Accurate And Efficient Eight-noded Solid-Shell Element And Simple And Robust Four-noded Quadrilateral Membrane Element With Explicit Stiffness Matrix

The solid-shell element is a new type of three-dimensional finite element model which could be used for the efficient finite element analysis of the engineering structure with plate and shell topological property. It has been used in the numerical analysis of nonlinear plate and shell structures, composite laminated structures, sheet metal forming simulation, and so on. However, the study of the solid-shell element is still far from perfection, for instance, the element formulation always encounters some locking problems. Therefore, the development of reliable and efficient solid-shell elements becomes a research focus in recent years.The four-noded membrane element is one of most useful two-dimensional finite element model which is most widely used in problems considering in-plane deformation and the development of four-noded flat-shell elements. Since the original Q4 element in which each in-plane displacement component is approximated by a bilinear displacement interpolation in terms of four nodal displacement variables suffers the shear locking when a membrane undergoes in-plane bending, the researchers have kept devoting themselves into developing accurate, efficient and robust four-noded membrane elements for several decades. This kind of research can not only promote the innovation of element formulation foundation, but also solve the engineering problems more efficiently.This thesis deals with the following tasks.By using the quasi-conforming element technique, an eight-noded solid-shell element with explicit element stiffness matrix is derived. There are three displacement degrees of freedom at each node of this solid-shell element. A suitable strain field over the element domain is assumed based on the characteristics of the strain components in a solid-shell element, so that the resulting solid-shell element can overcome the various locking problems encountered by the solid-shell elements based on the conventional formulations. Another remarkable advantage of the resulting quasi-conforming solid-shell element is that explicit element stiffness matrix is achieved. Consequently, the computational efficiency can be greatly improved. In addition, the two-dimensional analytical displacement trial function given by the theory of elasticity is used to improve the accuracy of the solid-shell element. Numerical examples indicate that the eight-noded quasi-conforming solid-shell element presented in this paper can not only overcome the various locking problems, but also provide high efficiency and good accuracy.By using the quasi-conforming element technique, a four-noded quadrilateral membrane element with 2 degrees of freedom at each node(Q4-type membrane element) is formulated in rectangular Cartesian coordinates. This new four-noded quadrilateral quasi-conforming element is only based on an assumed strain field with five independent strain parameters which account for the Poisson effect explicitly and are consistent with the analytical displacement solutions given by the governing equations of the plane elasticity problem. The performance of another four-noded quadrilateral assumed strain membrane element, which was developed in 1991 for the membrane part of a four-noded quadrilateral flat-shell element in the analysis of plane elasticity problems, is also presented here. There are no any internal parameters and numerical integration involved in the evaluation of the strain parameters in these two four-noded quadrilateral membrane elements, and their element stiffness matrices are computed explicitly in Cartesian coordinates. Consequently, the formulation of these four-noded quadrilateral quasi-conforming membrane elements is extremely simple, and the resulting elements are very computationally efficient. Both of these four-noded quadrilateral quasi-conforming membrane elements pass the patch test, are free from shear locking and insensitive to the element distortion. The numerical result comparison with other four-noded quadrilateral membrane elements shows that the four-noded quadrilateral quasi-conforming membrane elements presented here are not only reliable and robust, but also very accurate in both displacement and stress predictions.