A preconditioned conjugate gradient approach to structural reanalysis for general layout modifications

• Published in: International journal for numerical methods in engineering Vol. 70; no. 5; pp. 505 - 522
• Main Authors: Li, Zhengguang, Wu, Baisheng
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 30.04.2007; Wiley
• Subjects: Computational techniques; Exact sciences and technology; finite element; Fundamental areas of phenomenology (including applications); general layout modification; Mathematical methods in physics; PCG approach; Physics; Solid mechanics; Static elasticity (thermoelasticity...); static reanalysis; Structural and continuum mechanics; Conjugate gradient method; Stiffness matrix; finite element; Matrix factorization; Layout problem; Topology; Modeling; Finite element method; general layout modification; static reanalysis; Structure modification; PCG approach; Preconditioning; Structural analysis
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.1889

This paper presents a preconditioned conjugate gradient approach to structural static reanalysis for general layout modifications. It is suitable for all types of layout modifications, including the general case in which some original members and nodes are deleted and other new members and nodes are added concurrently. The approach is based on the preconditioned conjugate gradient technique. The preconditioner is constructed, and an efficient implementation for applying the preconditioner is presented, which requires the factorization of the stiffness matrix corresponding to the newly added degrees of freedom only. In particular, the approach can adaptively monitor the accuracy of approximate solutions. Numerical examples show that the condition number of the preconditioned matrix is remarkably reduced. Therefore, the fast convergence and accurate results can be achieved by the approach. Copyright © 2006 John Wiley & Sons, Ltd.