Stress-constrained topology optimization of continuum structures subjected to harmonic force excitation using sequential quadratic programming

• Published in: Structural and multidisciplinary optimization Vol. 59; no. 5; pp. 1747 - 1759
• Main Authors: Long, Kai, Wang, Xuan, Liu, Hongliang
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2019; Springer Nature B.V
• Subjects: Amplitudes; Computational Mathematics and Numerical Analysis; Constraints; Damping; Engineering; Engineering Design; Excitation; Optimization; Quadratic programming; Research Paper; Stiffness; Stress concentration; Theoretical and Applied Mechanics; Topology optimization; Topology optimization; Harmonic analysis; Stress constraints; Sequential quadratic programming; p-norm; Solid isotropic material with penalization
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-018-2159-0

In this paper, we propose a method for stress-constrained topology optimization of continuum structure sustaining harmonic load excitation using the reciprocal variables. In the optimization formulation, the total volume is minimized with a given stress amplitude constraint. The p -norm aggregation function is adopted to treat the vast number of local constraints imposed on all elements. In contrast to previous studies, the optimization problem is well posed as a quadratic program with second-order sensitivities, which can be solved efficiently by sequential quadratic programming. Several numerical examples demonstrate the validity of the presented method, in which the stress constrained designs are compared with traditional stiffness-based designs to illustrate the merit of considering stress constraints. It is observed that the proposed approach produces solutions that reduce stress concentration at the critical stress areas. The influences of varying excitation frequencies, damping coefficient and force amplitude on the optimized results are investigated, and also demonstrate that the consideration of stress-amplitude constraints in resonant structures is indispensable.