A parallel spectral element method for dynamic three-dimensional nonlinear elasticity problems

2009 ◽  
Vol 87 (1-2) ◽  
pp. 59-72 ◽  
Author(s):  
S. Dong ◽  
Z. Yosibash
Keyword(s):  
Nonlinear Elasticity ◽  
Spectral Element Method ◽  
Three Dimensional ◽  
Spectral Element ◽  
Elasticity Problems ◽  
Element Method

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.

scholarly journals Wave Propagation Analysis in Composite Laminates Containing a Delamination Using a Three-Dimensional Spectral Element Method

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Fucai Li ◽  
Haikuo Peng ◽  
Xuewei Sun ◽  
Jinfu Wang ◽  
Guang Meng
Keyword(s):  
Wave Propagation ◽  
Lamb Wave ◽  
Composite Laminates ◽  
Composite Structures ◽  
Spectral Element Method ◽  
Three Dimensional ◽  
Spectral Element ◽  
Wave Mode ◽  
Diagonal Form ◽  
Element Method

A three-dimensional spectral element method (SEM) was developed for analysis of Lamb wave propagation in composite laminates containing a delamination. SEM is more efficient in simulating wave propagation in structures than conventional finite element method (FEM) because of its unique diagonal form of the mass matrix. Three types of composite laminates, namely, unidirectional-ply laminates, cross-ply laminates, and angle-ply laminates are modeled using three-dimensional spectral finite elements. Wave propagation characteristics in intact composite laminates are investigated, and the effectiveness of the method is validated by comparison of the simulation results with analytical solutions based on transfer matrix method. Different Lamb wave mode interactions with delamination are evaluated, and it is demonstrated that symmetric Lamb wave mode may be insensitive to delamination at certain interfaces of laminates while the antisymmetric mode is more suited for identification of delamination in composite structures.

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