Related papers: Exploiting Lagrange duality for topology optimizat…
In this work, optimality conditions and classical results from duality theory are derived for continuous-time linear optimization problems with inequality constraints. The optimality conditions are given in the Karush-Kuhn-Tucker form. Weak…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
The objective of this paper is to introduce and demonstrate a robust method for multi-constrained topology optimization. The method is derived by combining the topological sensitivity with the classic augmented Lagrangian formulation. The…
We propose two different Lagrange multiplier methods for contact problems derived from the augmented Lagrangian variational formulation. Both the obstacle problem, where a constraint on the solution is imposed in the bulk domain and the…
In the current industry, the development of optimized mechanical components able to satisfy the customer requirements evolves quickly. Therefore, companies are asked for efficient solutions to improve their products in terms of stiffness…
A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…
Design optimization problems, e.g., shape optimization, that involve deformable bodies in unilateral contact are challenging as they require robust contact solvers, complex optimization methods that are typically gradient-based, and…
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…
This paper presents a novel phase-field-based methodology for solving minimum compliance problems in topology optimization under fixed external loads and body forces. The proposed framework characterizes the optimal structure through an…
This paper presents a method for the optimization of multi-component structures comprised of two and three materials considering large motion sliding contact and separation along interfaces. The structural geometry is defined by an explicit…
We study the martingale optimal transport problem with state-dependent trading frictions and develop a geometric and duality framework extending from the one time-step to the multi-marginal setting. Building on the left-monotone structure…
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…
In this paper we present a new Lagrange dual problem associated to a primal DC optimization problem under the additivity condition (AC). As usual for DC programming, even weak duality is not guaranteed for free and, due to this issue, we…
Topology optimization (TO) in two dimensions often presents a trade-off between structural performance and manufacturability, with unpenalized (variable-thickness) methods yielding superior but complex designs, and penalized (SIMP) methods…
A multiobjective optimization method is proposed for obtaining the optimal plane trusses simultaneously for various aspect ratios of the initial ground structure as a set of Pareto optimal solutions generated through a single optimization…
The present work proposes an extension of the third medium contact method for solving structural topology optimization problems that involve and exploit self-contact. A new regularization of the void region, which acts as the contact…
It is nowadays widely acknowledged that optimal structural design should be robust with respect to the uncertainties in loads and material parameters. However, there are several alternatives to consider such uncertainties in structural…
This paper revisits the fundamental equations for the solution of the frictionless unilateral normal contact problem between a rough rigid surface and a linear elastic half-plane using the boundary element method (BEM). After recasting the…
This paper presents a topology optimization approach to design 2D contact-aided compliant mechanisms (CCMs) that can trace the desired output paths with more than one kink while experiencing self and/or external contacts. Such CCMs can be…
Asymptotic post-buckling theory is applied to sizing and topology optimization of trusses and frames, exploring its potential and current computational difficulties. We show that a designs' post-buckling response can be controlled by…