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2 Computer Assisted Mechanics and Engineering Sciences

2 2001

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Hybrid-Trefftz stress elements for three-dimensional elastoplasticity

Bussamra F. L. S., Pimenta P. M., Freitas J. A. T.

Computer Assisted Mechanics and Engineering Sciences

2001

Vol. 8, No. 2-3

235-246

The stress model of the hybrid-Trefftz finite element formulation is applied to the elastoplastic analysis of solids. The stresses and the plastic multipliers in the domain of the element and the displacements on its boundary are approximated. Harmonic and orthogonal hierarchical polynomials are used to approximate the stresses, constrained to solve locally the Beltrami governing differential equation. They are derived from the associated Papkovitch-Neuber elastic displacement solution. The plastic multipliers are approximated by Dirac functions defined at Gauss points. The finite element equations are derived directly from the structural conditions of equilibrium, compatibility and elastoplasticity. The non-linear governing system is solved by the Newton method. The resulting Hessian matrices are symmetric and highly sparse. All the intervening arrays are defined by boundary integral expressions or by direct collocation. Numerical applications are presented to illustrate the performance of the model.

Developments with hybrid-Trefftz stress and displacement elements

Freitas J. A. T., Cismasiu C.

Computer Assisted Mechanics and Engineering Sciences

2001

Vol. 8, No. 2-3

289-311

The paper reports on the work on hybrid-Trefftz finite elements developed by the Structural Analysis Research Group, ICIST, Technical University of Lisbon. A dynamic elastoplastic problem is used to describe the technique used to establish the alternative stress and displacement models of the hybrid-Trefftz finite element formulations. They are derived using independent time, space and finite element bases, so that the resulting solving systems are symmetric, sparse, naturally p-adaptive and particularly well suited to parallel processing. The performance of the hybrid-Trefftz stress and displacement models is illustrated with a number of representative static and dynamic applications of elastic and elastoplastic structural problems.