Assessment of solutions from the consistently linearized eigenproblem by means of finite difference approximations

摘要

The consistently linearized eigenproblem (CLE) plays an important role in stability analysis of structures. Solution of the CLE requires computation of the tangent stiffness matrix (K) over tilde (T) and of its first derivative with respect to a dimensionless load parameter lambda, denoted as (K) over tilde (T). In this paper, three approaches of computation of (K) over tilde (T) are discussed. They are based on (a) an analytical expression for the derivative of the element tangent stiffness matrix (K) over tilde (e)(T), (b) a load-based finite difference approximation (LBFDA), and (c) a displacement-based finite difference approximation (DBFDA). The convergence rate, the accuracy, and the computing time of the LBFDA and the DBFDA are compared, using the analytical solution as the benchmark result. The numerical investigation consists of the analysis of a circular arch subjected to a vertical point load at the vertex, and of a thrust-line arch under a uniformly distributed load. The main conclusion drawn from this work is that the DBFDA is superior to the LBFDA. (C) 2015 The Authors. Published by Elsevier Ltd. All rights reserved.