Abstract
The addition of incompatible displacement modes to lower-order displacement-based elements is re-evaluated. Recent research has indicated that a simple numerical correction can be applied to the shape functions in order that the constant-strain patch test is passed. In this paper a new method of stress recovery is presented in which incompatible modes are introduced. A least-square approximation is used to calculate element stresses which are in microscopic equilibrium and tend to be in global equilibrium with the applied nodal loads on the finite element assemblage. Also, a consistent and robust method for the evaluation of thermal stresses is presented. The numerical methods presented are general and can be applied to all displacement-based finite elements. The basic formulation and examples which are presented in this paper are in three-dimensional elasticity using the eight-node isoparametric elements. Accuracy of the element is illustrated and it is demonstrated that both displacements and stresses are almost identical to those produced by Pian's hybrid stress elements.
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