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A generalized conforming finite element theory was presented to satisfy the C1 continuity condition for plate and shell element. The effectiveness of the theory in the linear analysis has been proved. This paper discusses the membrane locking phenomenon of shallow shell element based on the satisfaction of the requirement of rigid body motion, and a technique is developed to eliminate the membrane locking phenomenon. Accordingly a geometrically nonlinear generalized conforming rectangular shallow shell element with tangential degrees of freedom of midpoints of sides is formulated. Nonlinear numerical analysis of shell stability shows that the element exhibits high precision and fast convergence characteristics.

Many finite element models have very acceptable performance when the computing meshes are regular. However, as the level of mesh distortion is increasing, the accuracy of the solutions deteriorates rapidly. Therefore, how to formulate an element that is less sensitive to geometric distortion is an important question for study for a long period. In this paper, a simple quadrilateral membrane element with rotational degrees-of-freedom is developed with the approach of the generalized conforming element proposed by Long Yuqiu (1989). The new element exhibits excellent feature, that is, less sensitive to geometric distortion. A general method to formulate high precision finite element less sensitive to geometric distortion is provided in this paper.

The concept of generalized conforming elements and their applications to membrane, plate and shell problems are introduced in this paper. The generalized conforming element method proposed by the first author in 1987 provides a simple and efficient means to deal with structural problems, especially the C1continuous problems.In the first part of this paper, the theoretical basis of GCE is presented. GCE is a limiting-conforming element which is non-conforming in coarse meshes but tends to be conforming in the limiting case of refined meshes. It is formulated based on the modified potential energy principle and the concept of generalized compatibility conditions. It is a new way to construct the finite elements — combined application of the energy method and the weighted residual method.In the second part of this paper, various models of GCE are illustrated. A series of generalized conforming elements with excellent performance have been constructed, that is, thin and thick plate bending GCE, membrane GCE with drilling freedoms and thin shell GCE.