A partial assumed strain formulation for triangular solid shell element.
An assumed strain formulation is based on the Hellinger--Reissner variational principle with two unknown fields; assumed displacements and independently assumed strains. It is effective to alleviate locking without triggering undesirable spurious kinematic modes if proper assumed strain field is carefully selected in the formulation. Since \(C^{0}\) continuity does not require strains continuous across the element boundaries, the assumed strain field can be eliminated at an element level. However, elimination of the assumed strain field requires more operations including matrix inverse, where matrix size depends on the number of assumed strain parameters, at each element to obtain an element stiffness matrix. Therefore, small number of assumed strain parameters saves computation time. In this study a triangular solid element based on a partial assumed strain formulation is presented. The assumed strain field is divided into in-plane part and transverse part in the formulation. The transverse part of the assumed strain field is independently assumed to alleviate transverse shear locking. However, the in-plane part of the assumed strain field is replaced by displacement-dependent strain, which reduces the number of assumed strain parameters. Since the number of assumed strain parameters of the formulation is smaller than the conventional assumed strain formulation, the present formulation saves computation time for constructing stiffness matrix without sacrificing accuracy.
scientific article; zbMATH DE number 1768213