A nonlinear programming algorithm for finite element limit analysis using feasible arc searching technique

• Published in: International journal for numerical methods in engineering Vol. 124; no. 22; pp. 5102 - 5119
• Main Authors: Zhang, Rui, Xiao, Yao
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 30.11.2023
• Subjects: Algorithms; Convergence; Criteria; Empirical analysis; Feasibility; Finite element method; Geotechnical engineering; Limit analysis; Nonlinear programming; Optimization; Searching
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.7340

Abstract This article presents a nonlinear programming algorithm for finite element limit analysis (FELA) based on feasible arc searching technique (FAST). The proposed algorithm has the potential to significantly reduce the iteration numbers required for convergence, making it a valuable tool for solving complex optimization problems from FELA. The algorithm also introduces several new features to the existing methods, including: (i) a novel method for determining a reasonable updating step length; (ii) the avoidance of solving an additional “phase one problem” for finding an initial feasible point; and (iii) the proposition of an empirical criterion for detecting infeasibility problems. The effectiveness of the proposed approach has been demonstrated through several classic examples derived from geotechnical engineering. The initial two examples show the superior convergence speed of the novel approach compared to existing methods. Additionally, the third example highlights the efficacy of the feasibility detection criterion for problems involving both prescribed and unknown external forces.