Related papers: Topology optimization in Bernoulli free boundary p…
We study the exterior and interior Bernoulli problems for the half Laplacian and the interior Bernoulli problem for the spectral half Laplacian. We concentrate on the existence and geometric properties of solutions. Our main results are the…
Topology optimization has matured to become a powerful engineering design tool that is capable of designing extraordinary structures and materials taking into account various physical phenomena. Despite the method's great advancements in…
The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…
A new reformulation of a free boundary problem for the Stokes equations governing a viscous flow with overdetermined condition on the free boundary is proposed. The idea of the method is to transform the governing equations to a boundary…
We review some features of topology optimization with a lower bound on the critical load factor, as computed by linearized buckling analysis. The change of the optimized design, the competition between stiffness and stability requirements…
We indicate a new approach to the optimization of the clamped plates with holes. It is based on the use of Hamiltonian systems and the penalization of the performance index. The alternative technique employing the penalization of the state…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
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…
An important new trend in additive manufacturing is the use of optimization to automatically design industrial objects, such as beams, rudders or wings. Topology optimization, as it is often called, computes the best configuration of…
We discuss first order optimality conditions for geometric optimization problems with Neumann boundary conditions and boundary observation. The methods we develop here are applicable to large classes of state systems or cost functionals.…
In this paper we discuss a level set approach for the identification of an unknown boundary in a computational domain. The problem takes the form of a Bernoulli problem where only the Dirichlet datum is known on the boundary that is to be…
In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes a reference domain is introduced and it is optimized over a set of…
The problem of stabilization of a system of coupled PDEs of the forth-order by means of boundary control is investigated. The considered setup arises from the classical Euler-Bernoulli beam model, and constitutes a generalization of…
A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…
The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a nonsmoothed…
This paper proposes a computational framework for the design optimization of stable structures under large deformations by incorporating nonlinear buckling constraints. A novel strategy for suppressing spurious buckling modes related to…
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…
Progresses in additive manufacturing technologies allow the realization of finely graded microstructured materials with tunable mechanical properties. This paves the way to a wealth of innovative applications, calling for the combined…
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…
In this paper, we study superlinear systems that give rise to free boundaries. Such systems appear for example from the minimization of the energy functional $$ \int_{\Omega}\left(|\nabla\mathbf{u}|^2+\frac2p|\mathbf{u}|^p\right),\quad…