A complex variable boundary collocation method for plane elastic problems |
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Authors: | Z Zong |
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Affiliation: | (1) Institute of High Performance Computing, 1 Science Park Road, #01-01 The Capricorn Singapore Science Park II, Singapore 117528, Singapore e-mail: zongzhi@ihpc.a-star.edu.sg, SG |
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Abstract: | Lagrange interpolation is extended to the complex plane in this paper. It turns out to be composed of two parts: polynomial
and rational interpolations of an analytical function. Based on Lagrange interpolation in the complex plane, a complex variable
boundary collocation approach is constructed. The method is truly meshless and singularity free. It features high accuracy
obtained by use of a small number of nodes as well as dimensionality advantage, that is, a two-dimensional problem is reduced
to a one-dimensional one. The method is applied to two-dimensional problems in the theory of plane elasticity. Numerical examples
are in very good agreement with analytical ones. The method is easy to be implemented and capable to be able to give the stress
states at any point within the solution domain.
Received: 20 August 2002 / Accepted: 31 January 2003 |
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Keywords: | Plane elasticity Lagrange interpolation Complex variable Boundary collocation Meshless Singularity-free |
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