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Mixed finite element methods for linear elasticity with weakly imposed symmetry. (English) Zbl 1118.74046

Summary: We construct new finite element methods for the approximation of equations of linear elasticity in three space dimensions that produce direct approximations to both stresses and displacements. The methods are based on a modified form of Hellinger-Reissner variational principle that only weakly imposes the symmetry condition on stresses. Although this approach has been previously used by a number of authors, a key new ingredient here is a constructive derivation of the elasticity complex starting from de Rham complex. By mimicking this construction in the discrete case, we derive new mixed finite elements for elasticity in a systematic manner from known discretizations of de Rham complex. These elements appear to be simpler than the ones previously derived. For example, we construct stable discretizations where we use only piecewise linear elements to approximate the stress field and piecewise constant functions to approximate the displacement field.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
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