Related papers: Multi-material phase field approach to structural …
The rapidly evolving field of engineering design of functional surfaces necessitates sophisticated tools to manage the inherent complexity of high-dimensional design spaces. This survey paper offers a scoping review, i.e., a literature…
The modern design of industrial structures leads to very complex simulations characterized by nonlinearities, high heterogeneities, tortuous geometries... Whatever the modelization may be, such an analysis leads to the solution to a family…
The Finite element method (FEM) has long served as the computational backbone for topology optimization (TO). However, for designing structures undergoing large deformations, conventional FEM-based TO often exhibits numerical instabilities…
This paper is concerned with the problem of shape optimization of two-dimensional flows governed by the time-dependent Navier-Stokes equations. We derive the structures of shape gradients with respect to the shape of the variable domain for…
In the field of parametric partial differential equations, shape optimization represents a challenging problem due to the required computational resources. In this contribution, a data-driven framework involving multiple reduction…
An interior point method for the structural topology optimization is proposed. The linear systems arising in the method are solved by the conjugate gradient method preconditioned by geometric multigrid. The resulting method is then compared…
Phase separation of multicomponent liquid mixtures plays an integral part in many processes ranging from industry to cellular biology. In many cases the morphology of coexisting phases is crucially linked to the function of the separated…
Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models…
An efficient topology optimization method applicable to both continuum and rarefied gas flows is proposed in the framework of gas-kinetic theory. The areas of gas and solid are marked by the material density, based on which a fictitious…
The paper presents a new method for shape and topology optimization based on an efficient and scalable boundary integral formulation for elasticity. To optimize topology, our approach uses iterative extraction of isosurfaces of a…
In this paper we consider a shape optimization problem for the minimization of the erosion, that is caused by the impact of inert particles onto the walls of a bended pipe. Using the continuous adjoint approach, we formally compute the…
The differential-geometric structure of the manifold of smooth shapes is applied to the theory of shape optimization problems. In particular, a Riemannian shape gradient with respect to the first Sobolev metric and the Steklov-Poincar\'{e}…
Topology optimization (TO) is a family of computational methods that derive near-optimal geometries from formal problem descriptions. Despite their success, established TO methods are limited to generating single solutions, restricting the…
We investigate the systematic design of compliant morphing structures composed of materials reacting to an external stimulus. We add a perimeter penalty term to ensure existence of solutions. We propose a phase-field approximation of this…
This paper deals with shape irregularity issues in discrete topology optimization algorithms whereby the design is created using the automated distribution of material in the design region. Graph theory is employed to derive appropriate…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
This thesis deals with shape optimization for contact mechanics. More specifically, the linear elasticity model is considered under the small deformations hypothesis, and the elastic body is assumed to be in contact (sliding or with Tresca…
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…
Shape optimization methods have been proven useful for identifying interfaces in models governed by partial differential equations. Here we consider a class of shape optimization problems constrained by nonlocal equations which involve…
This paper sets up an approach for shape optimization problems constrained by variational inequalities (VI) in an appropriate shape space. In contrast to classical VI, where no explicit dependence on the domain is given, VI constrained…