Galerkin Stress Functions for Non-Local Theories of Elasticity.
COLUMBIA UNIV NEW YORK DEPT OF CIVIL ENGINEERING AND ENGINEERING MECHANICS
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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