Related papers: Minimal failure probability for ceramic design via…
In spite of the apparent similarity of micro-branching instabilities in different brittle materials, we propose that the physics determining the typical length- and time-scales characterizing the post-instability patterns differ greatly…
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…
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…
Design of a doubly-clamped beam structure capable of localizing mechanical and optical energy at the nanoscale is presented. The optical design is based upon photonic crystal concepts in which patterning of a nanoscale-cross-section beam…
In brittle fracture applications, failure paths, regions where the failure occurs and damage statistics, are some of the key quantities of interest (QoI). High-fidelity models for brittle failure that accurately predict these QoI exist but…
We develop an empirical potential for silicon which represents a considerable improvement over existing models in describing local bonding for bulk defects and disordered phases. The model consists of two- and three-body interactions with…
Many robotics tasks, such as path planning or trajectory optimization, are formulated as optimal control problems (OCPs). The key to obtaining high performance lies in the design of the OCP's objective function. In practice, the objective…
This contribution investigates the extension of the microplane formulation to the description of transversely isotropic materials such as shale rock, foams, unidirectional composites, and ceramics. Two possible approaches are considered: 1)…
We investigate extremality properties of shape functionals which are products of Newtonian capacity $\cp(\overline{\Om})$, and powers of the torsional rigidity $T(\Om)$, for an open set $\Om\subset \R^d$ with compact closure…
This paper is devoted to the analysis of multiphase shape optimization problems, which can formally be written as $\min\Big\{{g}(F_1(\Omega_1),\dots,F_h(\Omega_h))+ m\vert\,\bigcup_{i=1}^h\Omega_i\vert :\ \Omega_i\subset D,\ \Omega_i\cap…
We review various characterizations of uniform convexity and smoothness on norm balls in finite-dimensional spaces and connect results stemming from the geometry of Banach spaces with \textit{scaling inequalities} used in analysing the…
We consider the following eigenvalue optimization in the composite membrane problem with fractional Laplacian: given a bounded domain $\Omega\subset \mathbb{R}^n$, $\alpha>0$ and $0<A<|\Omega|$, find a subset $D\subset \Omega$ of area $A$…
We consider the problem of matching two shapes assuming these shapes are related by an elastic deformation. Using linearized elasticity theory and the finite element method we seek an elastic deformation that is caused by simple external…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
We introduce a method to design lightweight shell objects that are structurally robust under the external forces they may experience during use. Given an input 3D model and a general description of the external forces, our algorithm…
We consider shape optimization problems subject to elliptic partial differential equations. In the context of the finite element method, the geometry to be optimized is represented by the computational mesh, and the optimization proceeds by…
In this work, we present a novel approach for solving stochastic shape optimization problems. Our method is the extension of the classical stochastic gradient method to infinite-dimensional shape manifolds. We prove convergence of the…
The study reports a systematic evaluation of the role of spatially correlated mechanical elements on failure behavior of heterogeneous materials represented by fiber bundle models (FBM) with different load redistribution rules. The increase…
We consider the internal control of linear parabolic equations through on-off shape controls, i.e., controls of the form $M(t)\chi_{\omega(t)}$ with $M(t) \geq 0$ and $\omega(t)$ with a prescribed maximal measure. We establish small-time…
This paper considers the finite element approximation to parabolic optimal control problems with measure data in a nonconvex polygonal domain. Such problems usually possess low regularity in the state variable due to the presence of measure…