Sommario
Si passano in rassegna varie teorie delle piastre basate sugli spostamenti. Viene mostrato che molte delle teorie del terzo ordine che compaiono nella letteratura sono basate sullo stesso (o un equivalente) campo di spostamenti, e quindi conducono agli stessi risultati. Viene quindi presentata una teoria del terzo ordine coerente nelle deformazioni, che contiene come casi particolari la maggior parte delle esistenti teorie del terzo ordine. Viene anche rivista la teoria delle piastre a strati già proposta dall'autore. L'accuratezza delle teorie è valutata paragonando le soluzioni numeriche con quelle della teoria tri-dimensionale dell'elasticità.
Summary
A review of the developments in the displacement-based theories of plates is presented. It is shown that many of the third-order theories reported in the literature are based on the same or equivalent displacement field, and are thus lead to the same results. A strain-consistent third-order theory is presented, which contains most existing third-order plate theories as special cases. The layer-wise laminate plate theory proposed by the author is also reviewed. The accuracy of the theories is evaluated by comparing the numerical solutions with those of the three-dimensional elasticity theory.
References
Reddy J.N., Chandrasekhara K.,Recent advances in the nonlinear analysis of laminated composite plates and shells, Shock & Vib. Dig. Vol. 19(4), 1987, pp. 3–9.
Kapania R.K., Raciti S.,Recent advances in analysis of laminated beams and plates, Part I: Shear effects and buckling, AIAA J., Vol. 27(7), 1989, pp. 923–934.
Kapania R.K., Raciti S.,Recent advances in analysis of laminated beams and plates, Part II: Vibrations and wave propagation, AIAA J., Vol. 27(7), 1989, pp. 935–946.
Noor A.K., Burton W.S.,Assessment of shear deformation theories for multilayered composite plates, Appl. Mech. Rev., Vol. 42(1), 1989, pp. 1–13.
Reddy J.N.,A review of refined theories of laminated composite plates, Shock & Vib. Dig., Vol. 22(7), 1990, pp. 3–17.
Reddy J.N.,A general nonlinear third-order theory of plates with moderate thickness, J. Non-Linear Mech., to appear.
Reissner E.,The effect of transverse shear deformation on the bending of elastic plates, J. Appl. Mech., Vol. 12, 1945, pp. 69–77.
Reissner E.,A consistent treatment of transverse shear deformations in laminated anisotropic plates, AIAA J., Vol. 10(5), 1972, pp. 716–718.
Reissner E.,Note on the effect of trasverse shear deformation in laminated anisotropic plates, Comp. Meth. Appl. Mech. Engng., Vol. 20(3), 1979, pp. 203–209.
Reissner E.,Reflections on the theory of elastic plates, Appl. Mech. Rev., Vol. 38(11), 1985, pp. 1453–1464.
Ambartsumyan S.A.,Theory of Anisotropic Plates, Nauka, Moscow, 1987 (in Russian).
Basset A.B.,On the Extension and Flexure of Cylindrical and Spherical Thin Elastic Shells, Phil. Trans. Royal Soc., (London) Ser. A, Vol. 181, (6), 1890, pp. 433–480.
Bolle E.,Contribution au Probleme Lineaire de Flexion d'une Plaque Elastique, Bull. Tech. Suisse. Romande, Vol. 73, 1947, pp. 281–285 and 293–298.
Hencky H.,Uber due berucksichtigung der schubvedrzerrung in ebenen platten, Ing. Arch., Vol. 16, 1947, pp. 72–76.
Hildebrand F.B., et al.Notes on the Foundations of the Theory of Small Displacements of Orthotropic Shells, NACA TN-1833, Washington, D.C., 1949.
Mindlin R.D.,Influence of rotatory inertia and shear on flexural motions of Isotropic, elastic plates, J. Appl. Mech., Vol. 18, 1951, pp. 31–38.
Vlasov B.F.,Ob uravnieniakh izgiba plastinok (On the equations of the bending of plates), Dokla Aka. Nauk Azerbeijanskoi SSR, Vol. 3, 1957, pp. 955–959.
