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Modelling and Simulation in Engineering
Volume 2017, Article ID 1797561, 7 pages
https://doi.org/10.1155/2017/1797561
Research Article

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

1Fidesys LLC, Office 402, 1 Bld. 77, MSU Science Park, Leninskie Gory, Moscow 119234, Russia
2Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, GSP-1, 1 Leninskiye Gory, Main Building, Moscow 119991, Russia
3Tver State University, 33 Zhelyabov St., Tver 170100, Russia

Correspondence should be addressed to Konstantin Zingerman; ur.relbmar@namregniz

Received 28 August 2017; Accepted 13 November 2017; Published 6 December 2017

Academic Editor: Ricardo Perera

Copyright © 2017 Dmitriy Konovalov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.