Hybrid-Trefftz stress elements for elastoplasticity

The stress model of the hybrid Þnite element formulation is applied to the analysis of quasi-static, gradient-dependent elastoplastic structural problems. The Þnite element approximation consists in the direct estimate of the stress and plastic multiplier Þelds in the domain of the element and of the displacements and plastic multiplier gradients on its boundary. The Þnite element equations are derived directly from the relevant fundamental structural conditions, namely equilibrium, compatibility, elasticity and gradient-dependent plasticity. The Þnite element solving system for the Þnite step incremental analysis is encoded as a recursive sequence of symmetric parametric linear complementarity problems (SPLCP). The sequence of SPLCP is solved using a direct extension of the restricted basis linear programming algorithm. The implementation of the formulation and of the algorithm is illustrated with numerical applications