Splitting the elastic strain energy in thin plates of a transversely isotropic material

Abstract

In this paper, the elastic strain energy stored in thin plates of a transversely isotropic material is decomposed into distinct, non-interacting elements. Utilizing the characteristics of the elliptic paraboloid failure surface, which was previously shown to constitute an ideal criterion for yielding and failure of anisotropic media, and focusing our attention on transversely isotropic plates, it is proven that the total elastic strain energy density may be divided into discrete orthogonal parts. Moreover, applying the spectral decomposition principle on the compliance fourth-rank tensor S of transversely isotropic plates, orthogonal states of stress are obtained, each associated with a specific strain energy component. Both decompositions of the elastic strain energy suggested in this paper are energy equivalent and advantageous, exhibiting close resemblance with the splitting of the total elastic strain energy in dilatational and distortional constituents, valid only for isotropic materials.