Galerkin Stress Functions for Non-Local Theories of Elasticity.
Abstract
In the classical theory of elasticity, the potential energy density is a function of the strain whereas in the non-local theories the energy is a function of the strain and gradients of the strain, or parts thereof such as the rotation gradient which leads to couple stresses. For the classical theory, Galerkin exhibited a complete solution of the displacment equation of equilibrium in terms of a single vector function satisfying an equation of higher order but of simpler and more tractable form. In the present paper, after a review of the solutions for the classical and rotation gradient cases, the analogous solutions are exhibited for the non-local equations of higher and higher orders up to Cauchy's equation of infinite order for his asymptotic theory of an elastic medium with long range interactions between molecules in a periodic structure. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1971
- Accession Number
- AD0728795
Entities
People
- Raymond D. Mindlin
Organizations
- Columbia University