Limit analysis of anisotropic structures based on the kinematic theorem

The paper considers perfectly plastic materials with a yield condition of t he form Phi(sigma) = F(ij)sigma (ij) + F(ijkl)sigma (ij)sigma (kl) less tha n or equal to 1 corresponding to a second order truncation of the tensor po lynomial expression proposed by Tsai and Wu for failure criteria. Such an e xpression is often employed for materials exhibiting particular forms of an isotropic failure properties, including orthotropic ones, and accounts for non-symmetric strengths. The limit analysis problem is considered next. The formulation based on the kinematic theorem, reducing to the search of the constrained minimum of a convex functional, was successfully employed in th e isotropic case for numerical solutions and can be extended to the present context without modifications, provided that the expression for the dissip ation power as an explicit function of strain rates is available. For the m aterial considered, this expression is established in this paper. The resul t is specialized to plane stress orthotropy and an example is worked out. A lthough extremely simple, it permits the assessment of the influence of the ratio between tensile and compressive strength and of the inclination of t he orthotropy axes with respect to loading directions. (C) 2001 Elsevier Sc ience Ltd. All rights reserved.