A new structural reanalysis approach based on the polynomial-type extrapolation methods

• Published in: Structural and multidisciplinary optimization 2018-09, Vol.58 (3), p.1033-1049
• Main Authors: Hosseinzadeh, Yousef, Taghizadieh, Nasser, Jalili, Shahin
• Format: Article
• Language: English
• Subjects: Approximation; Computational Mathematics and Numerical Analysis; Design modifications; Engineering; Engineering Design; Extrapolation; Iterative methods; Least squares method; Polynomials; Research Paper; Theoretical and Applied Mechanics
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-018-1945-z

In this study, a new approach based on the polynomial-type extrapolation methods is applied to the approximate structural reanalysis under multiple and large changes in the initial design. In this approach, the sequences of approximate displacement of the modified structure are constructed by using a fixed-point iteration method. These sequences are then further analyzed by two polynomial-type vector extrapolation methods to find the approximate response of the modified structure more accurately, namely, the minimal polynomial extrapolation (MPE) and the reduced rank extrapolation (RRE). Based on a single initial design, the MPE and RRE methods approximate the displacement vector of the modified structure by solving a least-squares problem which is much smaller than the original system of equations of the exact analysis. The accuracy and efficiency of this reanalysis approach is evaluated on three large scale structural reanalysis problems under multiple and large changes in their initial designs. The obtained reanalysis results demonstrate that the MPE and RRE methods not only yield accurate results, but also are computationally efficient.