相关论文: Finite Element Approximation of Large-Scale Isomet…

This paper studies the discretization of a homogenization and dimension reduction model for the elastic deformation of microstructured thin plates proposed by Hornung, Neukamm, and Vel\v{c}i\'c in 2014. Thereby, a nonlinear bending energy…

We investigate a finite element discretization of an elastic bending-plate model with an effective prestrain. The model has been obtained via homogenization and dimension reduction by B\"onlein at al. (2023). Its energy functional is the…

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,…

Inspired by recent results on self-avoiding inextensible curves, we propose and experimentally investigate a numerical method for simulating isometric plate bending without self-intersections. We consider a nonlinear two-dimensional…

We propose a new discontinuous Galerkin (dG) method for a geometrically nonlinear Kirchhoff plate model for large isometric bending deformations. The minimization problem is nonconvex due to the isometry constraint. We present a practical…

This work presents a numerical formulation to model isotropic viscoelastic material behavior for membranes and thin shells. The surface and the shell theory are formulated within a curvilinear coordinate system, which allows the…

This paper investigates the optimal distribution of hard and soft material on elastic plates. In the class of isometric deformations stationary points of a Kirchhoff plate functional with incorporated material hardness function are…

Construction of optimal deformations is one of the long standing problems of computational mathematics. We consider the problem of computing quasi-isometric deformations with minimal possible quasi-isometry constant (global estimate for…

This paper studies elasto-plastic large deformation behavior of thin shell structures using the isogeometric computational approach with the main focus on the efficiency in modelling the multi-patches and arbitrary material formulations. In…

This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…

We introduce the isogeometric shape optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element…

This paper presents a general, nonlinear isogeometric finite element formulation for rotation-free shells with embedded fibers that captures anisotropy in stretching, shearing, twisting and bending -- both in-plane and out-of-plane. These…

This paper uses the HCT finite element method and mesh adaptation technology to solve the nonlinear plate bending problem and conducts error analysis on the iterative method, including a priori and a posteriori error estimates. Our…

This work presents a Finite Element Model Updating inverse methodology for reconstructing heterogeneous material distributions based on an efficient isogeometric shell formulation. It uses nonlinear hyperelastic material models suitable for…

We construct a finite element approximation of a strain-limiting elastic model on a bounded open domain in $\mathbb{R}^d$, $d \in \{2,3\}$. The sequence of finite element approximations is shown to exhibit strong convergence to the unique…

Using the notion of Gamma-convergence, we discuss the limiting behavior of the 3d nonlinear elastic energy for thin elliptic shells, as their thickness h converges to zero, under the assumption that the elastic energy of deformations scales…

Consider the scattering of an elastic plane wave by a rigid obstacle, which is immersed in a homogeneous and isotropic elastic medium in two dimensions. Based on a Dirichlet-to-Neumann (DtN) operator, an exact transparent boundary condition…

The approximation properties of a quadratic iso-parametric finite element method for a typical cavitation problem in nonlinear elasticity are analyzed. More precisely, (1) the finite element interpolation errors are established in terms of…

Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…

This paper is devoted to show a discrete adaptive finite element approximation result for the isotropic two-dimensional Griffith energy arising in fracture mechanics. The problem is addressed in the geometric measure theoretic framework of…