Related papers: Simulating Self-Avoiding Isometric Plate Bending
Physical strands or sheets that can be modelled as curves or surfaces embedded in three dimensions are ubiquitous in nature, and are of fundamental importance in mathematics, physics, biology and engineering. Often the physical…
We develop a new numerical method for thin plates falling in inviscid fluid that allows for leading-edge vortex shedding. The inclusion of leading-edge shedding restores physical dynamics to vortex-sheet models of falling bodies, and for…
In this paper, we develop a virtual element method (VEM) of high order to solve the fourth order plate buckling eigenvalue problem on polygonal meshes. We write a variational formulation based on the Kirchhoff-Love model depending on the…
In this paper, we propose a linear and monolithic finite element method for the approximation of an incompressible viscous fluid interacting with an elastic and deforming plate. We use the arbitrary Lagrangian-Eulerian (ALE) approach that…
The Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This…
Methods for discretizing port-Hamiltonian systems are of interest both for simulation and control purposes. Despite the large literature on mixed finite elements, no rigorous analysis of the connections between mixed elements and…
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…
A family of continuous piecewise linear finite elements for thin plate problems is presented. We use standard linear interpolation of the deflection field to reconstruct a discontinuous piecewise quadratic deflection field. This allows us…
This work focuses on the coupling of trimmed shell patches using Isogeometric Analysis, based on higher continuity splines that seamlessly meet the $C^1$ requirement of Kirchhoff-Love-based discretizations. Weak enforcement of coupling…
We investigate the finite bending and the associated bending instability of an incompressible dielectric slab subject to a combination of applied voltage and axial compression, using nonlinear electro-elasticity theory and its incremental…
We propose bending energies for isotropic elastic plates and shells. For a plate, we define and employ a surface tensor that symmetrically couples stretch and curvature such that any elastic energy density constructed from its invariants is…
A common technique used in factories to shape metal panels is shot peen forming. The impacts between the hard steel shot and the softer metal of the panel cause localized plastic deformation used to improve the fatigue properties of the…
Accurate simulations are essential for engineering applications, and intricate continuum mechanical material models are constructed to achieve this goal. However, the increasing complexity of the material models and geometrical properties…
This work presents a novel formulation and numerical strategy for the simulation of geometrically nonlinear structures. First, a non-canonical Hamiltonian (Poisson) formulation is introduced by including the dynamics of the stress tensor.…
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…
Penalty methods have proven to be particularly effective for achieving the required $C^1$-continuity in the context of multi-patch isogeometric Kirchhoff-Love shells. Due to their conceptual simplicity, these algorithms are readily…
This paper is devoted to proposing and analyzing a robust $C^0$ interior penalty method for a gradient-elastic Kirchhoff plate (GEKP) model over a convex polygon. The numerical method is obtained by combining the triangular Hermite element…
This paper analyses conforming and nonconforming virtual element formulations of arbitrary polynomial degrees on general polygonal meshes for the coupling of solid and fluid phases in deformable porous plates. The governing equations…
We explore the possibilities of applying structure-preserving numerical methods to a plasma hybrid model with kinetic ions and mass-less fluid electrons satisfying the quasi-neutrality relation. The numerical schemes are derived by finite…
A new finite element formulation for the Kirchhoff plate model is presented. The method is a displacement formulation with the deflection and the rotation vector as unknowns and it is based on ideas stemming from a stabilized method for the…