Reliability-Based Multi-Material 3D Topology Optimization: A Comparative Study Between SIMP and SESO Methods

Abstract

Topology optimization aims to improve structural design efficiency by determining the optimal material distribution within the solution domain. This paper presents an automated approach for three-dimensional multi-material topology optimization using the Solid Isotropic Material with Penalization (SIMP) and Smoothing-ESO (SESO) methods, implemented in MATLAB. The formulation employs hexahedral finite elements and a power-law interpolation scheme to minimize material discontinuities during the discrete optimization process. A three-dimensional linear elastic analysis is adopted for both methods, integrating commercial materials including steel, aluminum, and concrete. Additionally, the optimization program is coupled with a reliability-based topology optimization analysis module where Young's modulus, force, volume, and compliance are treated as random variables using the First-order Reliability Method (FORM), considering both normal and lognormal distributions with target reliability indices β = 3.0 and β = 2.5. Numerical examples, including a Michell-type structure and bridge design, demonstrate the method's effectiveness in achieving material efficiency while ensuring structural reliability. The results show significant reductions in high-performance material usage, confirming the approach's potential for practical engineering applications.