Related papers: Optimal control of plate shape with incompatible s…
We consider the shape-topological control of a singularly perturbed variational inequality. The geometry-dependent state problem that we address in this paper concerns a heterogeneous medium with a micro-object (defect) and a macro-object…
Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…
A topology optimization approach for designing large deformation contact-aided shape morphing compliant mechanisms is presented. Such mechanisms can be used in varying operating conditions. Design domains are described by regular hexagonal…
We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting the shape of the domain on which the eigenvalue problem is considered. Here, a phase-field function is used to…
This work concerns a structural topology optimisation problem for 4D printing based on the phase field approach. The concept of 4D printing as a targeted evolution of 3D printed structures can be realised in a two-step process. One first…
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 this paper we address the following design problem: what is the shape of a plate and the associated pre-stress that relaxes toward a given three-dimensional shell? As isometric transformations conserve the gaussian curvature,…
We investigate how thin structures change their shape in response to non-mechanical stimuli that can be interpreted as variations in the structure's natural curvature. Starting from the theory of non-Euclidean plates and shells, we derive…
A fundamental control problem for autonomous vehicle formations is formation shape control, in which the agents must maintain a prescribed formation shape using only information measured or communicated from neighboring agents. While a…
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…
Surface growth, i.e., the addition or removal of mass from the boundary of a solid body, occurs in a wide range of processes, including the growth of biological tissues, solidification and melting, and additive manufacturing. To understand…
We consider a sequence of linear hyper-elastic, inhomogeneous and fully anisotropic bodies in a reference configuration occupying a cylindrical region of height epsilon. We then study, by means of Gamma-convergence, the asymptotic behavior…
Shape matching has been a long-studied problem for the computer graphics and vision community. The objective is to predict a dense correspondence between meshes that have a certain degree of deformation. Existing methods either consider the…
In this paper we investigate an optimal control problem involving a toy model for the protection on a crop field. Precisely, we consider a protection on a crop field and we want to place intervention zones represented by a control, in order…
Programming the non-uniform growth of a responsive polymer gel has emerged as a powerful tool to shape sheets into prescribed three dimensional shapes. We demonstrate that shapes with zero Gaussian curvature, except at singularities,…
Formation control deals with the design of decentralized control laws that stabilize agents at prescribed distances from each other. We call any configuration that satisfies the inter-agent distance conditions a target configuration. It is…
This paper presents an angle-based approach for distributed formation shape stabilization of multi-agent systems in the plane. We develop an angle rigidity theory to study whether a planar framework can be determined by angles between…
Leaves and flowers frequently have a characteristic rippling pattern at their edges. Recent experiments found similar patterns in torn plastic. These patterns can be reproduced by imposing metrics upon thin sheets. The goal of this paper is…
We generalize the exactly solvable corner growth models by choosing the rate of the exponential distribution $a_i+b_j$ and the parameter of the geometric distribution $a_i b_j$ at site $(i, j)$, where $(a_i)_{i \ge 1}$ and $(b_j)_{j \ge 1}$…
Based on the thermodynamic variation, we rigorously derive the sharp-interface model for solid-state dewetting on a flat substrate in the form of cylindrical symmetry. The governing equations for the model belong to fourth-order geometric…