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New enhanced strain elements for incompressible problems. (English) Zbl 0937.74062
Summary: First, we present an enhanced strain element, based on the definition of extra compatibles modes of deformation added to the standard four-node finite element. The element is built with the objective of addressing incompressible problems and avoiding locking effects. By analyzing at the element level the deformation modes which form a basis for the incompressible subspace, extra modes of deformation are proposed in order to provide the maximum possible dimension to that subspace. Subsequently, an another element with more degrees of freedom is formulated using a mixed method. This is done by including an extra field of variables related to the derivatives of the displacement field of the extra compatible modes defined previously. The performance of the elements proposed is assessed in linear and nonlinear situations.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74K15 Membranes
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