The Research Of High Performance And Low Order Hybrid Stress Hexahedral Element

In this paper, we first constructed a high performance and low order hybridstress hexahedral element by stress optimation. As we know, rational choice ofstress mode is crucial to the construction of robust hybrid stress finite elementsbased on the Hellinger-Reissner principle. In this paper, an energy-compatibilitycondition is used for stress optimization in the derivation of accurate 8-node hexa-hedral elements for three-dimensional elasticity. Compatible isoparametric trilin-ear interpolations are employed to approximate the displacement field. For thestress approximation, a kind of 18-parameter implicit energy-compatible stressmode is obtained from the energy-compatibility condition, i.e. an energy orthog-onal relation between stress terms and Wilson incompatible strains. Numericaltests show that the resultant elements possess high accuracy at coarse meshes,are insensitive to mesh distortions and free from volume locking in the analysis ofbeams, plates and shells. Due to elimination of stress parameters at the elementlevel, the elements are of almost the same computational cost as that of H8.On the other hand,we can also obtain high performance by using com-bined/hybrid principle and adjusting the combined parameterαwith the mostsimple piecewise constant stresses. Follow this approach, with the Wilson bubbleadded or not, we derived two combined hybrid constant stress element CHHb(α)and CHH8(α) respectively. Numerical tests show that the element CHH8(α)will use di?erent parameterαin di?erent problem to obtain better performance while CHHb(α) can gain accurate results for nearly all the tests if we chooseα= 0.03.