Gradient-based concurrent topology and anisotropy optimization for mechanical structures

This project tackles the simultaneous design of a structure’s shape and its material anisotropy using a gradient‑based mathematical approach. Traditional topology‑optimization methods that use polar formalism usually depend on optimality‑criteria techniques and can only minimize compliance for materials that obey thermodynamic rules. To go beyond those limits, we apply a sequential approximation strategy that uses the Method of Moving Asymptotes (MMA). The new framework separates the problem into three parallel sub‑problems: one updates material density, another adjusts fiber orientation, and a third modifies anisotropic modules. Each sub‑problem follows its own approximation scheme. We test the formulation by running compliance‑minimization benchmarks and comparing the results with the Alternate Directions method for

orthotropic materials that are constrained by thermodynamic bounds. The gradient‑based method is also expanded to include geometric limits on the polar parameters, which define the feasible space for composite laminates. Our implementation gives a reliable computational tool for creating high‑performance composite structures. It shows noticeably higher stiffness than standard lamination‑parameter approaches. Finally, the project provides step‑by‑step guidance for setting up and evaluating these decoupled optimization algorithms inside finite‑element analysis software.

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