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Stress-based finite element analysis of plane plasticity problems. (English) Zbl 0957.74062

Summary: We develop a stress-based model of the finite element method for two-dimensional quasi-static plasticity problems. The self-equilibrating fields of stresses are constructed by means of the Airy stress function, which is approximated by three types of elements: the Bogner-Fox-Schmit rectangle, the Hsieh-Clough-Tocher triangle, and its reduced variant. Traction boundary conditions are imposed by the use of the Lagrange multiplier method which gives the possibility of calculation of displacements at boundary points. We apply the concept of multi-point-constraints elements in order to facilitate the application of this technique. An iterative algorithm, analogous to the closest-point-projection method commonly used in the displacement-based finite element model, is proposed for solving nonlinear equations for each load increment. Two numerical examples with stress- and displacement-controlled load are considered, and the results are compared with those obtained by displacement models of FEM. We also obtain bounds for limit loads.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)

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