Accuracy of momentum balance and surface forces for finite element computations in elasticity

by · Sep 22, 2014 · 842 views ·

Gerhard Starke, Universität Duisburg-Essen, Essen, Germany Joint work with Benjamin Müller Mixed variational formulations involving stresses and displacements as process variables are investigated for elasticity models. In particular, the accuracy of momentum balance and surface forces is studied for stress approximations in H(div) using, for example, Raviart-Thomas finite element spaces. We discuss the connection between a saddle point formulation based on the Hellinger-Reissner principle and a first-order system least squares formulation. The latter approach has the advantage of more flexibility in the choice of appropriate combinations of finite element spaces, e.g. Raviart-Thomas elements of degree k for the stresses may be combined with standard conforming elements of degree k + 1 for the displacements. The results are derived first for the linear elasticity case and then extended to nonlinear problems associated with hyperelastic material models and plasticity.

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