Theory and method for updating least-squares finite element model of symmetric generalized centro-symmetric matrices

• Published in: Journal of computational and applied mathematics Vol. 216; no. 2; pp. 484 - 497
• Main Authors: Xie, Dongxiu, Zhang, Zhongzhi, Liu, Zhongyun
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2008; Elsevier
• Subjects: Exact sciences and technology; Least square problem; Logic and foundations; Mathematical analysis; Mathematical logic, foundations, set theory; Mathematics; Model theory; Numerical analysis; Numerical analysis. Scientific computation; Sciences and techniques of general use; Symmetric generalized centro-symmetric matrix; The correction of the model; The perturbation analysis; The perturbation analysis; The correction of the model; Symmetric generalized centro-symmetric matrix; Least square problem; 15A06; 15A90; 15A29; Finite element method; Numerical analysis; Applied mathematics; Symmetric matrix; Least squares method; Symmetric generalized centro-symmetric matrix; Least square problem; The correction of the model; The perturbation analysis; Least squares problem; 15A90; 15A29; 15A06; Numerical method; Inverse problem
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2007.05.030

Let X , F be a displacement matrix and load matrix, respectively. C (obtained by calculations or measurements) is an estimate matrix of the analytical model. A method is presented for correction of the model C, based on the theory of inverse problem of matrices. The corrected model is symmetric generalized centro-symmetric with specified displacements and loads, satisfying the mechanics characters of finite-element model. The application of the method is illustrated. It is more important that a perturbation analysis is given, which is not given in the earlier papers. Numerical results show that the method is feasible and effective.