Improvements Of Quadrilateral Element With Drilling Dofs Using Hybrid Finite Element Methods

Finite element with drilling degrees of freedom is popular in engineering fields. By increasing degree of freedom of vertexs and using higher order of interpolation, this kind of membrane element can improve the accuracy without adding new nodes.In addition to, when combined with different plate bending element, some flat elements with 6 degree of freedom per node can be gained and the matrix singularities caused by traditional flat elements will be overcomed. Present paper is devoted to improvement of quadrilateral membrane element with drilling degrees of freedom by hybrid finite element methods: using combined hybrid finite elment method and using classical hybrid finite element method. Based on combined hybrid vanational principles,combined hybrid finite elment does not require LBB condition and the stress mode can be chosen arbitrarily so that the simpliest constant stress mode can be used. Meanwhile, for given meshes proper combination parameters will result in lower energy errors, in turn, improve the accuracy. It is shown that the improved versions of membrane element with drilling degrees of freedom can attain higher accuracy. Based on Hellinger-Reissner vanational principle, classical hybrid finit elements need optimazing stress modes. In this paper , according to energy compatibility and using propriatie bubble function, a kind of 7-parameter stree mode is proposed. Numerical experiments show that this hybrid element, ECAQ4, is of high coarse-mesh accuracy, insentive to mesh distortion, and poisson-locking free.