, D.: 1954 Asupra vectorului lui Galerkin în teoria elasticitätii si in hidrodinamica fluidelor vîscoase. Bul. St. Acad. R. P. Române 6, 555–571 (44).
Klyushnikov, V. D.: 1954 Derivation of the Beltrami-Michell equations from a variational principle [in Russian]. Prikl. Mat. Meh. 18, 250–252. (18).
Kröner, E.: 1954 Die Spannungsfunktionen der dreidimensionalen isotropen Elastizitätstheorie. Z. Physik 139, 175–188. Correction, Z. Phys. 143, 175 (1955). (17, 44).
Langhaar, H., and M. Stippes: 1954 Three-dimensional stress functions. J. Franklin Inst. 258, 371–382. (17).
Ling, C. B., and K. L. Yang: 1954 On symmetric strains in solids of revolution in curvilinear coordinates. Ann. Acad. Sinica Taipei 1, 507–516. (44).
Morrey, C. B., Jr.: 1954 Second order elliptic systems of differential equations. Contrib. Th. Partial Diff. Eqns. Annals of Math. Studies No. 33, 101–159. (32).
Musgrave, M. J. P.: 1954 On the propagation of elastic waves in aeolotropic media. Proc. Roy. Soc. Lond., Ser. (A) 226, 339–366. (71).
1954 Muskhelishvili, N. I.: Some Basic Problems of the Mathematical Theory of Elasticity [in Russian], 4th Ed. Moscow. (I have seen this work only in the English translation by J. R. M. Radok, Groningen: Noordhoff 1963.) (47, 50).
Ornstein, W.: 1954 Stress functions of Maxwell and Morera. Q. Appl. Math. 12, 198–201. (17).
Schumann, W.: 1954 Sur différentes formes du principe de B. de Saint-Venant. C. R. Acad. Sci., Paris 238, 988–99O. (54).
Slobodyansky, M. G.: 1954 The general form of solutions of the equations of elasticity for simply connected and multiply connected domains expressed by harmonic functions [in Russian]. Prikl. Mat. Meh. 18, 55–74. (44).
Sternberg, E.: 1954 On Saint-Venant’s principle. Q. Appl. Math. 11, 393–402. (54).
Aymerich, G.: 1955 Una proprietà dell’energia elastica. Boll. Un. Mat. Ital. (3) 10, 332–336. (34).
Arzhanyh, I. S.: 1955 Regular integral equations of the dynamics of an elastic body [in Russian]. Akad. Nauk Uzbek. SSR. Trudy Inst. Mat. Meh. 15, 79–85. (69).
1955 î Retarded potentials of the dynamics of an elastic body [in Russian]. Akad. Nauk Uzbek. SSR. Trudy Inst. Mat. Meh. 16, 5-22. (69).
1955 Babuska, I., K. Rektorys, and F. Vyöichlo: Mathematical Theory of Elasticity for the Plane Problem [in Czechoslovakian]. Prague. (I have seen this work only in the German translation by W. Heinrich, Berlin: Akademie 1960.) (56).
Hu, H.: 1955 On some variational principles in the theory of elasticity and the theory of plasticity. Sci. Sinica (Peking) 4, 33–54. (38).
Kaczkowski, Z.: 1955 The conjugate directions in an anisotropic body [in Polish]. Arch. Mech. Stos. 7, 52–86. (31).
Kröner, E.: 1955 Die Spannungsfunktionen der dreidimensionalen anisotropen Elastizitätstheorie. Z. Physik 141, 386–398. (17).
Kröner, E.: 1955 Die inneren Spannungen und der Inkompatibilitätstensor in der Elastizitätstheorie. Z. Angew. Phys. 7, 249–257. (17).
Lodge, A. S.: 1955 The transformation to isotropic form of the equilibrium equations for a class of anisotropic elastic solids. Q. J. Mech. Appl. Math. 8, 211–225. (31).
1955 Lur’e, A. I.: Three-dimensional problems in the theory of elasticity [in Russian]. Moscow: Gostekhizdat. (I have seen this work only in the English translation by D. B. McVean, New York: Interscience 1964.) (17, 44, 51).
Marguerre, K.: 1955 Ansätze zur Lösung der Grundgleichungen der Elastizitätstheorie. Z. Angew. Math. Mech. 35, 241–263. (17, 44).
Schaefer, H.: 1955 Die Spannungsfunktion einer Dyname. Abhandl. Braunschweig. Wiss. Ges. 7, 107–112. (17).
Sternberg, E., and R. A. Eubanks: 1955 On the concept of concentrated loads and an extension of the uniqueness theorem in the linear theory of elasticity. J. Rational Mech. Anal. 4, 135–168. (28, 51, 53).
1955 Washizu, K.: On the variational principles of elasticity and plasticity. Rept. 25-18, Cont. Nsori-07833 Massachusetts Institute of Technology, March. (38).
Dorn, W. S., and A. Schild: 1956 A converse to the virtual work theorem for deformable solids. Q. Appl. Math. 14, 209–213. (17, 36).
Duffin, R. J.: 1956 Analytic continuation in elasticity. J. Rational Mech. Anal. 5, 939–950. (42, 44).
Ericksen, J. L., and R. A. Toupin: 1956 Implications of Hadamard’s condition for elastic stability with respect to uniqueness theorems. Canad. J. Math. 8, 432–436. Reprinted in Foundations of Elasticity Theory. Intl. Sci. Rev. Ser. New York: Gordon and Breach 1965. (32, 57).
Eubanks, R. A., and E. Sternberg: 1956 On the completeness of the Boussinesq-Papkovitch stress functions. J. Rational Mech. Anal. 5, 735–746. (44).
Finzi, L.: 1956 Legame fra equilibrio e congruenza e suo significato fisico. Atti Accad. Lincei Rend. (8) 20, 205–211. (47).
Knopoff, L.: 1956 Diffraction of elastic waves. J. Acoust. Soc. Amer. 28, 217–229. (69).
Levin, M. L., and S. M. Rytov: 1956 Transition to geometrical approximations in elasticity theory [in Russian], Soviet Phys. Acoust. 2, 179–184. (73).
Miller, G. F., and M. J. P. Musgrave: 1956 On the propagation of elastic waves in aeolotropic media. III. Media of cubic symmetry. Proc. Roy. Soc. Lond. (A) 236, 352–383. (71).
1956 Pailloux, M. H.: Élasticité. Mem. Sci. Math. Acad. Sci. Paris 132. (71).
Radok, J. R. M.: 1956 On the solutions of problems of dynamic plane elasticity. Q. Appl. Math. 14, 289–298. (47).
Schaefer, H.: 1956 Die drei Spannungsfunktionen des zweidimensionalen ebenen Kontinuums. Österreich. Ing. Arch. 10, 267–277. (47).
Sokolnikoff, I. S.: 1956 Mathematical Theory of Elasticity. 2nd Ed. New York: McGraw-Hill. (14, 27, 36, 37, 44, 47).
