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Symmetry
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Finite Elements and Symmetry
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Finite Elements and Symmetry

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (30 November 2019) | Viewed by 14297

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editor

Prof. Rachid Touzani

E-Mail Website
Guest Editor
Laboratoire de Mathématiques Blaise Pascal, Université Clermont Auvergne, Clermont-Ferrand, France
Interests: numerical simulation; numerical solution; finite elements

Special Issue Information

Dear Colleagues,

As a numerical method for the approximate solution of partial differential equations, the finite element method has proven its efficiency, robustness and ability to handle most difficulties that arise in this area. The existence of an abundant literature, either theoretical or involving practical applications, shows the popularity of this method in numerical simulation.

An aspect that has not been so widely considered in the literature is the handling of symmetries, in various aspects, in the problems to solve. Symmetry appears under various aspects, such as:

  • Symmetries in domain geometry where this can be taken into account in order to simplify generation and adaptation of finite element meshes.
  • Symmetry in boundary conditions that can contribute to simplify variational formulations.
  • Symmetry in the model definition such as the use of symmetric tensors in continuum mechanics where this property can be sought in numerical simulation.
  • Expected symmetry in solution and symmetry breaking in nonlinear bifurcation problems.

Keywords

  • Finite element method
  • Numerical simulation
  • Numerical method
  • Domain geometry
  • Finite element meshes
  • Boundary conditions

Published Papers (5 papers)

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Research

28 pages, 593 KiB  
Article
Well Posedness and Finite Element Approximability of Three-Dimensional Time-Harmonic Electromagnetic Problems Involving Rotating Axisymmetric Objects
by Praveen Kalarickel Ramakrishnan and Mirco Raffetto
Symmetry 2020, 12(2), 218; https://doi.org/10.3390/sym12020218 - 02 Feb 2020
Cited by 7 | Viewed by 2244
Abstract
A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best [...] Read more.
A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best of authors’ knowledge. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve rotating or bianisotropic materials. All details of the applications of the theory are provided for electromagnetic problems involving rotating axisymmetric objects. Full article
(This article belongs to the Special Issue Finite Elements and Symmetry)
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18 pages, 4385 KiB  
Article
Free Vibration Analysis of Functionally Graded Shells Using an Edge-Based Smoothed Finite Element Method
by Tien Dat Pham, Quoc Hoa Pham, Van Duc Phan, Hoang Nam Nguyen and Van Thom Do
Symmetry 2019, 11(5), 684; https://doi.org/10.3390/sym11050684 - 17 May 2019
Cited by 9 | Viewed by 2880
Abstract
An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique for triangular shell element (MITC3), called ES-MITC3, for free vibration analysis of functionally graded shells is investigated in this work. In the formulation of the ES-MITC3, the [...] Read more.
An edge-based smoothed finite element method (ES-FEM) combined with the mixed interpolation of tensorial components technique for triangular shell element (MITC3), called ES-MITC3, for free vibration analysis of functionally graded shells is investigated in this work. In the formulation of the ES-MITC3, the stiffness matrices are obtained by using the strain-smoothing technique over the smoothing domains that are formed by two adjacent MITC3 triangular shell elements sharing an edge. The strain-smoothing technique can improve significantly the accuracy and convergence of the original MITC3. The material properties of functionally graded shells are assumed to vary through the thickness direction by a power–rule distribution of volume fractions of the constituents. The numerical examples demonstrated that the present ES-MITC3method is free of shear locking and achieves the high accuracy compared to the reference solutions in the literature. Full article
(This article belongs to the Special Issue Finite Elements and Symmetry)
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20 pages, 3971 KiB  
Article
Finite Element Modelling of a Composite Shell with Shear Connectors
by Hoang-Nam Nguyen, Tran Ngoc Canh, Tran Trung Thanh, Tran Van Ke, Van-Duc Phan and Do Van Thom
Symmetry 2019, 11(4), 527; https://doi.org/10.3390/sym11040527 - 11 Apr 2019
Cited by 27 | Viewed by 3236
Abstract
A three-layer composite shell with shear connectors is made of three shell layers with one another connected by stubs at the contact surfaces. These layers can have similar or different geometrical and physical properties with the assumption that they always contact and have [...] Read more.
A three-layer composite shell with shear connectors is made of three shell layers with one another connected by stubs at the contact surfaces. These layers can have similar or different geometrical and physical properties with the assumption that they always contact and have relative movement in the working process. Due to these characteristics, they are used widely in many engineering applications, such as ship manufacturing and production, aerospace technologies, transportation, and so on. However, there are not many studies on these types of structures. This paper is based on the first-order shear deformation Mindlin plate theory and finite element method (FEM) to establish the oscillator equations of the shell structure under dynamic load. The authors construct the calculation program in the MATLAB environment and verify the accuracy of the established program. Based on this approach, we study the effects of some of the geometrical and physical parameters on the dynamic responses of the shell. Full article
(This article belongs to the Special Issue Finite Elements and Symmetry)
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9 pages, 7445 KiB  
Article
Towards Infinite Tilings with Symmetric Boundaries
by Florian Stenger and Axel Voigt
Symmetry 2019, 11(4), 444; https://doi.org/10.3390/sym11040444 - 27 Mar 2019
Cited by 1 | Viewed by 2282
Abstract
Large-time coarsening and the associated scaling and statistically self-similar properties are used to construct infinite tilings. This is realized using a Cahn–Hilliard equation and special boundaries on each tile. Within a compromise between computational effort and the goal to reduce recurrences, an infinite [...] Read more.
Large-time coarsening and the associated scaling and statistically self-similar properties are used to construct infinite tilings. This is realized using a Cahn–Hilliard equation and special boundaries on each tile. Within a compromise between computational effort and the goal to reduce recurrences, an infinite tiling has been created and software which zooms in and out evolve forward and backward in time as well as traverse the infinite tiling horizontally and vertically. We also analyze the scaling behavior and the statistically self-similar properties and describe the numerical approach, which is based on finite elements and an energy-stable time discretization. Full article
(This article belongs to the Special Issue Finite Elements and Symmetry)
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17 pages, 1728 KiB  
Article
New Numerical Method for the Rotation form of the Oseen Problem with Corner Singularity
by Viktor A. Rukavishnikov and Alexey V. Rukavishnikov
Symmetry 2019, 11(1), 54; https://doi.org/10.3390/sym11010054 - 05 Jan 2019
Cited by 19 | Viewed by 2463
Abstract
In the paper, a new numerical approach for the rotation form of the Oseen system in a polygon Ω with an internal corner ω greater than 180 ∘ on its boundary is presented. The results of computational simulations have shown that the convergence [...] Read more.
In the paper, a new numerical approach for the rotation form of the Oseen system in a polygon Ω with an internal corner ω greater than 180 ∘ on its boundary is presented. The results of computational simulations have shown that the convergence rate of the approximate solution (velocity field) by weighted FEM to the exact solution does not depend on the value of the internal corner ω and equals O ( h ) in the norm of a space W 2 , ν 1 ( Ω ) . Full article
(This article belongs to the Special Issue Finite Elements and Symmetry)
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