Stress Function Approach in Anisotropic Elasticity Theory.

ON MAXWELL'S STRESS FUNCTIONS FOR SOLVING THREE DIMENSIONAL ELASTICITY PROBLEMS IN THE THEORY OF ELASTICITY

The governing equations of three dimensional elasticity problems include the six Beltrami-Michell stress compatibility equations, the three differential equations of equilibrium, and the six material constitutive relations; and these are usually solved subject to the boundary conditions. The system of fifteen differential equations is usually difficult to solve, and simplified methods are usual...

Surface instability in finite anisotropic elasticity under initial stress

The writer’s theory of surface instability of au elastic body under initial stress in finite strain is extended to anisotropic elasticity. The general characteristic equation for surface instability is derived. In addition, the surface deflexion under a normal load is evaluated for the subcritical case of initial stress. The analysis includes the case in which gravity is taken into account. It ...

Dislocation core field. I. Modeling in anisotropic linear elasticity theory

Theory of Stability of Multilayered Continua in Finite Anisotropic Elasticity

The writer’s general equations for the mechanics of continua under initial stress are applied to the formulation of a rigorous theory of stability of multilayered elastic media in a state of finite initial strain. The medium is assumed incompressible. It is either isotropic or anisotropic. The problem is analyzed in the context of the writer’s earlier discussions showing the existence of intern...

Theory of Elasticity and Consolidation for a Porous Anisotropic Solid

The author's previous theory of elasticity and consolidation for isotropic materials m. Appl. Phys. 12, 15.5-164 (1941)] is extended to the general case of anisotropy. The method of derivation is also different and more direct. The particular cases of transverse isotropy and complete isotropy are discussed.