Synge, J. L.: 1956 Flux of energy for elastic waves in anisotropic media. Proc. Roy. Irish Acad., Sect. A 58, 13–21. (71).
Temple, G., and W. G. Bickley: 1956 Rayleigh’s principle and its applications to engineering. New York: Dover. (56).
Basheleishvili, M. O.: 1957 On fundamental solutions of the differential equations of an anisotropic elastic body [in Russian]. Soobsö. Akad. Nauk Gruzin. SSR. 19, No. 4, 393–400. (51).
Bondarenko, B. A.: 1957 On a class of solutions of dynamical equations in the theory of elasticity [in Russian]. Akad. Nauk Uzbek. SSR. Trudy Inst. Mat. Men. 21, 41–49. (67).
Brdicka, M.: 1957 On the general form of the Beltrami equation and Papkovitch’s solution of the axially symmetric problem of the classical theory of elasticity. Czech. J. Phys. 7, 262–274. (17, 44).
Courant, R.: 1957 Differential and Integral Calculus, Vol. 2. New York: Interscience. (6).
Ericksen, J. L.: 1957 On the Dirichlet problem for linear differential equations. Proc. Amer. Math. Soc. 8, 521–522. (32).
Filonenko-Borodich, M. M.: 1957 On the problem of Lamé for the parallelepiped in the general case of surface loads [in Russian]. Prikl. Mat. Meh. 21, 550–559. (17).
Garabaldi, A. C.: 1957 Su una proprietà di media caratteristica per l’equazione dell’elastostatica. Rend. Sem. Mat. Univ. Padova 27, 306–318. (43).
Hill, R.: 1957 On uniqueness and stability in the theory of finite elastic strain. J. Mech. Phys. Solids 5, 229–241. (32, 34).
Horvay, G.: 1957 Saint-Venant’s principle: a biharmonic eigenvalue problem. J. Appl. Mech. 24, 381–386. (56).
1957 Mikhlin, S. G.: Variational Methods in Mathematical Physics [in Russian]. Moscow. (I have seen this work only in the English translation by T. Boddington, New York: Pergamon 1964.) (34, 37, 39).
Noll, W.: 1957 Verschiebungsfunktionen für elastische Schwingungsprobleme. Z. Angew. Math. Mech. 37, 81–87. (44).
Solomon, L.: 1957 Displacement potentials for the equations of elastostatics [in Roumanian], Buletinul Stiintific Ac. R.P.R., 9, 415–431. (44).
Solyanik-Krassa, K. V.: 1957 Stress functions of an axisymmetric problem in the theory of elasticity [in Russian]. Prikl. Mat. Meh. 21, 285–286. (44).
Sternberg, E., and R. A. Eubanks: 1957 On stress functions for elastokinetics and the integrations of the repeated wave equation. Q. Appl. Math. 15, 149–153. (67).
1957 Synge, J.L.: The Hypercircle in Mathematical Physics; a Method for the Approximate Solution of Boundary-Value Problems. Cambridge. (34, 51).
Synge, J.L.: 1957 Elastic waves in anisotropic media. J. Math. Phys. 35, 323–334. (71).
Thomas, T. Y.: 1957 The decay of waves in elastic solids. J. Math. Mech. 6, 759–768. (73).
1957 Washizu, K.: On the variational principles applied to dynamic problems of elastic bodies. ASRL TR 25-23. Massachusetts Institute of Technology. (65).
1958 Babich, V. M., and A. S. Alekseev: A ray method of computing wave front intensities [in Russian], Izv. Akad. Nauk SSSR, Ser. Geofiz. 17-31. (73).
Blokh, V. I.: 1958 On the representation of the general solution of the basic equations of the static theory of elasticity for an isotropic body with the aid of harmonic functions [in Russian]. Prikl. Mat. Meh. 22, 473–479. (44).
1958 Boley, B.: Some observations on Saint-Venant’s principle. Proc. Third U.S. National Congress Appl. Mech. 259-264. (54).
1958 De Hoop, A. T.: Representation theorems for the displacement in an elastic solid and their application to elastodynamic diffraction theory. Doctoral Dissertation, Technische Hogeschool, Delft. (69).
1958 Deev, V. M.: The solution of the spatial problem in the theory of elasticity [in Ukrainian]. Dopovidi Acad. Nauk Ukr. RSR 29-32. (44).
1958 Diaz, J. B., and L. E. Payne: Mean value theorems in the theory of elasticity. Proc. Third U. S. Natl. Congress Appl. Mech. 293-303. (8, 43, 55).
Diaz, J. B., and L. E. Payne:1958 On a mean value theorem and its converse for the displacements in the theory of elasticity. Port. Mat. 17, 123–126. (43).
Duffin, R. J., and W. Noll: 1958 On exterior boundary value problems in elasticity. Arch. Rational Mech. Anal. 2, 191–196. (32, 49, 50, 57).
Halmos, P.: 1958 Finite-Dimensional Vector Spaces. New York: Van Nostrand. (3, 23).
Hu, H.: 1958 On reciprocal theorems in the dynamics of elastic bodies and some applications. Sci. Sinica (Peking) 7, 137–150. (62).
Hu, H.: 1958 On two variational principles about the natural frequencies of elastic bodies. Sci. Sinica (Peking) 7, 293–312. (76).
Petrashen, G. I.: 1958 The investigations of the propagation of elastic waves [in Russian]. Vestn. Leningrad Univ. 13, No. 22, 119–136. (73).
Predeleanu, M.: 1958 Über die Verschiebungsfunktionen für das achsensymmetrische Problem der Elastodynamik. Z. Angew. Math. Mech. 38, 402–405. (67).
Reissner, E.: 1958 On variational principles in elasticity. Proc. Symp. Appl. Math. Vol. 8, Calculus of Variations and its Applications. New York: McGraw Hill. (38).
1958 Skuridin, G. A., and A. A. Gvozdev: Boundary conditions for the jumps of discontinuous solutions of the dynamical equations of the theory of elasticity [in Russian]. Izv. Akad. Nauk SSSR. Ser. Geofiz. 145-156. (73).
Smith, G. F., and R. S. Rivlin: 1958 The strain-energy function for anisotropic elastic materials. Trans. Amer. Math. Soc. 88, 175–193. (21, 26).
Sneddon, I. N.: 1958 Note on a paper by J. R. M. Radok. Q. Appl. Math. 16, 197. (47).
Sneddon, I. N. and D. S. Berry: 1958 The classical theory of elasticity. Handbuch der Physik 6. Berlin-Göttingen-Heidelberg: Springer. (67).
Teodorescu, P. P.: 1958 A plane problem of the theory of elasticity with arbitrary body forces [in Russian]. Rev. Méc. Appl. 3, 101–108. (47).
Washizu, K.: 1958 A note on the conditions of compatibility. J. Math. Phys. 36, 306–312. (18).
Buchwald, V. T.: 1959 Elastic waves in anisotropic media. Proc. Roy. Soc. Lond. (A) 253, 563–580. (73).
