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Related papers: The TDNNS method for Reissner-Mindlin plates

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This work presents a general finite element formulation based on a six--field variational principle that incorporates the consistent couple stress theory. A simple, efficient and local iteration free solving procedure that covers both…

Numerical Analysis · Mathematics 2022-07-07 Theodore L. Chang , Chin-Long Lee

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…

Numerical Analysis · Mathematics 2020-03-04 Peter Hornung , Martin Rumpf , Stefan Simon

Two types of finite element spaces on triangles are constructed for div-div conforming symmetric tensors. Besides the normal-normal continuity, the stress tensor is continuous at vertices and another trace involving combination of…

Numerical Analysis · Mathematics 2021-02-02 Long Chen , Xuehai Huang

We present two simple finite element methods for the discretization of Reissner--Mindlin plate equations with {\em clamped} boundary condition. These finite element methods are based on discrete Lagrange multiplier spaces from mortar finite…

Numerical Analysis · Mathematics 2013-05-13 Bishnu P. Lamichhane

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,…

Numerical Analysis · Mathematics 2017-02-15 Peter Hansbo , Mats G. Larson

We compute the rheological properties of inelastic hard spheres in steady shear flow for general shear rates and densities. Starting from the microscopic dynamics we generalise the Integration Through Transients (\textsc{itt}) formalism to…

Soft Condensed Matter · Physics 2020-03-03 W. Till Kranz , Fabian Frahsa , Annette Zippelius , Matthias Fuchs , Matthias Sperl

In this paper, we study an elastic bilayer plate composed of a nematic liquid crystal elastomer in the top layer and a nonlinearly elastic material in the bottom layer. While the bottom layer is assumed to be stress-free in the flat…

Analysis of PDEs · Mathematics 2022-03-09 Sören Bartels , Max Griehl , Stefan Neukamm , David Padilla-Garza , Christian Palus

In this paper a mixed spectral element formulation is presented for planar, linear elasticity. The degrees of freedom for the stress are integrated traction components, i.e. surface force components. As a result the tractions between…

Numerical Analysis · Mathematics 2018-03-06 K. Olesen , B. Gervang , J. N. Reddy , M. Gerritsma

In this paper we derive a new finite element method for nonlinear shells. The Hellan-Herrmann-Johnson (HHJ) method is a mixed finite element method for fourth order Kirchhoff plates. It uses convenient Lagrangian finite elements for the…

Numerical Analysis · Mathematics 2020-07-31 Michael Neunteufel , Joachim Schöberl

In this paper, we construct two lower order mixed elements for the linear elasticity problem in the Hellinger-Reissner formulation, one for the 2D problem and one for the 3D problem, both on macro-element meshes. The discrete stress spaces…

Numerical Analysis · Mathematics 2024-10-15 Jun Hu , Rui Ma , Yuanxun Sun

We develop multipoint stress mixed finite element methods for linear elasticity with weak stress symmetry on cuboid grids, which can be reduced to a symmetric and positive definite cell-centered system. The methods employ the lowest-order…

Numerical Analysis · Mathematics 2025-02-04 Ibrahim Yazici , Ivan Yotov

The lowest order nonconforming rectangular element in three dimensions involves 54 degrees of freedom for the stress and 12 degrees of freedom for the displacement. With a modest increase in the number of degrees of freedom (24 for the…

Numerical Analysis · Mathematics 2011-03-04 Gerard Awanou

We consider thin plates whose energy density is a quadratic function of the difference between the second fundamental form of the deformed configuration and a "natural" curvature tensor. This tensor either denotes the second fundamental…

Analysis of PDEs · Mathematics 2016-05-13 Lorenzo Freddi , Peter Hornung , Maria Giovanna Mora , Roberto Paroni

The design of mixed finite element methods in linear elasticity with symmetric stress approximations has been a longstanding open problem until Arnold and Winther designed the first family of mixed finite elements where the discrete stress…

Numerical Analysis · Mathematics 2015-04-15 Jun Hu

A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a new finite element method is hence presented. The MRA framework is formulated out of a mutually nesting displacement subspace…

Computational Physics · Physics 2016-05-25 Yi-Ming Xia

We propose and rigorously analyze a novel family of explicit low-regularity exponential integrators for the nonlinear Schr\"odinger (NLS) equation, based on a time-relaxation framework. The methods combine a resonance-based scheme for the…

Numerical Analysis · Mathematics 2025-10-06 Hang Li , Xicui Li , Katharina Schratz , Bin Wang

Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the…

Soft Condensed Matter · Physics 2009-11-13 Efi Efrati , Eran Sharon , Raz Kupferman

At low temperature, T -> 0, the yield stress of a perfect crystal is equal to its so called theoretical strength. The yield stress of non-perfect crystals is controlled by the stress threshold of dislocation mobility. A non-crystalline…

Materials Science · Physics 2011-07-01 Nikolai Lazarev , Alexander Bakai

In this paper, we propose a robust low-order stabilization-free virtual element method on quadrilateral meshes for linear elasticity that is based on the stress-hybrid principle. We refer to this approach as the Stress-Hybrid Virtual…

Numerical Analysis · Mathematics 2023-11-28 Alvin Chen , N. Sukumar

In the context of finite elasticity, we propose plate models describing the spontaneous bending of nematic elastomer thin films due to variations along the thickness of the nematic order parameters. Reduced energy functionals are deduced…

Analysis of PDEs · Mathematics 2017-02-03 Virginia Agostiniani , Antonio DeSimone