On dual conservation laws in planar elasticity
نویسنده
چکیده
Dual conservation laws of linear planar elasticity theory have been systematically studied based on stress function formalism. By employing generalized symmetry transformation or Lie–B€acklund transformation, a class of new dual conservation laws in planar elasticity have been discovered based on Noether theorem and its Bessel–Hagen generalization. These dual conservation laws represent variational symmetry properties of complementary potential energy, which stems from the symmetry properties of compatibility conditions––a biharmonic equation in two dimension. The physical implications of these dual conservation laws are discussed briefly. In particular, a dual-Eshelby tensor is constructed and compared with the Eshelby’s energy momentum tensor. 2004 Elsevier Ltd. All rights reserved.
منابع مشابه
Conservation Laws in Elasticity. IlL Planar Linear Anisotropic Elastostatics
The first order conservation laws for an arbitrary homogeneous linear planar elastic material are completely classified. In all cases, both isotropic and anisotropic, besides the standard Betti reciprocity laws, there are two infinite-dimensional families of conservation laws, each depending on an arbitrary analytic function of two complex variables.
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