1959 Dana, J. S.: Dana’s manual of mineralogy 17th ed., revised by C. S. Hurlbut, Jr. New York: John Wiley. (21).
Deev, V. M.: 1959 On the form of the general solution of the three-dimensional problem of the theory of elasticity expressed with the aid of harmonic functions [in Russian]. Prikl. Math. Meh. 23, 1132–1133; translated as J. Appl. Math. Mech. 23, 1619-1622. (44).
DiMaggio, F. L., and H. H. Bleich: 1959 An application of a dynamic reciprocal theorem. J. Appl. Mech. 26, 678–679. (61).
Gvozdev, A. A.: 1959 On the conditions at elastic wave fronts propagating in a non-homogeneous medium [in Russian]. Prikl. Math. Meh. 23, 395–397; translated as J. Appl. Math. Mech. 23, 556-561. (73).
1959 Hardy, G. H., J. E. Littlewood, and G. Polya: Inequalities. Cambridge. (56).
Hijab, W. A.: 1959 Application of Papkovitch functions to three-dimensional problems of elasticity. Proc. Math. Phys. Soc. U.A.R. No. 23, 99–115. (44).
Ignaczak, J.: 1959 Direct determination of stresses from the stress equations of motion in elasticity. Arch. Mech. Stos. 11, 671–678. (59).
Karal, F. C., and J. B. Keller: 1959 Elastic wave propagation in homogeneous and inhomogeneous media. J. Acoust. Soc. Am. 31, 694–705. (73).
Mikusinski, J.: 1959 Operational Calculus. New York: Pergamon. (10, 69).
Pearson, C. E.: 1959 Theoretical Elasticity. Cambridge: Harvard University Press. (67).
Schaefer, H.: 1959 Die Spannungsfunktionen des dreidimensionalen Kontinuums; statische Deutung und Randwerte. Ing. Arch. 28, 291–306. (17).
Signorini, A.: 1959 Questioni di elasticità non linearizzata e semilinearizzata. Rend. Mat. e Appl. 18, 95–139. (31).
1959 Skuridin, G. A.: Duhamel’s principle and asymptotic solutions of dynamical equations in the theory of elasticity. II [in Russian]. Izv. Akad. Nauk SSSR. Ser. Geofiz. 337-343. (73).
Slobodyansky, M. G.: 1959 On the general and complete form of solutions of the equations of elasticity [in Russian]. Prikl. Math. Meh. 23, 468–482; translated as J. Appl. Math. Mech. 23, 666-685. (44).
Truesdell, C.: 1959 Invariant and complete stress functions for general continua. Arch. Rational Mech. Anal. 3, 1–29. (17, 44).
Truesdell, C.: 1959 The rational mechanics of materials-past, present, future. Applied Mech. Rev. 12, 75–80. Corrected reprint, Applied Mechanics Surveys. Washington: Spartan Books. 1965. (22).
Waterman, P. C.: 1959 Orientation dependence of elastic waves in single crystals. Phys. Rev. (2) 113, 1240–1253. (71).
Bernstein, B., and R. Toupin: 1960 Korn inequalities for the sphere and for the circle. Arch. Rational Mech. Anal. 6, 51–64. (13).
Boley, B. A.: 1960 On a dynamical Saint-Venant principle. J. Appl. Mech. 27, 74–78. (54) (54).
Boley, B. A. and J. H. Weiner: 1960 Theory of Thermal Stresses. New York: Wiley. (14).
1960 Bondarenko, B. A.: Gradient and curl solutions of the dynamical equations of elasticity theory [in Russian]. Issled. Mat. Analizu Mehanike Uzbek. Izdat. Akad. Nauk Uzbek. SSR., Tashkent, 17-29. (67).
Duff, G. F. D.: 1960 The Cauchy problem for elastic waves in an anisotropic medium. Trans. Roy. Soc. Lond. (A) 252, 249–273. (74).
1960 Ericksen, J. L.: Tensor fields. Appendix to [1960, 17]. (27).
Gurtin, M. E., and E. Sternberg: 1960 On the first boundary-value problem of linear elastostatics. Arch. Rational Mech. Anal. 3, 177–187. (32, 34, 57).
Indenbom, V. L.: 1960 Reciprocity theorems and influence functions for the dislocation density tensor and the deformation incompatibility tensor [in Russian]. Dokl. Akad. Nauk SSSR 128, 906–909; translated as Soviet Phys. Doklady 4, 1125-1128. (30).
Rieder, G.: 1960 Topologische Fragen in der Theorie der Spannungsfunktionen. Abhandl. Braunschweig. Wiss. Ges. 7, 4–65-(17).
Rüdiger, D.: 1960 Eine Verallgemeinerung des Prinzips vom Minimum der potentiellen Energie elastischer Körper. Ing. Arch. 27, 421–428. (38, 41).
Sirotin, Y. I.: 1960 Group tensor spaces [in Russian]. Kristallografiya 5, 171–179; translated as Soviet Phys.-Cryst. 5, 157-165. (26).
Sternberg, E.: 1960 On some recent developments in the linear theory of elasticity. In Structural Mechanics. New York: Pergamon Press. (17, 54).
Sternberg, E.: 1960 On the integration of the equations of motion in the classical theory of elasticity. Arch. Rational Mech. Anal. 6, 34–50. (67).
Teodorescu, P. P.: 1960 Sur une représentation par potentiels dans le problème tridimensionnel de l’élastodynamique. C. R. Acad. Sci., Paris 250, 1792–1794. (67).
Truesdell, C.: 1960 A program toward rediscovering the rational mechanics of the age of reason. Arch. Hist. Exact Sc. 1, 3–36. Corrected reprint in Essays in the History of Mechanics. Berlin-Heidelberg-New York: Springer-Verlag 1968. (22).
1960 Truesdell, C.: The Rational Mechanics of Flexible or Elastic Bodies, 1638-1788. L. Euleri Opera Omnia (2) 112. Zurich: Füssli. (22).
1960 Truesdell, C. and R. Toupin: The classical field theories. In Vol. 31 of the Handbuch der Physik, edited by S. Flügge. Berlin-Göttingen-Heidelberg: Springer-Verlag. (12, 15, 16, 17, 18, 19, 71, 72, 73).
Babich, V. M.: 1961 Fundamental solutions of the dynamical equations of elasticity for nonhomogeneous media [in Russian]. Prikl. Mat. Meh. 25, 38–45,’ translated as J. Appl. Math. Mech. 25, 49-60. (68).
1961 Blokh, V. I.: Stress functions and displacement functions [in Russian]. Dopovidi Akad. Nauk. Ukr. RSR 455-458. (17, 44).
Bramble, J. H., and L. E. Payne: 1961 An analogue of the spherical harmonics for the equation of elasticity. J. Math. Phys. 15, 163–171. (32).
1961 A new decomposition formula in the theory of elasticity. J. Res. Nat. Bur. Std. 65B, 151-156. (44).
1961 On some new continuation formulas and uniqueness theorems in the theory of elasticity. J. Math. Anal. Appl. 3, 1-17. (40).
