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On optimization approaches of hybrid stress elements. (English) Zbl 0875.65070

Summary: A rational energy constraint to be used as the optimization condition (OPC) for hybrid finite element is presented. Based on OPC, the optimal stress pattern of the element is established in a general formulation. In this approach, the improvement of the element performance is carry out by a pretreatment of the initially assumed stress field. As an alternative way for the optimization of hybrid elements, the penalty-equilibrating approach is also suggested in the paper in which the equilibrium equation is enforced to the individual elements directly. Finally, a discussion on the stress distribution in an element is made. Some requirements on the rational \(\sigma\)-distribution are suggested. All of the points mentioned have been verified by means of some innovative hybrid elements in 2-D, 3-D and axisymmetric problems.

MSC:

65K05 Numerical mathematical programming methods
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