Related papers: Finite Element Approximation of Large-Scale Isomet…
We present an analysis for a mixed finite element method for the bending problem of Koiter shell. We derive an error estimate showing that when the geometrical coefficients of the shell mid-surface satisfy certain conditions the finite…
Nonlinear bending phenomena of thin elastic structures arise in various modern and classical applications. Characterizing low energy states of elastic rods has been investigated by Bernoulli in 1738 and related models are used to determine…
In the context of unfitted finite element discretizations the realization of high order methods is challenging due to the fact that the geometry approximation has to be sufficiently accurate. Recently a new unfitted finite element method…
We present a computational model of thin elastic bilayers that undergo large bending isometric deformations when actuated by non-mechanical stimuli. We propose a discontinuous Galerkin approximation of the variational formulation discussed…
We present a new way to discretize a geometrically nonlinear elastic planar Cosserat shell. The kinematical model is similar to the general 6-parameter resultant shell model with drilling rotations. The discretization uses geodesic finite…
Consider a time-harmonic acoustic plane wave incident onto an elastic body with an unbounded periodic surface. The medium above the surface is supposed to be filled with a homogeneous compressible inviscid air/fluid of constant mass…
In this work, we aim to develop energy-stable parametric finite element approximations for a sharp-interface model with strong surface energy anisotropy, which is derived from the first variation of an energy functional composed of…
In this paper, a nonconforming finite element method has been proposed and analyzed for the von Karman equations that describe bending of thin elastic plates. Optimal order error estimates in broken energy and $H^1$ norms are derived under…
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 many applications, thin shell-like structures are integrated within or attached to volumetric bodies. This includes reinforcements placed in soft matrix material in lightweight structure design, or hollow structures that are partially or…
This paper presents three different constitutive approaches to model thin rotation-free shells based on the Kirchhoff-Love hypothesis. One approach is based on numerical integration through the shell thickness while the other two approaches…
We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space. The model describes the motion of the film\slash vapor interface…
The bending of bilayer plates is a mechanism which allows for large deformations via small externally induced lattice mismatches of the underlying materials. Its mathematical modeling, discussed herein, consists of a nonlinear fourth order…
Bilayer plates are compound materials that exhibit large bending deformations when exposed to environmental changes that lead to different mechanical responses in the involved materials. In this article a new numerical method which is…
An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other…
The Intrinsic Surface Finite Element Method (ISFEM) was recently proposed to solve Partial Differential Equations (PDEs) on surfaces. ISFEM proceeds by writing the PDE with respect to a local coordinate system anchored to the surface and…
The Kohn-Sham equation is a powerful, widely used approach for computation of ground state electronic energies and densities in chemistry, materials science, biology, and nanosciences. In this paper, we study the adaptive finite element…
An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…
In this paper we establish the convergence of a numerical scheme based, on the Finite Element Method, for a time-independent problem modelling the deformation of a linearly elastic elliptic membrane shell subjected to remaining confined in…
We employ surface differential calculus to derive models for Kirchhoff plates including in-plane membrane deformations. We also extend our formulation to structures of plates. For solving the resulting set of partial differential equations,…