1961 A priori bounds in the first boundary-value problem in elasticity. J. Res. Nat. Bur. Std. 65 B, 269-276. (52).
Farnell, G. W.: 1961 Elastic waves in trigonal crystals. Can. J. Phys. 39, 65–80. (71).
Fichera, G.: 1961 Il teorema del massimo modulo per l’equazione dell’elastostatica. Arch. Rational Mech. Anal. 7, 373–387. (42).
1961 Goldberg, R. R.: Fourier Transforms. Cambridge. (32).
Gurtin, M. E., and E. Sternberg: 1961 A note on uniqueness in classical elastodynamics. Q. Appl. Math. 19, 169–171. (63).
1961 Theorems in linear elastostatics for exterior domains. Arch. Rational Mech. Anal. 8, 99-119. (8, 34, 48, 49, 50).
1961 Hill, R.: Bifurcation and uniqueness in non-linear mechanics of continua. Problems Contin. Mech. (Muskhelisvili Anniv. Vol.), 155-164. Phila.: Soc. Indust. Appl. Math. (32).
Hill, R.: 1961 Uniqueness in general boundary-value problems for elastic or inelastic solids. J. Mech. Phys. Solids 9, 114–130. (32).
Hill, R.: 1961 Discontinuity relations in mechanics of solids. Progress in Solid Mechanics. Vol. II, 245–276. Amsterdam: North-Holland. (72).
Musgrave, M. J. P.: 1961 Elastic waves in anisotropic media. Progress in Solid Mechanics. Vol. II, 61–85. (71).
Naghdi, P. M., and C. S. Hsu: 1961 On a representation of displacements in linear elasticity in terms of three stress functions. J. Math. Mech. 10, 233–245. (44).
Payne, L. E., and H. F. Weinberger: 1961 On Korn’s inequality. Arch. Rational Mech. Anal. 8, 89–98. (13).
1961 Reissner, E.: On some variational theorems in elasticity. Problems of Continuum Mechanics (Muskhelishvili Anniversary Volume), 370-381. Phila.: Soc. Indust. Appl. Math. (38).
Rüdiger, D.: 1961 Ein neues Variationsprinzip in der Elastizitätstheorie. Ing. Arch. 30, 220–224. (38).
Solomon, L.: 1961 On the degree of arbitrariness in the determination of the functions of Papkovitch [in Roumanian]. Comun. Acad. RPR., 11, 1039–1045. (44).
Sveklo, V. A.: 1961 On the solution of dynamic problems in the plane theory of elasticity for anisotropic media [in Russian]. Prikl. Mat. Meh. 25, 885–896; translated as J. Appl. Math. Mech. 25, 1324-1339. (47).
Truesdell, C.: 1961 General and exact theory of waves in finite elastic strain. Arch. Rational Mech. Anal. 8, 263–296. Reprinted in Problems of Non-linear Elasticity. Intl. Sci. Rev. Ser. New York: Gordon and Breach 1965 and also in Wave Propagation in Dissipative Materials. Berlin-Heidelberg-New York: Springer 1965. (73).
Alexandrov, A. Y., and I. I. Solovev: 1962 One form of solution of three-dimensional axisymmetric problems of elasticity theory by means of functions of a complex variable and the solution of these problems for the sphere [in Russian]. Prikl. Mat. Mech. 26, 138–145; translated as J. Appl. Math. Mech. 26, 188-198. (44).
Blokh, V. I.: 1962 On some consequences of two variational principles in the mechanics of solid deformable bodies. Akad. Nauk. Ukr. RSR Prikl. Meh. 8, 56–62. (18).
Bramble, J. H., and L. E. Payne: 1962 On the uniqueness problem in the second boundary-value problem in elasticity. Proc. Fourth U. S. National Congress Appl. Mech. 1, 469–473. (32).
1962 Some uniqueness theorems in the theory of elasticity. Arch. Rational Mech. Anal. 9, 319-328. (32).
Courant, R.: 1962 Partial Differential Equations. Vol. 2 of Methods of Mathematical Physics by R. Courant and D. Hilbert. New York: Interscience, (6, 74).
Gobert, J.: 1962 Une inégalité fondamentale de la théorie de l’élasticité. Bull. Soc. Roy Sci. Liège 31, 182–191. (13).
Gurtin, M.: 1962 On Helmholtz’s theorem and the completeness of the Papkovitch-Neuber stress functions for infinite domains. Arch. Rational Mech. Anal. 9, 225–233. (44).
Gutzwiller, M. C.: 1962 Note on Green’s function in anisotropic elasticity. Q. Appl. Math. 20, 249–256. (68).
Hashin, Z., and S. Shtrikman: 1962 On some variational principles in anisotropic and nonhomogeneous elasticity. J. Mech. Phys. Solids 10, 335–352. (34).
Kneshke, A., u. D. Rüdiger: 1962 Eine Erweiterung des Hamiltonschen Prinzips zur Integration mechanischer Anfangs-Randwertaufgaben. Ing. Arch. 31, 101–112. (65).
Minagawa, S.: 1962 Riemannian three-dimensional stress-function space. RAAG Mem. 3, 69–81. (17).
Murtazaev, D.: 1962 Fundamental solutions of systems of equations in elasticity theory [in Russian]. Izv. Vyss. Uöebn. Zaved. Matematika No. 1 (26) 109–117. (51, 68).
1962 Sternberg, E., and M. Gurtin: On the completeness of certain stress functions in the linear theory of elasticity. Proc. Fourth U. S. Nat. Cong. Appl. Mech. 793-797. (44, 67).
Stroh, A. N.: 1962 Steady state problems in anisotropic elasticity. J. Math. Phys. 41, 77–103. (71).
Strubecker, K.: 1962 Airysche Spannungsfunktion und isotrope Differentialgeometrie. Math. Z. 78, 189–198. (47).
Adler, G.: 1963 Maggiorazione delle tensioni in un corpo elastico mediante gli spostamenti superficiali. Atti Accad. Lincei Rend. (8) 34, 369–371. (42).
Bourgin, D. G.: 1963 Modern Algebraic Topology. New York: Macmillan. (71).
Diaz, J. B., and L. E. Payne: 1963 New mean value theorems in the linear theory of elasticity. Contrib. Diff. Eqts. 1, 29–38. (43).
Ericksen, J. L.: 1963 Non-existence theorems in linear elasticity theory. Arch. Rational Mech. Anal. 14, 180–183. (33).
Fedorov, F. I.: 1963 The theory of elastic waves in crystals. Comparison with isotropic medium [in Russian]. Kristallografiya 8, 213–220; translated as Soviet Phys.-Cryst. 8, 159-163. (70).
Fichera, G.: 1963 Problemi elastostatici con vincoli unilaterali: II problema di Signorini con ambigue condizioni al contorno. Atti Accad. Naz. Lincei Mem. (8) 7, 91–140. English translation in: Estratto dai Seminari dell’Istituto Nazionale di Alta Matematica 1962-1963. Rome: Edizioni Cremonese 1964. (31).
