Topology optimization of thermal fluid-structure systems using body-fitted meshes and parallel computing

International audienceAn efficient framework is described for the shape and topology optimization of realistic three-dimensional, weakly-coupled fluid-thermal-mechanical systems. At the theoretical level, the proposed methodology relies on the boundary variation of Hadamard for describing the sensitivity of functions with respect to the domain. From the numerical point of view, three key ingredients are used: (i) a level set based mesh evolution method allowing to describe large deformations of the shape while maintaining an adapted, high-quality mesh of the latter at every stage of the optimization process; (ii) an efficient constrained optimization algorithm which is very well adapted to the infinite-dimensional shape optimization context; (iii) efficient preconditioning techniques for the solution of large finite element systems in a reasonable computational time. The performance of our strategy is illustrated with two examples of coupled physics: respectively fluid-structure interaction and convective heat transfer. Before that, we perform three other test cases, involving a single physics (structural, thermal and aerodynamic design), for comparison purposes and for assessing our various tools: in particular, they prove the ability of the mesh evolution technique to capture very thin bodies or shells in 3D

The topological ligament in shape optimization: a connection with thin tubular inhomogeneities

In this article, we propose a formal method for evaluating the asymptotic behavior of a shape functional when a thin tubular ligament is added between two distant regions of the boundary of a domain. In the contexts of the conductivity equation and the linear elasticity system, we relate this issue to a perhaps more classical problem of thin tubular inhomogeneities: we analyze the solutions to versions of the physical partial differential equations which are posed inside a fixed "background" medium, and whose material coefficients are altered inside a tube with vanishing thickness. Our main contribution from the theoretical point of view is to propose a heuristic energy argument to calculate the limiting behavior of these solutions with a minimum amount of effort. We retrieve known formulas when they are available, and we manage to treat situations which are, to the best of our knowledge, not reported in the literature (including the setting of the 3d linear elasticity system). From the numerical point of view, we propose three different applications of the formal "topological ligament" approach derived from these expansions. At first, it is an original way to account for variations of a domain, and it thereby provides a new type of sensitivity for a shape functional, to be used concurrently with more classical shape and topological derivatives in optimal design frameworks. Besides, it suggests new, interesting algorithms for the design of the scaffold structure sustaining a shape during its fabrication by a 3d printing technique, and for the design of truss-like structures. Several numerical examples are presented in two and three space dimensions to appraise the efficiency of these methods