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A local point interpolation method (LPIM) for static and dynamic analysis of thin beams

Gu, YuanTong & Liu, Gui-Rong (2001) A local point interpolation method (LPIM) for static and dynamic analysis of thin beams. Computer Methods in Applied Mechanics and Engineering, 190(42), pp. 5515-5528.

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Abstract

The Local Point Interpolation Method (LPIM) is a newly developed truly meshless method, based on the idea of Meshless Local Petrov-Galerkin (MLPG) approach. In this paper, a new LPIM formulation is proposed to deal with 4th order boundary-value and initial-value problems for static and dynamic analysis (stability, free vibration and forced vibration) of beams. Local weak forms are developed using weighted residual method locally. In order to introduce the derivatives of the field variable into the interpolation scheme, a technique is proposed to construct polynomial interpolation with Kronecker delta function property, based only on a group of arbitrarily distributed points. Because the shape functions so-obtained possess delta function property, the essential boundary conditions can be implemented with ease as in the conventional Finite Element Method (FEM). The validity and efficiency of the present LPIM formulation are demonstrated through numerical examples of beams under various loads and boundary conditions.

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ID Code: 13905
Item Type: Journal Article
Keywords: Meshless Method, Static Analysis, Dynamic analysis, Weak Formulation, Strong Formulation
DOI: 10.1016/S0045-7825(01)00180-3
ISSN: 0045-7825
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)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MANUFACTURING ENGINEERING (091000)
Divisions: Past > QUT Faculties & Divisions > Faculty of Built Environment and Engineering
Copyright Owner: Copyright 2001 Elsevier
Copyright Statement: Reproduced in accordance with the copyright policy of the publisher.
Deposited On: 30 Jun 2008
Last Modified: 11 Aug 2011 01:39

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