Gazis, D. C., I. Tadjbakhsh, and R. A. Toupin: 1963 The elasticity tensor of a given symmetry nearest to an anisotropic elastic tensor. Acta Cryst. 16, 917–922. (22).
Graffi, D.: 1963 Sui teoremi di reciprocità nei fenomeni non stazionari. Atti Accad. Sci. Bologna (11) 10, 33–40. (19, 61).
Gurtin, M. E.: 1963 A generalization of the Beltrami stress functions in continuum mechanics. Arch. Rational Mech. Anal. 13, 321–329. (17).
Gurtin, M. E.: 1963 A note on the principle of minimum potential energy for linear anisotropic elastic solids. Q. Appl. Math. 20, 379–382. (32, 34).
Gurtin, M. E.: 1963 Variational principles in the linear theory of viscoelasticity. Arch. Rational Mech. Anal. 13, 179–191. (36).
Hayes, M.: 1963 Wave propagation and uniqueness in prestressed elastic solids. Proc. Roy. Soc. Lond. (A) 274, 500–506. (32).
Hill, R.: 1963 New derivations of some elastic extremum principles. Progress in Applied Mechanics, the Prager Anniversary Volume. New York: Macmillan. 99–106. (34).
Ignaczak, J.: 1963 A completeness problem for the stress equation of motion in the linear theory of elasticity. Arch. Mech. Stosow. 15, 225–234. (59, 62).
1963 John, F.: Estimates for the error in the equations of nonlinear plate theory. New York University, Courant Institute of Math. Sc. Rept. IMM-NYU 308. (55).
Kawatate, K.: 1963 A note on the stress function. Rep. Res. Inst. Appl. Mech. Kyushi Univ. 11, 21–27. (17).
1963 Kupradze, V. D.: Potential Methods in the Theory of Elasticity [in Russian]. Moscow. (I have seen this work only in the English translation by H. Gutfreund, Jerusalem: Monson 1965.) (27, 30, 45, 49, 75).
Kupradze, V. D.: 1963 Dynamical problems in elasticity. Vol. Ill of Progress in Solid Mechanics. New York: Wiley. (27, 30, 45, 49, 75).
Melnik, S. I.: 1963 Estimates for the St. Venant principle [in Russian]. Perm. Gos. Univ. Uéen. Zap. Mat. 103, 178–18O. (55).
1963 Mills, N.: Uniqueness in classical linear isotropic elasticity theory. M. Sci. Thesis, University of Newcastle upon Tyne. (32).
1963 Pastori, M.: Equilibrio e congruenza nei sistemi continui. Aspetto formale e geometrico. Aspetto energetico ed estensioni. Confer. Sem. Mat. Univ. Bari, 95-96. (17).
Tang, L.-M., and H.-C. Sun: 1963 Three-dimensional elasticity problems solved by complex variable method. Sci. Sinica (Peking) 12, 1627–1649. (44).
Teodorescu, P. P.: 1963 Sur l’utilisation des potentiels réels dans le problème plan de la théorie de l’élasticité. Bull. Math. Soc. Sci. Math. Phys. R.P. Romaine (N.S.) 7 (55), 77–111. (47).
Truesdell, C.: 1963 The meaning of Betti’s reciprocal theorem. J. Res. Nat. Bur. Std. B 67, 85–86. (30).
Volkov, S. D., and M. L. Komissarova: 1963 Certain representations of the general solutions of the boundary-value problems of elasticity theory [in Russian]. Inzh. Zh. 3, 86–92. (44).
Adler, G.: 1964 Majoration des tensions dans un corps élastique à l’aide des déplacements superficiels. Arch. Rational Mech. Anal. 16, 345–372. (42).
Aleksandrov, A. Y., and I. I. Solovev: 1964 On a generalization of a method of solution of axially symmetric problems in the theory of elasticity by means of analytic functions to spatial problems without axial symmetry [in Russian]. Dokl. Akad. Nauk SSSR 154, 294–297; translated as Soviet Phys. Dokl. 9, 99-102. (44).
Bers, L., F. John, and M. Schechter: 1964 Partial Differential Equations. New York: Interscience. (74).
Bramble, J. H., and L. E. Payne: 1964 Some mean value theorems in elastostatics. SIAM J. 12, 105–114. (43).
Coleman, B. D., and W. Noll: 1964 Material symmetry and thermostatic inequalities in finite elastic deformations. Arch. Rational Mech. Anal. 15, 87–111. (21).
Chen, Y.: 1964 Remarks on variational principles in elastodynamics. J. Franklin Inst. 278, 1–7. (65).
Fedorov, F. I.: 1964 On the theory of waves in crystals, [in Russian]. Mosk. Univ. Vestn. Fiz. Ast. (3) 6, 36–40. (71).
Gurtin, M. E.: 1964 Variational principles in linear elastodynamics. Arch. Rational Mech. Anal. 16, 34–50. (19, 62, 64, 65).
Herrmann, L. R.: 1964 Stress functions for the asymmetric, orthotropic elasticity equations. AIAA J. 2, 1822–1824. (44).
Ionov, V. N., and G. A. Vvodenskiï: 1964 On the possible forms of the general solution of the equilibrium equations in curvilinear coordinates [in Russian]. Izv. Vyss. Uéebn. Zaved. Mat. (43) 6, 59–66. (17).
Jeffrey, A.: 1964 A note on the derivation of the discontinuity conditions across contact discontinuities, shocks, and phase fronts. Z. Angew. Math. Phys. 15, 68–71. (73).
Keller, H. B.: 1964 Propagation of stress discontinuities in inhomogeneous elastic media. SIAM Rev. 6, 356–382. (73).
Knops, R.: 1964 Uniqueness for the whole space in classical elasticity. J. Lond. Math. Soc. 39, 708–712. (32).
Martin, J.: 1964 A displacement bound technique for elastic continua subjected to a certain class of dynamic loading. J. Mech. Phys Solids 12, 165–175. (60).
Nôno, T.: 1964 Sur les champs de tensions. J. Sci. Hiroshima Univ. Ser. A-I. 28, 209–221. (17).
Payton, R. G.: 1964 An application of the dynamic Betti-Rayleigh reciprocal theorem to moving point loads in elastic media. Q. Appl. Math. 21, 299–313. (61).
Rieder, G.: 1964 Die Berechnung des Spannungsfeldes von Einzelkräften mit Hilfe räumlicher Spannungsfunktionen und ihre Anwendung zur quellenmäßigen Darstellung der Verschiebung bei Eigenspannungszuständen. Österr. Ing. Arch. 18, 173–201. (17).
Rieder, G.: 1964 Die Randbedingungen für den Spannungsfunktionentensor an ebenen und gekrümmten belasteten Oberflächen. Österr. Ing. Arch. 18, 208–243. (17).
Rieder, G.: 1964 Über eine Spezialisierung des Schaefersehen Spannungsfunktionenansatzes in der räumlichen Elastizitätstheorie. Z. Angew. Math. Mech. 44, 329–330. (17).
