Topology optimization of anisotropic solids under uncertainity

Abstract

This thesis presents a framework for topology and fiber-orientation optimization of anisotropic fiber-reinforced composites under dynamic loading. The method couples Solid Isotropic Material with Penalization (SIMP) and orthotropic material modeling to simultaneously optimize material density and fiber orientation angles. Dynamic loading is governed by the dynamic equilibrium equation, and time-integrated compliance is minimized. Modal analysis and transient dynamic response are embedded in the loop to ensure performance under time-varying rather than static loads. The formulation extends classical topology optimization to orthotropic materials through rotated constitutive matrices dependent on fiber angle. Dynamic analysis uses the unconditionally stable Newmark–beta scheme, and density updates employ the Optimality Criteria method with Heaviside projection filtering. Sensitivity analysis uses the adjoint method to compute gradients for both density and orientation variables. Verification studies confirm correct implementation of governing equations and finite element discretization. Static–dynamic comparisons show that dynamic loading introduces additional load-redirecting members to control vibration and inertial effects, yielding up to 11.75% extra compliance reduction. Material layouts remain highly similar (98.3% agreement), while fiber orientations differ markedly, with maximum angles 67% higher in dynamic cases. The framework converges with minimal grey regions (1.5%), sharp material–void transitions, and feasible computational cost, providing a foundation for extensions to 3D analysis, manufacturing constraints, and robust optimization under uncertain loads.