The families of nonconforming mixed finite elements for linear elasticity on simplex grids

Sun, Yanping; Chen, Shaochun; Yang, Y.B.

doi:10.1016/j.amc.2019.03.017

Cited by 2 publications

(4 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For a two-dimensional homogeneous isotropic material domain X & R 2 , as shown in Figure 1, the equilibrium governing equations of linear elasticity read (Sun et al, 2019):…”

Section: Modeling Wave Runup By Elastic Deformations In the Topographymentioning

confidence: 99%

A hybrid finite volume/finite element method for shallow water waves by static deformation on seabeds

Al-Ghosoun

Osman

Seaı̈d

2020

View full text Add to dashboard Cite

Purpose The purpose of this study is twofold: first, to derive a consistent model free-surface runup flow problems over deformable beds. The authors couple the nonlinear one-dimensional shallow water equations, including friction terms for the water free-surface and the two-dimensional second-order solid elastostatic equations for the bed deformation. Second, to develop a robust hybrid finite element/finite volume method for solving free-surface runup flow problems over deformable beds. The authors combine the finite volume for free-surface flows and the finite element method for bed elasticity. Design/methodology/approach The authors propose a new model for wave runup by static deformation on seabeds. The model consists of the depth-averaged shallow water system for the water free-surface coupled to the second-order elastostatic formulation for the bed deformation. At the interface between the water flow and the seabed, transfer conditions are implemented. Here, hydrostatic pressure and friction forces are considered for the elastostatic equations, whereas bathymetric forces are accounted for in the shallow water equations. As numerical solvers, the authors propose a well-balanced finite volume method for the flow system and a stabilized finite element method for elastostatics. Findings The developed coupled depth-averaged shallow water system and second-order solid elastostatic system is well suited for modeling wave runup by deformation on seabeds. The derived coupling conditions at the interface between the water flow and the bed topography resolve well the condition transfer between the two systems. The proposed hybrid finite volume element method is accurate and efficient for this class of models. The novel technique used for wet/dry treatment accurately captures the moving fronts in the computational domain without generating nonphysical oscillations. The presented numerical results demonstrate the high performance of the proposed methods. Originality/value Enhancing modeling and computations for wave runup problems is at an early stage in the literature, and it is a new and exciting area of research. To the best of our knowledge, solving wave runup problems by static deformation on seabeds using a hybrid finite volume element method is presented for the first time. The results of this research study, and the research methodologies, will have an important influence on a range of other scientists carrying out research in related fields.

show abstract

“…For a two-dimensional homogeneous isotropic material domain X & R 2 , as shown in Figure 1, the equilibrium governing equations of linear elasticity read (Sun et al, 2019):…”

Section: Modeling Wave Runup By Elastic Deformations In the Topographymentioning

confidence: 99%

A hybrid finite volume/finite element method for shallow water waves by static deformation on seabeds

Al-Ghosoun

Osman

Seaı̈d

2020

View full text Add to dashboard Cite

show abstract

“…The linear elasticity discusses how solid objects deform and become internally stressed under prescribed loading conditions and is widely used in structural analysis and engineering design. Because of the wide application background of the elasticity problems, various numerical methods have been developed (see previous studies 1–32,33,34 ). For instance, Bui et al 1,2 studied a meshfree method for the elastodynamic problems.…”

Section: Introductionmentioning

confidence: 99%

“…Arnold et al 21–23 constructed nonconforming mixed finite elements for plane elasticity. Sun et al 25 presented a new family of nonconforming tetrahedral and triangular elements for the stress‐displacement system of linear elasticity problem. Hu and Zhang 28 developed a family of conforming mixed finite elements on triangular grids for solving the classical Hellinger–Reissner mixed problem of the elasticity equations.…”

Section: Introductionmentioning

confidence: 99%

“…However, if the displacement fields in nearly incompressible materials are approximated by using standard conforming finite elements, the approximate numerical solutions deteriorate as λ → ∞ (or Poisson ratio

ν \to \frac{1}{2}

), the so‐called locking phenomenon (see Babuška 35,36 ) will occur. In order to deal with the phenomenon of locking, various numerical methods for the linear elasticity equations/eigenvalue problems have been proposed (e.g., see previous studies 3,5–35 ).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A locking‐free shifted inverse iteration based on multigrid discretization for the elastic eigenvalue problem

Zhang

Yang

2021

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

The families of nonconforming mixed finite elements for linear elasticity on simplex grids

Cited by 2 publications

References 34 publications

A hybrid finite volume/finite element method for shallow water waves by static deformation on seabeds

A hybrid finite volume/finite element method for shallow water waves by static deformation on seabeds

A locking‐free shifted inverse iteration based on multigrid discretization for the elastic eigenvalue problem

Contact Info

Product

Resources

About