Stress-Based Topology Optimization for Steady-State and Transient Thermoelastic Design

Topology optimization is a powerful design tool, benefiting from a broadened design space that can be efficiently navigated with gradient-based optimization algorithms. Complex design problems which often involve coupled multidisciplinary domains may require the use of gradient-based optimization techniques to satisfy demanding design requirements. In addition to multiphysics analysis, structural optimization problem formulations must consider design stresses in order to produce feasible designs. Popular alternative formulations may produce overly stiff designs which do not consider areas of stress concentration. Current topology optimization methods use physics modeling which is too simplistic for many design scenarios, and many do not consider design stress within the problem formulation. Finally, designs generated using topology optimization should be finely refined to achieve a smooth and detailed design. This thesis increases the scope of physics-modeling available for topology optimization, while also considering critical design stress limits. First, due to the high-vibration environments that are common with aerospace structures, unwanted frequency response of the structure must be avoided. To address the high computational cost of eigenvalue problems, the natural frequency problem is solved using a Jacobi–Davidson eigenvalue solution method that is compatible with iterative solution techniques. Second, many aerospace vehicles require structures that operate at high temperatures while simultaneously being subjected to mechanical loads. In this thesis, thermoelastic physics with both steady-state and transient heat transfer analysis are developed for topology optimization. Each of these modeling domains requires significant computational cost. The work in this thesis presents a novel adaptive mesh refinement technique which both increases the resolution of the design while reducing computational cost, making these modeling approaches more viable for topology optimization design.Ph.D