Dual-mixed \(hp\) finite element methods using first-order stress functions and rotations. (English) Zbl 0980.74057

From the summary: We consider a two-field dual-mixed variational formulation of three-dimensional elasticity in terms of non-symmetric stress tensor and skew-symmetric rotation tensor. The translational equilibrium equations are satisfied a priori by introducing the tensor of first-order stress functions. It is pointed out that the use of six properly chosen first-order stress function components leads to a (three-dimensional) weak formulation, which is analogous to displacement-pressure formulation of elasticity and velocity-pressure formulation of Stokes flow. The subsequent selection of stable mixed \(hp\) finite element spaces is based on this analogy.


74S05 Finite element methods applied to problems in solid mechanics
74B10 Linear elasticity with initial stresses
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