A Meshless Local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids

Gu, YuanTong & Liu, Gui-Rong (2001) A Meshless Local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids. Computational Mechanics, 27(3), pp. 188-198.

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The Meshless Local Petrov-Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using Moving Least Squares (MLS) interpolants and local weak forms. In this paper, a MLPG formulation is proposed for free and forced vibration analyses. Local weak forms are developed using weighted residual method locally from the dynamic partial differential equation. In the free vibration analysis, the essential boundary conditions are implemented through the direct interpolation form and imposed using orthogonal transformation techniques. In the forced vibration analysis, the penalty method is used in implementation essential boundary conditions. Two different time integration methods are used and compared in the forced vibration analyses using the present MLPG method. The validity and efficiency of the present MLPG method are demonstrated through a number of examples of two-dimensional solids.

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119 citations in Web of Science®
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ID Code: 13906
Item Type: Journal Article
Refereed: Yes
Keywords: Meshless Method, Meshless Local, Galerkin Method, Free Vibration, Forced Vibration, Numerical Analysis
DOI: 10.1007/s004660100237
ISSN: 1432-0924
Subjects: Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MECHANICAL ENGINEERING (091300) > Mechanical Engineering not elsewhere classified (091399)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > CIVIL ENGINEERING (090500) > Structural Engineering (090506)
Divisions: Past > QUT Faculties & Divisions > Faculty of Built Environment and Engineering
Copyright Owner: Copyright 2001 Springer
Copyright Statement: The original publication is available at SpringerLink
Deposited On: 30 Jun 2008 00:00
Last Modified: 10 Aug 2011 15:39

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