Accession Number:
AD0728795
Title:
Galerkin Stress Functions for Non-Local Theories of Elasticity.
Descriptive Note:
Technical rept.,
Corporate Author:
COLUMBIA UNIV NEW YORK DEPT OF CIVIL ENGINEERING AND ENGINEERING MECHANICS
Personal Author(s):
Report Date:
1971-10-01
Pagination or Media Count:
22.0
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 Cauchys equation of infinite order for his asymptotic theory of an elastic medium with long range interactions between molecules in a periodic structure. Author
Descriptors:
Subject Categories:
- Mechanics