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On the stabilization of the rectangular 4-node quadrilateral element. (English) Zbl 0804.73058
Summary: The standard bilinear displacement field of the plane linear elastic rectangular four-node quadrilateral element is enhanced by incompatible modes. The resulting gradient operators are separated into constant and linear parts corresponding to underintegration and stabilization of the element stiffness matrix. Minimization of potential energy is used to generate exact analytical expressions for the hourglass stabilization of the rectangle. The stabilized element is shown to coincide with the element obtained by the mixed assumed strain method.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
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