Conjugated Gradient Sensitivity Analysis in BESO for Compliant Mechanism Design

The Bi-directional Evolutionary Structural Optimization (BESO) method is a Topology Optimization (TO) approach where the structure is defined by binary elements, with design variables restricted to 0 (void) or 1 (solid). Unlike other TO methods, BESO does not employ continuous relaxation of variables, enabling direct generation of discrete topologies without any post-processing. The BESO determines which design variable is modified based on sensitivity analysis, where variables with high sensitivity numbers significantly influence the variation of the objective function. Currently, the BESO sensitivity analysis is typically estimated using a first-order interpolation, which computes the first derivative of the objective function with respect to the design variables under a continuous interpolation assumption. However, the finite variation of the objective function should be considered to perform a suitable sensitivity analysis for the discrete BESO method. To address this limitation, the Conjugated Gradient Sensitivity (CGS) approach was previously proposed, providing a more accurate approximation of the objective function for discrete variable changes. This method has been only applied for compliance minimization problems, so its potential application to other objective functions remains unexplored. Therefore, this work aims to extend the CGS approach to the design of Compliant Mechanisms (CMs). Preliminary results demonstrate that the CGS approach successfully achieves well-known local minima topologies for the mechanisms tested, with equivalent computational costs than the conventional approach. Established objective functions for CM design were evaluated to assess their compatibility with this approach. This study highlights potential shortcomings in the use of first order interpolation for CMs design with BESO, which presents challenges due to the complexity of CM optimization. Furthermore, this work aims to provide tools for addressing advanced problems in CM design, such as nonlinear considerations, design-dependent loads, and multiple-input-multi-output (MIMO) systems. By improving the sensitivity analysis for discrete TO methods, this research contributes to the broader application of BESO in complex structural optimization tasks.