Identification of non-ideal structural boundary conditions by using spectral element method

1999 ◽  
Author(s):  
Usik Lee ◽  
Dukkyu Jeon
Keyword(s):  
Boundary Conditions ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Structural Boundary ◽  
Element Method

Wavelet Element Method for Computing Band Structures of Phononic Crystals

2013 ◽  
Author(s):  
Zhangyi Liu ◽  
Jiu Hui Wu
Keyword(s):  
Boundary Conditions ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Structural Features ◽  
Phononic Crystals ◽  
Basis Functions ◽  
Bounded Domains ◽  
Biorthogonal Wavelet ◽  
First Order ◽  
Element Method

In this paper we combine biorthogonal wavelet systems with the philosophy of Spectral Element Method to obtain a biorthogonal wavelet system on fairly general bounded domains. We also extend the boundary adaption of wavelet elements to first order derivatives allowing the construction of basis functions that exactly satisfy boundary conditions. Since this method allows us to take advantage of structural features of phononic crystals and the boundary conditions are satisfied rigorously, a better accuracy and higher efficiency can be obtained.

scholarly journals Accurate Simulation of Circular and Elliptic Cylindrical Invisibility Cloaks

2015 ◽  
Vol 17 (3) ◽  
pp. 822-849 ◽  
Author(s):  
Zhiguo Yang ◽  
Li-Lian Wang
Keyword(s):  
Boundary Conditions ◽  
Spectral Element Method ◽  
Spectral Element ◽  
Exterior Region ◽  
Material Parameters ◽  
Singular Transformation ◽  
Legendre Spectral Element Method ◽  
Invisibility Cloaks ◽  
The Ideal ◽  
Element Method

AbstractThe coordinate transformation offers a remarkable way to design cloaks that can steer electromagnetic fields so as to prevent waves from penetrating into thecloaked region(denoted by Ω0, where the objects inside are invisible to observers outside). The ideal circular and elliptic cylindrical cloaked regions are blown up from a point and a line segment, respectively so the transformed material parameters and the corresponding coefficients of the resulted equations are highly singular at the cloaking boundary ∂Ω0. The electric field or magnetic field is not continuous across ∂Ω0. The imposition of appropriatecloaking boundary conditions(CBCs) to achieve perfect concealment is a crucial but challenging issue.Based upon the principle that a well-behaved electromagnetic field in the original space must be well-behaved in the transformed space as well, we obtain CBCs that intrinsically relate to the essential “pole” conditions of a singular transformation. We also find that for the elliptic cylindrical cloak, the CBCs should be imposed differently for the cosine-elliptic and sine-elliptic components of the decomposed fields. With these at our disposal, we can rigorously show that the governing equation in Ω0can be decoupled from the exterior region, and the total fields in the cloaked region vanish under mild conditions. We emphasize that our proposal of CBCs is different from any existing ones.Using the exact circular (resp., elliptic) Dirichlet-to-Neumann (DtN) non-reflecting boundary conditions to reduce the unbounded domainto a bounded domain, we introduce an accurate and efficient Fourier-Legendre spectral-element method (FLSEM) (resp., Mathieu-Legendre spectral-element method (MLSEM)) to simulate the circular cylindrical cloak (resp., elliptic cylindrical cloak). We provide ample numerical results to demonstrate that the perfect concealment of waves can be achieved for the ideal circular/elliptic cylindrical cloaks under our proposed CBCs and accurate numerical solvers.

scholarly journals On the Modeling of Beam Reinforced Thin Plates Using the Spectral Element Method

2008 ◽  
Vol 15 (3-4) ◽  
pp. 425-434 ◽  
Author(s):  
N.B.F. Campos ◽  
J.R.F. Arruda
Keyword(s):  
Boundary Conditions ◽  
Spectral Element Method ◽  
Low Frequency ◽  
Element Model ◽  
Spectral Element ◽  
Computational Effort ◽  
Boundary Element Methods ◽  
Thin Plates ◽  
Arbitrary Boundary ◽  
Element Method

Modeling beam reinforced thin plates at mid and high frequencies through the most commonly used methods such as finite and boundary element methods frequently leads to unsatisfactory results, since the accuracy of these methods depends on the relation between the dimensions of the elements in which the structure was discretized and the wavelength. Due to this characteristic, the modeling using these techniques will require that the size of the elements becomes smaller as the frequency increases, while its number needs to be increased. For structures that are usual in some areas, like the aerospace industry, this will be possible only with an unreasonable computational effort, which is responsible for restricting the use of these methods practically to low-frequency applications. Semi-analytical methods such as the spectral element method do not need mesh refinement at higher frequencies, but they were very limited in the geometries and boundary conditions that can be treated. This paper presents a spectral element for rectangular thin plates reinforced symmetrically along the sides with Euler beams, which can be used to model plates with arbitrary boundary conditions. The method was verified by comparing its results with those obtained from a Finite Element model.

scholarly journals The Implementation of Spectral Element Method in a CAE System for the Solution of Elasticity Problems on Hybrid Curvilinear Meshes

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Dmitriy Konovalov ◽  
Anatoly Vershinin ◽  
Konstantin Zingerman ◽  
Vladimir Levin
Keyword(s):  
Mathematical Simulation ◽  
High Performance ◽  
Spectral Element Method ◽  
New Technologies ◽  
Spectral Element ◽  
High Tech ◽  
Engineering Analysis ◽  
Elasticity Problems ◽  
Cae System ◽  
Element Method

Modern high-performance computing systems allow us to explore and implement new technologies and mathematical modeling algorithms into industrial software systems of engineering analysis. For a long time the finite element method (FEM) was considered as the basic approach to mathematical simulation of elasticity theory problems; it provided the problems solution within an engineering error. However, modern high-tech equipment allows us to implement design solutions with a high enough accuracy, which requires more sophisticated approaches within the mathematical simulation of elasticity problems in industrial packages of engineering analysis. One of such approaches is the spectral element method (SEM). The implementation of SEM in a CAE system for the solution of elasticity problems is considered. An important feature of the proposed variant of SEM implementation is a support of hybrid curvilinear meshes. The main advantages of SEM over the FEM are discussed. The shape functions for different classes of spectral elements are written. Some results of computations are given for model problems that have analytical solutions. The results show the better accuracy of SEM in comparison with FEM for the same meshes.

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