Structures under Multiple Design-Dependent Loads: Topology Optimization Enabled by Load Thresholding and Sensitivity Scaling

Abstract

Abstract Topology optimization of structures subjected to both design-independent loads, such as point forces and constant elevated temperatures, and design-dependent loads, including distributed temperature and pressure abound. However, fewer studies have addressed the optimization of structures when multiple design-dependent load cases interact. This study focuses on optimizing a rotating structure subject to an elevated temperature distribution and a point force. Firstly, we establish theoretical frameworks for thermoelastic stress loads, steady-state heat transfer, and rotational inertia loads. Secondly, we introduce the concept of load thresholding for managing complex load conditions. Thirdly, we develop a weighted multi-objective topology optimization framework and perform sensitivity analysis for a combination of design-dependent loads (centrifugal and thermoelastic stress loads) and design-independent point force. To enhance numerical stability, we incorporate scale factors into the consolidated sensitivity equation. Our results demonstrate that the adoption of load thresholding, sensitivity scaling, and reduced weight factors (typically below 0.5) for TSLs and centrifugal loads not only reduces numerical instabilities but also yields structures with lower compliance values and more distinctive topologies.