Multi-material topology optimization considering natural frequency constraint

Purpose The purpose of this paper is to propose an effective and efficient numerical method that can consider natural frequency in multi-material topology optimization (MMTO) and which is scalable for complex three-dimensional (3D) problems. Design/methodology/approach The optimization algorithm is developed by combining custom FORTRAN code for MMTO with the open-source software Mystran, which is used as a finite element analysis (FEA) solver. The proposed algorithm allows the designer to shift the fundamental frequency of the design beyond a defined frequency spectrum from the initial designing phase. The methodology is formulated in a smooth and differentiable manner, with the sensitivity expressions, required by gradient-based optimization solvers, presented. Findings Natural frequency constraint has been successfully implemented into MMTO. The use of open-source software Mystran as an FEA solver in the algorithm provides ability to solve complex problems. Mystran offers powerful built-in functions for eigenvalue extraction using methods like Givens, modified Givens, inverse power and the Lanczos method, which provide the ability to solve complex models. The algorithm is successfully able to solve both two- and three-material MMTO jobs for two-dimensional and 3D geometries. Originality/value Natural frequency constraint consideration into topology optimization is very challenging due to three common issues: localized eigenmodes, mode switching and high computational cost. The proposed algorithm addresses these inherent issues, implements natural frequency constraint to MMTO and solves for complex models, which is hardly possible using conventional methods.