SUMMARYPlate bending finite elements based on the Reissner/Mindlin theory offer improved possibilities to pursue reliable finite element analyses. The physical behaviour near the boundary can be modelled in a realistic manner and inherent limitations in the Kirchhoff plate bending elements when modelling curved boundaries can easily be avoided. However, the boundary conditions used are crucial for the quality of the solution. We identify the part of the Reissner/Mindlin solution that controls the boundary layer and examine the behaviour near smooth edges and corners. The presence of boundary layers of different strengths for different sets of boundary conditions is noted. For a corner with soft simply supported edges the boundary layer removes the singular behaviour of Kirchhoff type from the stress resultants. We demonstrate the theoretical results by some numerical studies on simple plate structures which are discretized by an accurate, higher-order plate element. The results provide guidance in choosing efficient meshes and appropriate boundary conditions in finite element analyses.

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In large-scale numerical simulations of sheet metal-forming processes there is a need for assessing wrinkle formation tendencies at early stages of the computations. An algorithmic procedure for early prediction of wrinkles is presented, that makes use of the continuum mechanical behaviour of elastoplastic structures near buckling. The procedure has been implemented into an explicit finite element code and the performance is demonstrated on some example problems.