Sternberg, E., and S. Al-Khozai: 1964 On Green’s functions and Saint Venant’s principle in the linear theory of viscoelasticity. Arch. Rational Mech. Anal. 15, 112–146. (51, 54).
Stickforth, J.: 1964 Zur Anwendung des Castiglianoschen Prinzips und der Beltramischen Spannungsfunktionen bei mehrfach zusammenhängenden elastischen Körpern unter Berücksichtigung von Eigenspannungen. Tech. Mitt. Krupp Forsch.-Ber. 22, 83–92. (18).
Teodorescu, P. P.: 1964 A hundred years of research on the plane problem of the theory of elasticity [in Romanian]. Stud. Cere. Mat. 15, 355–367. (45).
Yu, Y.-Y.: 1964 Generalized Hamilton’s principle and variational equation of motion in nonlinear elasticity theory, with application to plate theory. J. Acoust. Soc. Am. 36, 111–120. (65).
Zorski, H.: 1964 On the equations describing small deformations superposed on finite deformations. Proc. Intl. Sympos. Second-order Effects, Haifa 1962, 109–128. (32).
1965 Alexsandrov, I. Y.: Solution of axisymmetric and other three-dimensional problems in the theory of elasticity by means of analytical functions. Appl. Theory of Functions in Continuum Mechanics (Proc. Int. Sympos. Tbilisi. 1963) Vol. I, 97-118. Moscow: Izdat. Nauka. (44).
Bramble, J. H., and L. E. Payne: 1965 Some converses of mean value theorems in the theory of elasticity. J. Math. Anal. Appl. 10, 553–567. (43).
Brugger, K.: 1965 Pure modes for elastic waves in crystals. J. Appl. Phys. 36, 759–768. (71).
Brun, L.: 1965 Sur l’unicité en thermoélasticité dynamique et diverses expressions analogues à la formule de Clapeyron. C. R. Acad. Sci., Paris 261, 2584–2587. (60, 63).
1965 Fedorov, F. I.: Theory of Elastic Waves in Crystals [in Russian]. Moscow: Nauka Press (I have seen this work only in the English translation by J. E. S. Bradley, New York: Plenum 1968.) (70, 71).
De Veubeke, B. F.: 1965 Displacement and equilibrium models in the finite element method. Stress Analysis. New York: Wiley. (38).
Ericksen, J. L.: 1965 Nonexistence theorems in linearized elastostatics. J. Diff. Eqts. 1, 446–451. (33).
Friedrichs, K. O., and H. B. Keller: 1965 A finite difference scheme for generalized Neumann problems. Numerical Solution of Partial Differential Equations. New York: Academic. (39).
Gurtin, M. E., and R. A. Toupin: 1965 A uniqueness theorem for the displacement boundary-value problem of linear elastodynamics. Q. Appl. Math. 23, 79–81. (63).
John, F.: 1965 Estimates for the derivatives of the stresses in a thin shell and interior shell equations. Comm. Pure Appl. Math. 18, 235–267. (55).
Keller, H. B.: 1965 Saint-Venant’s procedure and Saint Venant’s principle. Q. Appl. Math. 22, 293–304. (54).
Knops, R. J.: 1965 Uniqueness of axisymmetric elastostatic problems for finite regions. Arch. Rational Mech. Anal. 18, 107–116. (32).
Knops, R. J.: 1965 Uniqueness of the displacement boundary-value problem for the classical elastic half-space. Arch. Rational Mech. Anal. 20, 373–377. (32, 50).
Minagawa, S.: 1965 On Riemannian and non-Riemannian stress function spaces with reference to two-dimensional stress functions. Reports of the Research Institute for Strength and Fracture of Materials. Tohuku Univ. 1, 15–31. (17).
1965 Muskhelishvili, N. I.: Applications of the theory of functions of a complex variable to the theory of elasticity. Appl. Theory of Functions in Continuum Mechanics (Proc. Int. Sympos. Tbilisi, 1963) Vol. I, 32-55 (Russian); 56-75 (English) Moscow: Izdat Nauka. (45).
Reissner, E.: 1965 A note on variational principles in elasticity. Int. J. Solids Structures 1, 93–95. (38).
Stickforth, J.: 1965 On the derivation of the conditions of compatibility from Castigliano’s principle by means of three-dimensional stress functions. J. Math. Phys. 44, 214–226. (18).
1965 Stippes, M.: Steady state waves in anisotropic media. Ann. Meeting Soc. Eng. Sci., Nov., 1965 (unpublished). (71).
Teodorescu, P. P.: 1965 Über das dreidimensionale Problem der Elastokinetik. Z. Angew. Math. Mech. 45, 513–523. (59).
Toupin, R. A.: 1965 Saint-Venant and a matter of principle. Trans. N.Y. Acad. Sci. 28, 221–232. (54, 55).
Toupin, R. A.: 1965 Saint-Venant’s principle. Arch. Rational Mech. Anal. 18, 83–96. (24, 55).
Truesdell, C., and W. Noll: 1965 The non-linear field theories of mechanics. In Vol. 33 of the Handbuch der Physik, edited by S. Flügge. Berlin-Heidelberg-New York: Springer Verlag. (12, 16, 19, 20, 21, 23, 73).
Ainola, L. I.: 1966 A reciprocal theorem for dynamic problems of the theory of elasticity [in Russian]. Prikl. Math. Meh. 31, 176–177; translated as J. Appl. Math. Mech. 31, 190-192. (61).
Ben-Amoz, M.: 1966 Variational principles in anisotropic and non-homogeneous elasto-kinetics. Q. Appl. Math. 24, 82–86. (65).
Beran, M., and J. Molyneux: 1966 Use of classical variational principles to determine bounds for the effective bulk modulus in heterogeneous media. Q. Appl. Math. 24, 107–118. (34).
Bernikov, H. B.: 1966 Generalization of the Boussinesq-Galerkin solution to anisotropic bodies [in Russian]. Dokl. Akad. Nauk. Tadzh. SSR 9, No. 6, 3–6. (44).
Burckhardt, J. J.: 1966 Die Bewegungsgruppen der Kristallographie. Basel und Stuttgart: Birkhäuser Verlag. (21).
Carlson, D.: 1966 Completeness of the Beltrami stress functions in continuum mechanics. J. Math. Anal. Appl. 15, 311–315. (17).
Dou, A.: 1966 Upper estimate of the potential elastic energy of a cylinder. Comm. Pure Appl. Math. 19, 83–93. (54).
Doyle, J. M.: 1966 Integration of the Laplace transformed equations of classical elasto-kinetics. J. Math. Anal. Appl. 13, 118–131. (69).
Hayes, M.: 1966 On the displacement boundary-value problem in linear elastostatics. Q. J. Mech. Appl. Math. 19, 151–155. (32).
Karnopp, B. H.: 1966 Complementary variational principles in linear elastodynamics. Tensor (N.S.) 17, 300–307. (65).
1966 Key, S.: A convergence investigation of the direct stiffness method. Ph. D. Thesis. Dept. Aero. Eng. University of Washington. (39).
