Analytical solutions to general anti-plane shear problems in finite elasticity

  • Gao, David Yang
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Publication date
December 2015
Publisher
Springer Science and Business Media LLC
ISSN
0935-1175
Journal
Continuum Mechanics and Thermodynamics
Citation count (estimate)
11

Abstract

This paper presents a pure complementary energy variational method for solving a general anti-plane shear problem in finite elasticity. Based on the canonical duality–triality theory developed by the author, the nonlinear/nonconvex partial differential equations for the large deformation problem are converted into an algebraic equation in dual space, which can, in principle, be solved to obtain a complete set of stress solutions. Therefore, a general analytical solution form of the deformation is obtained subjected to a compatibility condition. Applications are illustrated by examples with both convex and nonconvex stored strain energies governed by quadratic-exponential and power-law material models, respectively. Results show that the non...

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