An adaptive quadratic approximation for structural and topology optimization

In dual sequential methods for structural and topology optimization, approximations based on diagonal quadratic Taylor series expansion methods are frequently used to construct tractable sub-problems. However, when approximating the second-order terms, some inconsistent enforcements are usually employed to ensure the convexity of the approximations (Groenwold et al. (2010)), which may cause convergence problems in the optimization process. In this paper, an adaptive quadratic approximation (AQA) is proposed to improve robustness and convergence performance of the optimization process. Numerical results on representative structural and topology optimization problems show the efficiency of the new proposed method over other existing algorithms.