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Hybrid‐Trefftz stress elements for elastoplasticity
Author(s) -
De Freitas J. A. Teixeira,
Wang Z. M.
Publication year - 1998
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19981030)43:4<655::aid-nme416>3.0.co;2-1
Subject(s) - finite element method , mathematics , mixed finite element method , extended finite element method , parametric statistics , finite element limit analysis , plasticity , compatibility (geochemistry) , boundary knot method , mathematical analysis , linear elasticity , boundary value problem , mathematical optimization , boundary element method , structural engineering , engineering , statistics , physics , chemical engineering , thermodynamics
The stress model of the hybrid finite element formulation is applied to the analysis of quasi‐static, gradient‐dependent elastoplastic structural problems. The finite element approximation consists in the direct estimate of the stress and plastic multiplier fields in the domain of the element and of the displacements and plastic multiplier gradients on its boundary. The finite element equations are derived directly from the relevant fundamental structural conditions, namely equilibrium, compatibility, elasticity and gradient‐dependent plasticity. The finite element solving system for the finite 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. © 1998 John Wiley & Sons, Ltd.