title: Assessment of solutions from the consistently linearized eigenproblem by means of finite difference approximations.
abstract: 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 [Formula: see text] and of its first derivative with respect to a dimensionless load parameterλ, denoted as [Formula: see text]. In this paper, three approaches of computation of [Formula: see text] are discussed. They are based on (a) an analytical expression for the derivative of the element tangent stiffness matrix [Formula: see text], (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.
authors.affiliation: Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13/202, 1040 Vienna, Austria.
authors.forename: X
authors.initials: X
authors.lastname: Jia
authors.affiliation: Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz 13/202, 1040 Vienna, Austria ; National RPGE Chair Professor, Tongji University, Siping Road 1239, Shanghai, China.
authors.forename: H A
authors.initials: HA
authors.lastname: Mang
keywords: Buckling; Co-rotational beam element; Consistently linearized eigenproblem; Derivatives of the tangent stiffness matrix; Load-based and displacement-based finite difference approximations