A 3D finite element with planar symmetry for limit analysis computations

A formulation for finite element limit analysis of a certain class of 3D perfectly plastic solids governed by von Mises’ plasticity condition is presented. A planar symmetry constraint for both geometry and displacement field is assumed to analyze plane problems where the variable nature of transverse dissipation must be considered. A mixed locking free and low distortion sensitive element is formulated on the basis of the natural approach. The solution procedure exploits the kinematic theorem of limit analysis, cast in the form of a minimum problem for a convex but non-smooth dissipation functional. Applications to a notched specimen and to a bolted joint are presented to stress the importance of transverse effects in some problems commonly modeled as purely 2D.