Efficient construction of a reduced system in multi-domain system with free subdomains

• Published in: Finite elements in analysis and design 2011-09, Vol.47 (9), p.1025-1035
• Main Authors: Kim, Hyungi, Cho, Maenghyo, Kim, Hyuk, Choi, Hyoung-Gil
• Format: Article
• Language: English
• Subjects: Boundaries; Computational efficiency; Computing time; Degrees of freedom; Dynamical systems; Eigenvalues; Exact sciences and technology; Fundamental areas of phenomenology (including applications); High-fidelity dual stage; Mathematical analysis; Mathematical models; Physics; Pseudo-inverse method; Reduced system; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Sub-domain method; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
• ISSN: 0168-874X; 1872-6925
• DOI: 10.1016/j.finel.2011.03.018

Approximate techniques have been developed to calculate eigenvalues of structural system in a reduced manner. However, the construction of a reduced system is problematic with regard to localized selection of the important degrees of freedom and excessive computing time. Recently, a scheme that combines a subdomain method and a reduced system has been proposed as a means of overcoming these problems. Although the combined method is more efficient than previous reduction methods, we still suffer from one aspect: namely, it tends to produce a number of subdomains without any boundary constraints when partitioning the global domain. The Ritz vector estimation is required to be extracted in the selection process of the primary degrees of freedom. The Ritz vector of each subdomain can be easily obtained through a general static analysis of a subdomain with a boundary constraint. In contrast, a pseudo-inverse calculation takes considerable computing time to obtain the reduced system of a floating subdomain without any boundary constraints. This problem can be overcome by using the reduced pseudo-inverse method based on static condensation, which is not related to the selection of the primary degrees of freedom for eigenvalue analysis of given structure. Numerical examples demonstrate that the proposed scheme effectively reduces the computational cost in the process of primary degree-of-freedom selection. In addition, the reduced system based on the proposed scheme can accurately predict the eigenvalues of a global system as well as the time response under dynamic loads.