Finite Element Analysis of Shell Structures with an Eighteen-Node Three Dimensional Solid Element Based on a New Mixed Formulation

摘要

An eighteen node, three dimensional, solid element with 54 degrees of freedom is presented for the finite element analysis of thin plates and shells. The element is based on the Hellinger Reissner principle with independent assumed strain. The independent strain is divided into higher and lower order terms. A modified stress strain relation decoupling inplane and normal strain is used to model thin shell behavior. Numerical results demonstrate that this element is effectively free of locking even for very thin plates and shells. In addition, the element is kinematically stable. In fact, the stiffness matrix associated with the higher order independent strain is a stabilization matrix.