Two-Level High-Resolution Structural Topology Optimization with Equilibrated Cells

Abstract

In today’s industry, the rapid evolution in the design and development of optimized mechanical components to meet customer requirements represents a significant challenge for companies. These companies seek efficient solutions to enhance their products in terms of stiffness and strength. One powerful approach is Topology Optimization, which aims to determine the optimal material distribution within a predefined domain to maximize the overall component’s stiffness. Achieving high-resolution solutions is also crucial for accurately defining the final material distribution. While standard Topology Optimization tools can propose optimal solutions for entire components, they struggle with small-scale details (such as trabecular structures) due to prohibitive computational costs. To address this issue, our proposed approach introduces a two-level topology optimization methodology considering density-based techniques. The proposed methodology includes three steps: The first one subdivides the whole component in cells and generates a coarse optimized low-definition material distribution, assigning a different density to each cell. Since the output stresses from the coarse problem are not equilibrated into each cell, they must not be directly used in the fine level. Thus, the second step uses the equilibrating traction recovery approach to convert the cell nodal forces into equilibrated lateral tractions over the cell boundary. Finally, taking as input data the densities from the coarse optimization and imposing these lateral tractions as Neumann boundary conditions, each cell is optimized at fine level. The main goal of this work is to efficiently solve high-resolution topology optimization problems using a two-level mechanically-continuous method, which would be unaffordable with standard computing facilities and the current techniques.