Anisotropic elasto‐plastic finite element analysis of thick and thin plates and shells

Abstract

Abstract An elasto‐plastic analysis of anisotropic plates and shells is undertaken by means of the finite element displacement method. A thick shell formulation accounting for shear deformation is considered, which is based on a degenerate three‐dimensional continuum element. The accommodation of variable material properties, not only along the surface of the structure but also through the thickness, is made possible by a discrete layered approach. Although isoparametric elements of the Serendipity family give satisfactory solutions for thick and moderately thin shells the results exhibit ‘locking’ for an increasing ratio of span to thickness. To develop a numerical model which is applicable to thick or thin plates and shells, the nine‐node Lagrangian element and the Heterosis element are also introduced into the present model. Plastic yielding is based on the Huber‐Mises yield surface extended by Hill for anisotropic materials. The yield function is generalized by introducing anisotropic parameters of plasticity which are updated during the material strain hardening history. Numerical examples are presented and compared with available solutions. The effects of anisotropy on these solutions are also discussed.