Related papers: Variational Methods for Optimal Multimaterial Comp…
Discovering relationships between materials' microstructures and mechanical properties is a key goal of materials science. Here, we outline a strategy exploiting Bayesian optimization to efficiently search the multidimensional space of…
This paper presents a Lagrangian approach to simulating multibody dynamics in a tensegrity framework with an ability to tackle holonomic constraint violations in an energy-preserving scheme. Governing equations are described using…
Metamaterials are engineered materials composed of specially designed unit cells that exhibit extraordinary properties beyond those of natural materials. Complex engineering tasks often require heterogeneous unit cells to accommodate…
We introduce a novel geometric framework for optimal experimental design (OED). Traditional OED approaches, such as those based on mutual information, rely explicitly on probability densities, leading to restrictive invariance properties.…
Electric machine design optimization is a computationally expensive multi-objective optimization problem. While the objectives require time-consuming finite element analysis, optimization constraints can often be based on mathematical…
We discuss a mathematical framework for analysis of optimal control problems on infinite-dimensional manifolds. Such problems arise in study of optimization for partial differential equations with some symmetry. It is shown that some…
In this paper we study the mixed virtual element approximation to an elliptic optimal control problem with boundary observations. The objective functional of this type of optimal control problem contains the outward normal derivatives of…
Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint sytems. While the optimal DR-planning problem is NP-hard even for general 2D bar-joint constraint…
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and…
This work addresses the optimal control of multibody systems being actuated with control forces in order to find a dynamically feasible minimum-energy trajectory of the system. The optimal control problem and its constraints are integrated…
We propose an inexact proximal augmented Lagrangian framework with explicit inner problem termination rule for composite convex optimization problems. We consider arbitrary linearly convergent inner solver including in particular stochastic…
We present an approach to solving problems in micromechanics that is amenable to massively parallel calculations through the use of graphical processing units and other accelerators. The problems lead to nonlinear differential equations…
We consider convex optimization problems with prioritized equality constraints, which may be infeasible. In many applications, such as network optimization and image reconstruction, it is often desirable to compute solutions that satisfy…
Long range order and symmetry in heterogeneous materials architected on crystal lattices lead to elastic and inelastic anisotropies and thus limit mechanical functionalities in particular crystallographic directions. Here, we present a…
We give a geometric description of variational principles in mechanics, with special attention to constrained systems. For the general case of nonholonomic constraints, a unified variational approach is given, and the equations of motion of…
When expressed in Lagrangian variables, the equations of motion for compressible (barotropic) fluids have the structure of a classical Hamiltonian system in which the potential energy is given by the internal energy of the fluid. The…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo…
The modelling of heterogeneous and architected materials poses a significant challenge, demanding advanced homogenisation techniques. However, the complexity of this task can be considerably simplified through the application of micropolar…
The present paper represents a continuation of our previous one. There, a continuous dependence result for the solution of an elliptic variational-hemivariational inequality was obtained and then used to prove the existence of optimal pairs…