Related papers: Topological optimization and minimal compliance in…
This work 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…
In recent years, semidefinite relaxations of common optimization problems in robotics have attracted growing attention due to their ability to provide globally optimal solutions. In many cases, it was shown that specific handcrafted…
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…
This paper presents a density-based topology optimization approach considering additive manufacturing limitations. The presented method considers the minimum size of parts, the minimum size of cavities, the inability of printing overhanging…
We consider an optimization problem related to elliptic PDEs of the form $-{\rm div}(a(x)\nabla u)=f$ with Dirichlet boundary condition on a given domain $\Omega$. The coefficient $a(x)$ has to be determined, in a suitable given class of…
This paper is devoted to the theoretical and numerical study of an optimal design problem in high-temperature superconductivity (HTS). The shape optimization problem is to find an optimal superconductor shape which minimizes a certain cost…
The increasing availability of full-field displacement data from imaging techniques in experimental mechanics is determining a gradual shift in the paradigm of material model calibration and discovery, from using several simple-geometry…
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…
In this paper, we show the optimality of a certain class of disturbance-affine control policies in the context of one-dimensional, constrained, multi-stage robust optimization. Our results cover the finite horizon case, with minimax…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…
The topological derivative represents the sensitivity of a domain-dependent functional with respect to a local perturbation of the domain and is a valuable tool in topology optimization. Motivated by an application from electrical…
We consider a class of liquid crystal free-boundary problems for which both the equilibrium shape and internal configuration of a system must simultaneously be determined, for example in films with air- or fluid-liquid crystal interfaces…
We propose an adaptive finite element algorithm to approximate solutions of elliptic problems whose forcing data is locally defined and is approximated by regularization (or mollification). We show that the energy error decay is…
This article deals with a particular class of shape and topology optimization problems: the optimized design is a region $G$ of the boundary $\partial \Omega$ of a given domain $\Omega$, which supports a particular type of boundary…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
While topological derivatives have proven useful in applications of topology optimisation and inverse problems, their mathematically rigorous derivation remains an ongoing research topic, in particular in the context of nonlinear partial…
Plasticity is inherent to many engineering materials such as metals. While it can degrade the load-carrying capacity of structures via material yielding, it can also protect structures through plastic energy dissipation. To fully harness…
We develop approximation algorithms for set-selection problems with deterministic constraints, but random objective values, i.e., stochastic probing problems. When the goal is to maximize the objective, approximation algorithms for probing…
We consider shape optimization problems for elasticity systems in architecture. A typical question in this context is to identify a structure of maximal stability close to an initially proposed one. We show the existence of such an…