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Related papers: The TDNNS method for Reissner-Mindlin plates

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We introduce conformal mixed finite element methods for $2$D and $3$D incompressible nonlinear elasticity in terms of displacement, displacement gradient, the first Piola-Kirchhoff stress tensor, and pressure, where finite elements for the…

Numerical Analysis · Mathematics 2019-10-31 Arzhang Angoshtari

We present a time-dependent Ginzburg-Landau model of nonlinear elasticity in solid materials. We assume that the elastic energy density is a periodic function of the shear and tetragonal strains owing to the underlying lattice structure.…

Statistical Mechanics · Physics 2009-11-10 Akira Onuki , Akira Furukawa , Akihiko Minam

The Mindlin plate equations with the consideration of thickness-shear deformation as an independent variable have been used for the analysis of vibrations of quartz crystal resonators of both rectangular and circular types. The Mindlin or…

Materials Science · Physics 2016-11-17 Ji Wang , Hui Chen , Tingfeng Ma , Jianke Du , Lijun Yi , Yook-Kong Yong

Laminated glass units exhibit complex response as a result of different mechanical behavior and properties of glass and polymer foil. We aim to develop a finite element model for elastic laminated glass plates based on the refined plate…

Computational Engineering, Finance, and Science · Computer Science 2016-08-10 Alena Zemanová , Jan Zeman , Michal Šejnoha

We develop a multipoint stress mixed finite element method for linear elasticity with weak stress symmetry on quadrilateral grids, which can be reduced to a symmetric and positive definite cell centered system. The method is developed on…

Numerical Analysis · Mathematics 2019-08-06 Ilona Ambartsumyan , Eldar Khattatov , Jan M. Nordbotten , Ivan Yotov

This paper presents a simple weak Galerkin (WG) finite element method for the Reissner-Mindlin plate model that partially eliminates the need for traditionally employed stabilizers. The proposed approach accommodates general, including…

Numerical Analysis · Mathematics 2025-12-11 Chunmei Wang , Shangyou Zhang

We present a new isogeometric method for the discretization of the Reissner-Mindlin plate bending problem. The proposed scheme follows a recent theoretical framework that makes possible to construct a space of smooth discrete deflections…

Numerical Analysis · Mathematics 2015-05-28 L. Beirão da Veiga , A. Buffa , C. Lovadina , M. Martinelli , G. Sangalli

Compressible Mooney-Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of soft tissues for biomedical tissues, undergoing large elastic deformations. We propose a…

Numerical Analysis · Mathematics 2025-10-20 Suzanne M. Shontz , Stephen A. Vavasis

We describe experiments that probe the evolution of shear jammed states, occurring for packing fractions $\phi_S \leq \phi \leq \phi_J$, for frictional granular disks, where above $\phi_J$ there are no stress-free static states. We use a…

Soft Condensed Matter · Physics 2015-06-05 Jie Ren , Joshua A. Dijksman , Robert P. Behringer

We compute displacement and stress due to a normal fault by means of two-dimensional plane-strain finite-element analysis. To do so, we apply a system of forces to the fault nodes and develop an iterative algorithm serving to determine the…

Geophysics · Physics 2007-05-23 Antonietta Megna , Salvatore Barba , Stefano Santini

We continue the study of a dynamic evolution model for perfectly plastic plates, recently derived from three-dimensional Prandtl-Reuss plasticity. We extend the previous existence result by introducing non-zero external forces in the model,…

Analysis of PDEs · Mathematics 2019-03-14 Paolo Gidoni , Giovanni Battista Maggiani , Riccardo Scala

A nonlinear analysis of high-frequency thickness-shear vibrations of AT-cut quartz crystal plates is presented with the two-dimensional finite element method. We expanded both kinematic and constitutive nonlinear Mindlin plate equations and…

Materials Science · Physics 2014-02-20 Ji Wang , Yangyang Chen , Rongxing Wu , Lihong Wang , Huimin Jing , Jianke Du , Yuantai Hu , Guoqing Li

New low-order $H(\textrm{div})$-conforming finite elements for symmetric tensors are constructed in arbitrary dimension. The space of shape functions is defined by enriching the symmetric quadratic polynomial space with the $(d+1)$-order…

Numerical Analysis · Mathematics 2024-02-22 Xuehai Huang , Chao Zhang , Yaqian Zhou , Yangxing Zhu

We provide a finite element discretization of $\ell$-form-valued $k$-forms on triangulation in $\mathbb{R}^{n}$ for general $k$, $\ell$ and $n$ and any polynomial degree. The construction generalizes finite element Whitney forms for the…

Numerical Analysis · Mathematics 2025-07-23 Kaibo Hu , Ting Lin

In this paper, we propose a novel and efficient differential quadrature element based on Lagrange interpolation to solve a sixth order partial differential equations encountered in non-classical beam theories. These non-classical theories…

Computational Engineering, Finance, and Science · Computer Science 2018-02-23 Md. Ishaquddin , S. Gopalakrishnan

Hybridizable \(H(\textrm{div})\)-conforming finite elements for symmetric tensors on simplices with barycentric refinement are developed in this work for arbitrary dimensions and any polynomial order. By employing barycentric refinement and…

Numerical Analysis · Mathematics 2025-10-27 Long Chen , Xuehai Huang

The paper proposes a new fragmentation mechanism of dendrite arms. The theoretical basis of this mechanism is a shift in the thermodynamical equilibrium at the solid-liquid interface due to the presence of elastic energy. This effect is…

Materials Science · Physics 2008-10-14 S. Ananiev , P. Nikrityuk , K. Eckert

We present an analytical model for the time-developing turbulent boundary layer (TD-TBL) over a flat plate. The model provides explicit formulae for the temporal behavior of the wall-shear stress and both the temporal and spatial…

Chaotic Dynamics · Physics 2009-11-13 Victor S. L'vov , Anna Pomyalov , Antonino Ferrante , Said Elghobashi

The linear Reissner-Mindlin shell theory is reformulated in the frame of the tangential differential calculus (TDC) using a global Cartesian coordinate system. The rotation of the normal vector is modelled with a difference vector approach.…

Numerical Analysis · Computer Science 2019-05-22 D. Schöllhammer , T. P. Fries

It is well-known that it is comparatively difficult to design nonconforming finite elements on quadrilateral meshes by using Gauss-Legendre points on each edge of triangulations. One reason lies in that these degrees of freedom associated…

Numerical Analysis · Mathematics 2015-06-15 Jun Hu , Shangyou Zhang