Stress Constrained 3D Optimization of Prestressed Concrete

Concrete exhibits high compressive strength but limited tensile strength, which restricts its applications where it's structurally efficient with respect to cost, manufacturability and strength. Prestressing is commonly used to counteract tensile stress by introducing compressive forces but the combination of prestressed concrete and optimization is still under development. An important aspect is to consider material failure criteria while optimizing to achieve realistic concrete designs which are not susceptible to fatigue and cracking from too high stress. This thesis extends an existing 3D optimization framework for prestressed concrete by introducing a stress constraint based on the Drucker-Prager yield criterion. To ensure numerical robustness, epsilon-relaxation is used to mitigate stress singularities and local stress constraints are aggregated into a single global constraint using the Kresselmeier-Steinhauser function. Numerical examples demonstrate that the stress constraint enforces the optimized designs to comply with the maximum allowable compressive and tensile strengths of the material.