Knowles, J. K.: 1966 On Saint Venant’s principle in the two-dimensional linear theory of elasticity. Arch. Rational Mech. Anal. 21, 1–22. (55, 56).
Knowles, J. K. and E. Sternberg: 1966 On Saint Venant’s principle and the torsion of solids of revolution. Arch. Rational Mech. Anal. 22, 100–120. (55).
Kolodner, I.: 1966 Existence of longitudinal waves in anisotropic media. J. Acoust. Soc. Am. 40, 730–731. (71).
Komkov, V.: 1966 Application of Rail’s theorem to classical elastodynamics. J. Math. Anal. Appl. 14, 511–521. (65).
Mikhlin, S. G.: 1966 On Cosserat functions. Problems in Mathematical Analysis. Vol. 1. Boundary Value Problems and Integral Equations [in Russian]. Leningrad University Press. (I have seen this work only in the English translation. New York: Consultant’s Bureau 1968, 55–64.) (32).
1966 Muskhelishvili: Some Basic Problems of the Mathematical Theory of Elasticity [in Russian] 5th Ed. Moscow. (I have not seen this work.) (45).
Nariboli, G. A.: 1966 Wave propagation in anisotropic elasticity. J. Math. Anal. Appl. 16, 108–122. (73).
Oravas, G., and L. McLean: 1966 Historical developments of energetical principles in elastomechanics. Appl. Mech. Rev. 19, 647–656, 919-933. (34, 38).
Radzhabov, R. R.: 1966 The construction of the Green’s tensor for the first boundary-value problem of the theory of elasticity [in Russian]. Voprosy Kibernet. Vychisl. Mat. Vyp. 6, 96–111. (53).
Robinson, A.: 1966 Non-Standard Analysis. Amsterdam: North-Holland. (56a).
Roseman, J. J.: 1966 A pointwise estimate for the stress in a cylinder and its application to Saint-Venant’s principle. Arch. Rational Mech. Anal. 21, 23–48. (55).
Shield, R. T., and C. A. Anderson: 1966 Some least work principles for elastic bodies. Z. Angew. Math. Phys. 17, 663–676. (30).
Sternberg, E., and J. K. Knowles: 1966 Minimum energy characterizations of Saint Venant’s solution to the relaxed Saint-Venant problem. Arch. Rational Mech. Anal. 21, 89–107. (40, 41).
Stippes, M.: 1966 On stress functions in classical elasticity. Q. Appl. Math. 24, 119–125. (17, 44).
Tonti, E.: 1966 Condizioni iniziali nei principi variazionali. Rend. 1st. Lombardo (A) 100, 982–988. (65).
Truesdell, C.: 1966 Existence of longitudinal waves. J. Acoust. Soc. Am. 40, 729–730. (71).
Truesdell, C.: 1966 The Elements of Continuum Mechanics. Berlin-Heidelberg-New York: Springer. (27).
Azhymudinov, T., and G. Mamaturdiev: 1967 Representation of eigenvalues of the first boundary-value problem of elasticity theory by means of a contour-integral. Izv. Akad. Nauk UzSSR Ser. Fiz.-Mat. Nauk 11, No. 3, 3–9. (76).
Beatty, M. F.: 1967 A reciprocal theorem in the linearized theory of couple-stresses. Acta Mech. 3, 154–166. (30).
Bézier, P.: 1967 Sur quelques propriétés des solutions de problèmes de l’élastostatique linéaire. C. R. Acad. Sci., Paris (A) 265, 365–367. (48, 50, 51).
Carlson, D.: 1967 A note on the Beltrami stress functions. Z. Angew. Math. Mech. 47, 206–207. (17).
Chadwick, P., and E. A. Trowbridge: 1967 Elastic wave fields generated by scalar wave functions. Proc. Cambridge Phil. Soc. 63, 1177–1187. (67).
Hlavacek, I.: 1967 Derivation of non-classical variational principles in the theory of elasticity. Apl. Mat. 12, 15–29. (38).
Hlavacek, I.: 1967 Variational principles in the linear theory of elasticity for general boundary conditions. Apl. Mat. 12, 425–448. (38, 41).
Hashin, Z.: 1967 Variational principles of elasticity in terms of the polarization tensor. Int. J. Eng. Sci. 5, 213–223. (34).
Hill, R.: 1967 Eigenmodal deformations in elastic/plastic continua. J. Mech. Phys. Solids 15, 371–386. (63).
1967 Kilchevskii, M. O., and O. F. Levchuk: One of the forms of the general solution of the elastodynamic equations [in Ukrainian]. Dopovidi Akad. Nauk. Ukr. RSR (A) 801-804. (67).
Prager, W.: 1967 Variational principles of linear elastostatics for discontinuous displacements, strains and stresses. Recent Progress in Applied Mechanics. The Folke Odqvist Volume. New York: Wiley. 463–474. (38, 41).
Roseman, J. J.: 1967 The principle of Saint Venant in linear and non-linear plane elasticity. Arch. Rational Mech. Anal. 26, 142–162. (56).
1967 Schüler, K. W., and R. L. Fosdick: Generalized Beltrami stress functions. Dept. Mech. Rept., Illinois Inst. Tech. (17, 47).
Stippes, M.: 1967 A note on stress functions. Int. J. Solids Structures 3, 705–711. (17, 44).
Tong, P., and T. H. H. Pian: 1967 The convergence of finite element method in solving linear elastic problems. Int. J. Solids Structures 3, 865–879. (39).
Tonti, E.: 1967 Principii variazionali nell’elastostatica. Atti Accad. Lincei Rend. (8) 42, 390–394. (18, 38).
Tonti, E.: 1967 Variational principles in elastostatics. Meccanica 2, 201–208. (18, 38).
Turteltaub, M. J., and E. Sternberg: 1967 Elastostatic uniqueness in the half-space. Arch. Rational Mech. Anal. 24, 233–242. (50).
Zienkiewicz, O. C., and Y. K. Cheung: 1967 The Finite Element Method in Structural and Continuum Mechanics. New York: McGraw-Hill. (39).
Bross, H.: 1968 Das Fundamentalintegral der Elastizitätstheorie für kubische Medien. Z. Angew. Math. Phys. 19, 434–446. (51).
Cakala, S., Z. Domanski, and H. Milicer-Gruzewska: 1968 Construction of the fundamental solution of the system of equations of the static theory of elasticity and the solution of the first boundary-value problem for a half space [in Polish]. Zeszyty Nauk. Politech. Warszaw. Mat. No. 14, 151–164. (51).
Dafermos, C. M.: 1968 Some remarks on Korn’s inequality. Z. Angew. Math. Phys. 19, 913–920. (13).
Edelstein, W. S., and R. L. Fosdick: 1968 A note on non-uniqueness in linear elasticity theory. Z. Angew. Math. Phys. 19, 906–912. (32).
Fosdick, R. L.: 1968 On the displacement boundary-value problem of static linear elasticity theory. Z. Angew. Math. Phys. 19, 219–233. (57).
