Limit analysis of anisotropic structures based on the kinematic theorem

Abstract

Abstract The paper considers perfectly plastic materials with a yield condition of the form Φ σ =F ij σ ij +F ijkl σ ij σ kl ⩽1 corresponding to a second order truncation of the tensor polynomial expression proposed by Tsai and Wu for failure criteria. Such an expression is often employed for materials exhibiting particular forms of anisotropic 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 the isotropic case for numerical solutions and can be extended to the present context without modifications, provided that the expression for the dissipation power as an explicit function of strain rates is available. For the material considered, this expression is established in this paper. The result is specialized to plane stress orthotropy and an example is worked out. Although extremely simple, it permits the assessment of the influence of the ratio between tensile and compressive strength and of the inclination of the orthotropy axes with respect to loading directions.