The Conservation Laws of Three Dimensional Linearized Elasticity Theory

Author: Fletcher, Donnie Carlton

Year: 1974

Degree: Dissertation (Ph.D.)

Advisor: Knowles, James K.

Committee Member: Unknown, Unknown

Option: Engineering

DOI: 10.7907/TC8V-H381

Abstract

For linearized isotropic elastodynamics and elastostatics, Noether's theorem on invariant variational principles is used to obtain all conservation laws arising from a reasonably general group of infinitesimal transformations. A theorem regarding the completeness of the derived laws is proved, and the conservation laws are then used to derive the wave speed equation for the Rayleigh problem on the surface of an anisotropic half space. An example of additional laws following from the same group but from a more general version of Noether's theorem is given in an appendix devoted to a discussion of limitations on the completeness theorem.

Files

• Fletcher_dc_1974.pdf (application/pdf)