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In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the…
We formulate a general shape and topology optimization problem in structural optimization by using a phase field approach. This problem is considered in view of well-posedness and we derive optimality conditions. We relate the diffuse…
In classical inverse linear optimization, one assumes a given solution is a candidate to be optimal. Real data is imperfect and noisy, so there is no guarantee this assumption is satisfied. Inspired by regression, this paper presents a…
Architected materials achieve unique mechanical properties through precisely engineered microstructures that minimize material usage. However, a key challenge of low-density materials is balancing high stiffness with stable deformability up…
We consider a cantilever beam which possesses a possibly non-uniform permanent magnetization, and whose shape is controlled by an applied magnetic field. We model the beam as a plane elastic curve and we suppose that the magnetic field acts…
The effective potential formalism is applied to glass forming liquids, choosing a coupling potential such that the "order parameter", conjugated to the coupling strength, is the mean square displacement of the particles from their position…
Our goal is to develop a design framework for multifunctional mechanical metamaterials that can tune their rigidity while optimizing other desired properties. Towards this goal, we first demonstrate that underconstrained central force…
We introduce a compact yet highly expressive design space for shellular metamaterials. By employing only a few dozen degrees of freedom, this design space represents geometries ranging from simple planar configurations to complex triply…
Shape control is critical to ensure the quality of composite fuselage assembly. In current practice, the structures are adjusted to the design shape in terms of the $\ell_2$ loss for further assembly without considering the existing…
We argue that the standard classification of isometric deformations into infinitesimal v.s. finite is inadequate for the study of compliant shell mechanisms. Indeed, many compliant shells, particularly ones that are periodically corrugated,…
This paper focus on the minimization of a possibly nonsmooth objective function over the Stiefel manifold. The existing approaches either lack efficiency or can only tackle prox-friendly objective functions. We propose a constraint…
This article aims to introduce the paradigm of distributional robustness from the field of convex optimization to tackle optimal design problems under uncertainty. We consider realistic situations where the physical model, and thereby the…
Weak sharp minimality is a notion emerged in optimization, whose utility is largeley recognized in the convergence analysis of algorithms for solving extremum problems as well as in the study of the perturbation behaviour of such problems.…
While colloids are promising building blocks for the self-assembly of materials with novel microstructures, their numerous tunable parameters inhibit brute force searching for appropriate parameter combinations that yield self-assembly of a…
One of the fundamental goals of nanotechnology is to exploit selective and directional interactions between molecules to design particles that self-assemble into desired structures, from capsids, to nano-clusters, to fully formed crystals…
Rapid prototyping is an emerging technology for the fast make of engineering components. A common technique is to laser cut a two-dimensional (2D) part from polymethyl methacrylate (PMMA) sheet. However, both manufacturing defects and…
We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local regions around points, in either average or maximum sense. The…
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…
Given two probability measures $\mu$ and $\nu$ in "convex order" on $\R^d$, we study the profile of one-step martingale plans $\pi$ on $\R^d\times \R^d$ that optimize the expected value of the modulus of their increment among all…
Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for…