Journal
THIN-WALLED STRUCTURES
Volume 49, Issue 7, Pages 923-932Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.tws.2011.03.001
Keywords
Finite volume method; Orthogonal moving least-square; Euler-Bernoulli beam; Thin plate
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In this paper a new method untitled orthogonal meshless finite volume method (OMFVM) is developed for solving elastostatic problems in Euler-Bernoulli beam and thin plate. In this method, the weak formulation of a conservation law is discretized by restricting it to a discrete set of test functions. In contrast to the usual finite volume approach, the test functions are not taken as characteristic functions of the control volumes in a spatial grid, but are chosen from a Heaviside step function. The present approach eliminates the expensive process of directly differentiating the OMLS interpolations in the entire domain. This method was evaluated by applying the formulation to a variety of patch test and thin beam problems. The formulation successfully reproduced exact solutions. Numerical examples demonstrate the advantages of the present methods: (i) lower-order polynomial basis can be used in the OMLS interpolations; (ii) smaller support sizes can be used in the OMFVM approach; and (iii) higher accuracies and computational efficiencies are obtained. (C) 2011 Elsevier Ltd. All rights reserved.
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