Title: Assessment of solutions from the consistently linearized eigenproblem by means of finite difference approximations
Language: English
Authors: Jia, Xin
Mang, Herbert A. 
Category: Research Article
Issue Date: 2015
Journal: Computers and Structures
ISSN: 1879-2243
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 and of its first derivative with respect to a dimensionless load parameter λ, denoted as . In this paper, three approaches of computation of are discussed. They are based on (a) an analytical expression for the derivative of the element tangent stiffness matrix , (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.
Keywords: Buckling; Consistently linearized eigenproblem; Co-rotational beam element; Derivatives of the tangent stiffness matrix; Load-based and displacement-based finite difference approximations
DOI: 10.1016/j.compstruc.2015.01.016
Library ID: AC15534599
URN: urn:nbn:at:at-ubtuw:3-8017
Organisation: E202 - Institut für Mechanik der Werkstoffe und Strukturen 
Publication Type: Article
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