Multiple quadrature underintegrated finite elements. (English) Zbl 0811.73063
An approach for hourglass control is proposed such that the stabilization operators are obtained simply by taking the partial derivatives of the generalized strain rate vector with respect to the natural coordinates so that the elements require no stabilization parameter. To improve accuracy over the traditional one-point-quadrature elements, several quadrature points are used to integrate the internal forces, especially for tracing the plastic fronts in the mesh during loading and unloading in elastic- plastic analysis. Two- and four-point-quadrature elements are proposed for use in the two- and three-dimensional elements, respectively. Other multiple-quadrature points can also be employed. Several numerical examples such as thin beam, plate and shell problems are presented to demonstrate the applicability of the proposed elements.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 74K20 | Plates |
| 74K15 | Membranes |
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