These slides were presented at the NAFEMS World Congress 2025, held in Salzburg, Austria from May 19–22, 2025.

Abstract

Traditional structural optimization workflows typically adjust one type of design variable linked to a physical property in the finite element model per optimization run'”such as section thickness, material density, or nodal coordinates. When multiple property types need to be modified, optimizations are performed sequentially. This approach requires CAD reconstruction and manual intervention to change the setups between runs, resulting in dependencies on the optimization sequence. Additionally, the optimized design may not reach its full potential due to the inability to harness synergies between design variable types and increased dependency on the optimization sequence. To address these limitations, a novel approach has been developed to enable the simultaneous optimization of multiple design variable types within a single optimization run. By consolidating the process, this method reduces the number of cycles and eliminates the need to do CAD reconstruction or manually change setups between optimization runs, leading to optimized designs with enhanced physical performance. It achieves this by leveraging the relationships between various design variable types in the finite element model. The approach utilizes the agnostic nature of non-linear optimization algorithms to handle multiple design variable types simultaneously. These algorithms require only a vector of design variable values and their corresponding objective function and constraint sensitivities as input. Based on this input, the nonlinear optimization algorithm approximates a convex problem and iteratively calculates new design variable values. Abaqus processes an updated model based on new values determined by Tosca, incorporating the interactions between different types of design variables during sensitivity analysis. The tight Tosca-Abaqus integration further enhances efficiency by enabling simultaneous sensitivity calculations for all design variable types. A runtime performance penalty is avoided by modifying the initial finite element model as opposed to generating a new one each cycle, which allows Abaqus to skip repeated model checks. This integrated workflow supports advanced features, including contact mechanics, material non-linearities, and geometric non-linearities. In collaboration with a major automotive manufacturer as a pilot customer, we demonstrate the effectiveness of this approach through a combined sizing and bead optimization of a car door. By leveraging the relationship between bead stiffeners and section thickness, this approach achieves a greater reduction in mass than traditional methods, without compromising structural integrity. For comparison, an equivalent sequential optimization was conducted. This approach required manual modifications to the setup between optimization runs. Additionally, the sequential method proved less effective in utilizing bead stiffeners, as it could not simultaneously reduce section thickness to satisfy mass constraints. In contrast, the new simultaneous optimization method effectively harnessed the interplay between bead stiffeners and thickness adjustments, leading to superior design outcomes and better run time performance. While demonstrated with section thicknesses and bead heights as design variable types, the same approach is applicable to combinations of other design variable types, such as density (topology optimization) or nodal coordinates (shape optimization). Additionally, various geometric restrictions can be integrated into the workflow to account for manufacturing processes, ensuring its applicability to a wide range of structural optimization challenges.