The Higher-Order Stiffness Matrix of a Simple Triangular Flat Plate Element for Nonlinear Analysis of Shell Structures

摘要

A simple method to derive the higher-order stiffness matrix of a three-node triangular flat plate element is presented in this study. The derivation of the higher-order stiffness matrix of a triangular flat plate element is based upon a physical concept, i.e. by regarding that there is a set of incremental equilibrium nodal forces existing on the element as a result of the stretching effect in each incremental step in the element. Assume that the incremental stretching effect is generated before element undergoing a small rigid body rotation, then let the element undergo a small rigid body motion, the higher-order stiffness matrix can be derived just changing the initial nodal forces in the geometric stiffness matrix as the incremental nodal forces because of the analogous form between geometric stiffness matrix and higher-order stiffness matrix in physical concepts. In this manner an explicit expression of the higher-order stiffness matrix of triangular plate element can be obtained easily. Then it can be assembled with the linear stiffness matrix and geometric stiffness matrix to form a tangent stiffness matrix that can be used at the force recovery stage in an element in the non-linear analysis of plate and shell structures. Finally, a numerical example will be used to demonstrate the proposed triangular flat plate element with higher-order stiffness matrix in the non-linear analysis of structures and to compare with the results given by conventional method.