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Galerkin Stress Functions for Non-Local Theories of Elasticity.

機(jī)譯：非局部彈性理論的Galerkin應(yīng)力函數(shù)。

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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 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)

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