Summary
This note develops a method for the solution of the elastokinetic boundary value problem for time dependent surface tractions and/or displacements, as well as body forces which are functions of time and space. The method of Williams is extended to resolve three-dimensional problems of elastodynamics by classical mathematical techniques.
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Abbreviations
- x i :
-
position vector
- t :
-
time
- u i :
-
displacement vector
- τ ij :
-
stress tensor
- F i :
-
vector characterizing body force per unit volume
- \(\mathop {T_i }\limits^v \) :
-
stress vector acting on surface S with unit outer normal v i
- ρ :
-
density
- λ, μ :
-
Lamé's constants
- δ ij :
-
Kronecker delta
References
Tranter, C. J., Phil. Mag. 33 (1942) 614.
Leonard, R. W., On Solutions for the Transient Response of Beams, NASA TR R-21, 1959.
Sheng, J., AIAA J. 3 (1965) 1698.
Sokolnikoff, I. S., Mathematical Theory of Elasticity, 2nd edition, McGraw-Hill, New York 1956.
Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity, 4th edition, Dover, New York 1944.
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Reismann, H. On the forced motion of elastic solids. Appl. Sci. Res. 18, 156–165 (1968). https://doi.org/10.1007/BF00382343
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DOI: https://doi.org/10.1007/BF00382343