Jemielita G.,Techniczna teori plyt sredniej grubbosci (Technical theory of plates with moderate thickness), Rozprawy Inzynierskie, Polska Akademia Nauk, Vol. 23(3), 1975, pp. 483–499.
Schmidt R.,A refined nonlinear theory of plates with transverse shear deformation The J. Indus. Math. Soc., Vol. 27(1), 1975, pp. 483–499.
Krishna Murty A.V.,Higher-order theory for vibration of thick plates, AIAA J., Vol. 15(12), 1977, pp. 1823–1824.
Lo K.H., Christensen R.M., Wu E.M.,A high-order theory of plate deformation: Part 1: Homogeneous plates, J. Appl. Mech., Vol. 44(4), 1977, pp. 663–668.
Lo K.H., Christensen R.M., Wu E.M.,A high-order theory of plate deformation: Part 2: Laminated plates, J. Appl. Mech. Vol. 44(4), 1977, pp. 669–676.
Levinson M.,An accurate, simple theory of the statics and dynamics of elastic plates, Mech. Res. Commun., Vol. 7(6), 1980, pp. 343–350.
Murthy M.V.V.,An improved transverse shear deformation theory for laminated anisotropic plates, NASA Technical Paper, 1903, November 1981.
Reddy J.N.,Energy and Variational Methods in Applied Mechanics, John Wiley, New York, 1984.
Reddy J.N.,A simple higher-order theory for laminated composite plates, J. Appl. Mech., Vol. 51, 1984, pp. 745–752.
Reddy J.N.,A refined nonlinear theory of plates with transverse shear deformation. Int. J. Solids Structures, Vol. 20(9/10), 1985, pp. 881–896.
Reddy J.N.,A small strain and moderate rotation theory of laminated anisotropic plates, J. Appl. Mech., Vol. 54, 1987, pp. 623–626.
Reddy J.N.,On the generalization of displacement-based laminate theories,Appl. Mech. Reviews, Vol. 42(11), Part 2, 1989, pp. S213-S222.
Epsten M., Glockner P.G.,Nonlinear analysis of multilayered shells, Int. J. Solids Struct., Vol. 13, 1977, pp. 1081–1089.
Rehfield L.W., Murthy P.L.N.,Toward a new engineering theory of bending: fundamentals, AIAA J., Vol. 20(5), 1982, pp. 693–699.
Rehfield L.W., Valisetty R.R.,A comprehensive theory for planar bending of composite laminates, Comput. & Struct., Vol. 15(1–4), 1983, pp. 441–447.
Hinrichsen R.L., Palazotto A.N.,Nonlinear finite element analysis of thick composite plates using cubic spline functions, AIAA J., Vol. 24(11), 1986, pp. 1836–1842.
Reddy J.N.,Generalization of two-dimensional theories of laminated composite plates, Commun. Appl. Numer. Meth. Vol. 3, 1987, pp. 173–180.
Reddy J.N.,An Introduction to the Finite Element Method, McGraw-Hill, New York, 1984.
Barbero E.J., Reddy J.N., Teply J.L.,An accurate determination of stresses in thick laminates using a generalized plate theory, Int. J. Numer. Meth. Engng., Vol. 29, 1990, pp. 1–14.
Khdeir A.A., Reddy J.N., Librescu L.,Le'vy type solutions for symmetrically laminated rectangular plates using first-order shear deformation theory, J. Appl. Mech., Vol. 54, 1987, pp. 640–642.
Reddy J.N., Khdeir A.A.,Buckling and vibration of laminated composite plates using various plate theories, AIAA J., Vol. 27(12), 1989, pp. 1808–1817.
Pagano N.J.,Exact solutions for rectangular bidirectional composites and sandwich plates, J. Compos. Mater., Vol. 4, 1970, pp. 20–34.
Sreenivas S.,A refined analysis of composite laminates, J. Sound & Vib., Vol. 30(4), 1973, pp. 495–507.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Reddy, J.N. On refined theories of composite laminates. Meccanica 25, 230–238 (1990). https://doi.org/10.1007/BF01559685
Issue Date:
DOI: https://doi.org/10.1007/BF01559685