Simplified stress resultants plasticity on a geometrically nonlinear constant stress shell element

The geometrically nonlinear constant stress triangle of Morley is implemented and extended to include material nonlinearity. The facet element was designed in a total Lagrangian approach and is valid for moderate rotations. In a search for a simple plasticity formulation, stress resultants plasticity (involving a solution of single scalar yield function) is employed. A modification is introduced in the Ilyushin yield surface such that it is rendered a hyperellipse to avoid corner discontinuities. Explicit plasticity equations are derived so as to avoid the most involving matrix operations and attain faster computations. In this work it is aimed to study the performance of the element and assess its application to practical problems such as plate buckling in offshore structures. The formulation appears to work well.