A Combination Of Hybrid Element With Rotational Degrees Of Freedom

Based on the weighed average of domain-decomposed Hellinger-Reissner principle and its dual, combined hybrid variational principle with non-saddle point type has been presented recently. It satisfies inf-sup condition naturally in both infinity and finite dimension space cases. Once displacement and stress interpolations satisfy approach condition, this method is able to assure the stability and convergence. So it is credible and can be implemented easily.In this thesis, the internal energy relationship among various principles is introduced. The trend that combined hybrid energy function changes with combined coefficient is analyzed. The energy-error can be reduced continuously by the modified coefficient, which gets the optimal computing result on the whole.In order to improve the accuracy and efficiency, Allman shape function which includes drilling degrees of freedom is used to replace the ordinary 4-nodes element's displacement interpolation. Compared with common quadratic elements, this kind of interpolation method achieves the same accuracy by adding a rotation degree of freedom on every vertex without using midpoints of edges or interior points. Whether consider from the running time or the space that data occupied, this sort of element is more effective than 8-nodes quadrilateral. And the method can guarantee stability and convergence.Different kinds of bubble are presented to enrich the displacement interpolation function. To obey the rule of accuracy enhancement of combined hybrid method, stress modes which fit the completely energy compatible condition with bubble function are developed. Thus 5 new quadrilateral elements based on combined hybrid principle are obtained: CHDB1, CHD1, CHDB2, CHD2, CHD01.Compared with elements based on modified principle and interpolate rotation degrees of freedom independently, the five new elements use less variable and simpler in calculation. Because of completely energy compatible, it is more convenient to adjust the energy of these elements.The numerical results show that elements presented in this paper can achieve high precision in coarse-mesh condition and converge quickly to the exact result, in addition to nonsensitivity to the deformation of meshes. They can simulate pure bending very well, eliminate parasitical shear, and avoid thickness locking as well as Poisson lockingphenomena. They meet all the requirements of high performance finite elements method, and are able to solve large scale science and engineering problems.