Finite variation sensitivity analysis for discrete topology optimization of continuum structures

This paper proposes two novel approaches to perform more suitable sensitivity analyses for discrete topology optimization methods. To properly support them, we introduce a more formal description of the Bi-directional Evolutionary Structural Optimization (BESO) method, in which the sensitivity analysis is based on finite variations of the objective function. The proposed approaches are compared to a naive strategy; to the conventional strategy, referred to as First-Order Continuous Interpolation (FOCI) approach; and to a strategy previously developed by other researchers, referred to as High-Order Continuous Interpolation (HOCI) approach. The novel Woodbury Sensitivity (WS) approach provides exact sensitivity values and is a better alternative to HOCI. Although HOCI and WS approaches may be computationally prohibitive, they provide useful expressions for a better understanding of the problem. The novel Conjugate Gradient Sensitivity (CGS) approach provides sensitivity values with arbitrary precision and is computationally viable for a small number of steps. The CGS approach is a better alternative to FOCI since, for appropriate initial conditions, it is always more accurate than the conventional strategy. The standard compliance minimization problem with volume constraint is considered to illustrate the methodology. Numerical examples are presented together with a broad discussion about BESO-type methods.

Automated summary

This paper presents two novel sensitivity analysis approaches for discrete topology optimization methods, introducing a formal description of the BESO method to support them. These approaches provide different advantages in terms of accuracy and computational efficiency compared to conventional strategies, offering possibilities for better understanding of the problem.