Topology optimization with automated derivative computation for multidisciplinary design problems

Topology optimization has drawn increasing attention as a method to aid the design of engineering systems. Gradient-based optimization is typically used to solve these problems because of its efficiency in dealing with a large number of design variables. However, there is a large amount of implementation effort required for both the forward model formulation and the derivative computation of the model, especially for multiphysics problems. This paper addresses these challenges by presenting a general-purpose topology optimization platform called ATOmiCS, built in a modular framework to facilitate the formulation of complex, multiphysics problems with fully automated derivative computation. ATOmiCS automates the derivative computation by coupling FEniCS—a multiphysics partial differential equation solver with accessible symbolic partial derivatives—with OpenMDAO, a modular framework for multidisciplinary design optimization that can automatically solve the adjoint equation for the total derivatives. ATOmiCS is implemented as an open-source toolbox with online documentation and has been used in a graduate-level class. The features of ATOmiCS are demonstrated using three case studies: compliance minimization of cantilever beams with linear and nonlinear elasticity models, compliance minimization of a battery pack with the thermoelastic equation and an unstructured mesh, and optimization of liquid crystal elastomer using a modified elastic equation for shape matching. The results demonstrate the characteristics that, as a whole, make ATOmiCS a unique topology optimization toolbox: modularity and flexibility with respect to operations such as filtering and penalization; ease of implementation of governing equations, type of elements, and solvers for systems of equations; and fully automated derivative computation for gradient-based optimization.