A new time-marching scheme that suppresses spurious oscillations in the dynamic rupture problem of the spectral element method: the weighted velocity Newmark scheme

Abstract The solution to nonlinear structural dynamics problems with time marching schemes can be very expensive, particularly if the desired time-periodic response takes many cycles to form. Two cost reduction methods, which need not be considered separately, are formulated in this work. The first projects the nonlinear system of equations onto a reduced basis defined by a set of modes computed with proper orthogonal decomposition. The second utilises a monolithic time spectral element method, whereby the system of ordinary differential equations is converted into a single algebraic system of equations. The spectral element method can be formulated such that only the time-periodic response is computed. These techniques are implemented for a planar elastic beam, actuated at its base to emulate a flapping motion. Nonlinear elastic terms are computed with a corotational finite element method, while inertial terms are computed with a standard multibody dynamics formulation. For a variety of actuation frequencies and kinematic motions, results are given in terms of POD modes, reduced order model accuracy, and computational cost, for both the time marching and the monolithic time schemes.

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Dynamic strain analysis using spectral element method

10.26678/abcm.diname2019.din2019-0029 ◽

2019 ◽

Author(s):

THIAGO SILVA ◽

Marcela Machado ◽

Leila Khalij

Keyword(s):

Spectral Element Method ◽

Strain Analysis ◽

Spectral Element ◽

Dynamic Strain ◽

Element Method

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Dynamic modeling and analysis of the PZT-bonded composite Timoshenko beams: Spectral element method

Journal of Sound and Vibration ◽

10.1016/j.jsv.2012.06.020 ◽

2013 ◽

Vol 332 (6) ◽

pp. 1585-1609 ◽

Cited By ~ 32

Author(s):

Usik Lee ◽

Daehwan Kim ◽

Ilwook Park

Keyword(s):

Dynamic Modeling ◽

Spectral Element Method ◽

Spectral Element ◽

Timoshenko Beams ◽

Modeling And Analysis ◽

Bonded Composite ◽

Element Method

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Metric Identities and the Discontinuous Spectral Element Method on Curvilinear Meshes

Journal of Scientific Computing ◽

10.1007/s10915-005-9070-8 ◽

2006 ◽

Vol 26 (3) ◽

pp. 301-327 ◽

Cited By ~ 105

Author(s):

David A. Kopriva

Keyword(s):

Spectral Element Method ◽

Spectral Element ◽

Element Method

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

Modelling and Simulation in Engineering ◽

10.1155/2017/1797561 ◽

2017 ◽

Vol 2017 ◽

pp. 1-7 ◽

Cited By ~ 3

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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