Level set topology optimization for Fluid-Structure Interaction problems
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The development and maturation of additive manufacturing (AM) have significantly contributed to an exponential growth of topology optimization (TO) projects. This is primarily because AM allows to manufacture the optimal computed shape, which can sometimes be extremely complex. In the last years, a variety of approaches have been developed and have been applied to different fields, such as solid and fluid mechanics, and, in a reduced number, multi-physics. Regarding the implementation of TO code, many have been proposed using MATLAB®, but also Python. However, they rely whether on finite element analysis codes or open-source libraries rather than commercial software, which can be essential for stringent industries such as nuclear. With the aim of paving the way for applications inside nuclear industry, a level set topology optimization code is developed coupling Python with Cast3M. This approach involves solving the Hamilton-Jacobi equation to dynamically and implicitly track the interface, where its evolution velocity is given by the shape derivative. Building on previous works, the method is expanded to address multiphysics scenarios, considering boundary conditions, solid and fluid governing equations as constraints of the optimization problem. The mathematical development of this Fluid-Structure Interaction (FSI) constrained optimization is presented initially for an arbitrary objective function. Subsequently, it is extended to a specific multi-objective framework that aims at minimizing structure compliance, mass and pressure drop. Finally, the method’s validation is demonstrated using well-known benchmarking from the literature. This work represents the first step towards developing a comprehensive multiphysics and multiscale topology optimization method coupling commercial finite element and volume software with Python.