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

Subject Categories:

  • Mechanics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE