Overhang Penalization in Additive Manufacturing via Phase Field Structural Topology Optimization

Explore a mathematical lecture analyzing phase field approaches for structural topology optimization in additive manufacturing contexts. Learn about novel penalization techniques for overhangs using anisotropic energy functionals, examining both convex and non-convex examples that demonstrate oscillatory boundary behavior known as the dripping effect. Discover rigorous mathematical analysis methods for topology optimization problems involving non-continuously-differentiable anisotropies, including derivation of first-order necessary optimality conditions through subdifferential calculus. Understand connections between phase field methods and sharp interface shape optimization through formally matched asymptotic expansions. Review numerical results demonstrating the effectiveness of proposed approaches in preventing overhang development during additive manufacturing processes, with particular focus on regions requiring support structures during construction.