Gurtin, M. E., V. J. Mizel, and W.O. Williams: 1968 A note on Cauchy’s stress theorem. J. Math. Anal. Appl. 22, 398–401. (15).
Hayes, M., and R. J. Knops: 1968 On the displacement boundary-value problem of linear elastodynamics. Q. Appl. Math. 26, 291–293. (63).
Horàk, V.: 1968 Inverse Variationsprinzipien der Mechanik fester Körper. Z. Angew. Math. Mech. 48, 143–146. (38).
Indenbom, V. L., and S. S. Orlov: 1968 Construction of Green’s function in terms of Green’s function of lower dimensions [in Russian]. Prikl. Math. Meh. 32, 414–420; translated as J. Appl. Math. Mech. 414-420. (53).
Karnopp, B. H.: 1968 Reissner’s variational principle and elastodynamics. Acta Mech. 6, 158–164. (65).
Knops, R. J., and L. E. Payne: 1968 Uniqueness in classical elastodynamics. Arch. Rational Mech. Anal. 27, 349–355. (63).
Solomon, L.: 1968 Élasticité Linéaire. Paris: Masson. (27, 38, 44, 47).
Truesdell, C.: 1968 Comment on longitudinal waves. J. Acoust. Soc. Am. 43, 170. (71).
Turteltaub, M. J., and E. Sternberg: 1968 On concentrated loads and Green’s functions in elastostatics. Arch. Rational Mech. Anal. 29, 193–240. (51, 52, 53).
Washizu, K.: 1968 Variational methods in elasticity and plasticity. New York: Pergamon. (38).
Wheeler, L. T., and E. Sternberg: 1968 Some theorems in classical elastodynamics. Arch. Rational Mech. Anal. 31, 51–90. (60, 61, 68, 69, 74).
Berg, C. A.: 1969 The physical meaning of astatic equilibrium in Saint Venant’s principle for linear elasticity. J. Appl. Mech. 36, 392–396. (18, 29).
Brun, L.: 1969 Méthodes énergétiques dans les systèmes évolutifs linéaires. J. Mécanique 8, 125–191. (60, 63).
de La Penha, G., and S. B. Childs: 1969 A note on Love’s stress function. AIAA J. 7, 540. (44).
Kavwal, R. P.: 1969 Integral equations formulation of classical elasticity. Q. Appl. Math. 27, 57–65. (52).
Nowak, M.: 1969 Equations of motion of an elastic free-free body. Bull. Acad. Polon. Sci., Ser. Sci. Tech. 17, 31–36. (68).
Rubenfeld, L. A., and J. B. Keller: 1969 Bounds on elastic moduli of composite media. SIAM J. Appl. Math. 17, 495–510. (34).
Schultz, M. H.: 1969 Error bounds on the Rayleigh-Ritz-Galerkin method. J. Math. Anal. Appl. 27, 524–533. (39).
Stippes, M.: 1969 Completeness of the Papkovitch potentials. Q. Appl. Math. 26, 477–483. (44).
Youngdahl, C. K.: 1969 On the completeness of a set of stress functions appropriate to the solution of elasticity problems in general cylindrical coordinates. Int. J. Eng. Sci. 7, 61–79. (44).
Benthien, G., and M. E. Gurtin: 1970 A principle of minimum transformed energy in elastodynamics. J. Appl. Mech. 31, 1147–1149. (66).
Hlaväöek, I., and J. Necas: 1970 On inequalities of Korn’s type. I. Boundary-value problems for elliptic systems of partial differential equations. II. Applications to linear elasticity. Arch. Rational Mech. Anal. 36, 305–334. (28).
Wheeler, L. T.: 1970 Some results in the linear dynamical theory of anisotropic elastic solids. Q. Appl. Math. 28, 91–101. (61, 74).
Zienkiewicz, O. C.: 1970 The finite element method; from intuition to generality. Appl. Mech. Rev. 23, 249–256. (39).
Fichera, G.: 1971 Existence theorems in elasticity. Below in Volume VIa/2 of the Handbuch der Physik, edited by C. Truesdell. Berlin-Heidelberg-New York: Springer. (5, 7, 13, 31, 33, 36, 78).
Knops, R. J., and L. E. Payne: 1971 Uniqueness theorems in linear elasticity. In: Springer Tracts in Natural Philosophy (ed. B. D. Coleman), Vol. 19. Berlin-Heidelberg-New York: Springer. (32, 40, 63).
1971 Maiti, M., and G. R. Makan: On an integral equation approach to displacement problems of classical elasticity. Q. Appl. Math. To appear. (52).
1971 Segenreich, S. A.: On the strain energy distribution in self equilibrated cylinders.
1971 Thesis. COPPE, Federal Univ. Rio de Janeiro.
Addendum
Teleman, S.: 1956 The method of orthogonal projection in the theory of elasticity. Rev. Math. Pures Appl. 1, 49–66.
Roseau, M.: 1957 Sur un théorème d’unicité applicable à certains problèmes de diffraction d’ondes élastiques. CR. Acad. Sci., Paris 245, 1780–1782.
Campanato, S.: 1959 Sui problemi al contorno per sistemi de equazioni differenziali lineari del tipo dell’elasticità. Ann. Scuola Norm. Pisa (3) 13, 223–258, 275-302.
1961 Baïkuziev, K.: Some methods of solving the Cauchy problem of the mathematical theory of elasticity [in Russian]. Izv. Akad. Nauk USSR Ser. Fiz.-Mat. 3-12.
Gegelia, T. G.: 1962 Some fundamental boundary-value problems in elasticity theory in space [in Russian]. Akad. Nauk Gruzin. SSSR Trudy Tbiliss. Mat. Inst. Razmadze 28, 53–72.
Kupradze, V. D.: 1962 Singular integral equations and boundary-value problems of elasticity theory [in Russian]. Tbiliss. Gos. Univ. Trudy Ser. Meh.-Mat. Nauk. 84, 63–75.
Rieder, G.: 1962 Iterationsverfahren und Operatorgleichungen in der Elastizitätstheorie. Abhandl. Braunschweig. Wiss. Ges. 14, 109–343.
1962 Deev, V. M.: Representation of the general solution of a three-dimensional problem of elasticity theory by particular solutions of Lamé’s equations [in Ukrainian]. Dopovidi Akad. Nauk. Ukr. RSR 1464-1467.
Volkov, S. D., and M. L. Komissarova: 1963 Certain representations of the general solutions of the boundary-value problems of elasticity theory [in Russian]. Inzh. Zh. 3, 86–92.
Kurlandzki, J.: 1964 Mathematical formulation of a certain method for solving boundary problems of mechanics. Proc. Vibration Problems 5, 117–124.
Niemeyer, H.: 1965 Über die elastischen Eigenschwingungen endlicher Körper. Arch. Rational Mech. Anal. 19, 24–61.
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Gurtin, M.E. (1973). The Linear Theory of Elasticity. In: Truesdell, C. (eds) Linear Theories of Elasticity and Thermoelasticity. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-39776-3_1
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