Abstract
The paper deals with the numerical implementations of local integral equation formulation for the solution of two-dimensional (2-d) problems in linear elastic media with continuously variable Young’s modulus. Two kinds of the finite element based interpolation are developed for approximation of field variables on local sub-domains around nodal points. One of these approximations can be classified as meshless, since the elements are generated automatically from the predefined nodal points on the analyzed domain. The other one utilizes the predefined mesh of elements. Besides the element based interpolations we present also the meshless Point Interpolation Method. The accuracy, convergence, numerical stability and efficiency of the proposed techniques are tested by numerical examples with using the exact benchmark solutions.
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References
Idelson SR, Onate E (2006) To mesh or not to mesh. That is the question…, Computer Methods in Applied Mechanics and Engineering 195: 4681–4696
Atluri SN, Shen S (2002) The meshless local Petrov-Galerkin (MLPG) method. Tech Science Press, Encino
Atluri SN (2004) The meshless method (MLPG) for domain & BIE discretizations. Tech Science Press, Forsyth
Hughes TJR (1987) The Finite Element Method. Linear Static and Dynamic Finite Element Analysis. Prentice-Hall, Englewood Cliffs, NJ
Sladek V, Sladek J, Zhang Ch (2005) Local integro-differential equations with domain elements for numerical solution of PDE with variable coefficients. Journal of Engineering and Mathematics 51: 261–282
LIU GR (2003) Mesh free methods, Moving beyond the finite element method. CRC, Boca Raton, FL
Sladek V, Sladek J, Tanaka M (2005) Local integral equations and two meshless polynomial interpolations with application to potential problems in non-homogeneous media. CMES-Computer Modeling in Engineering and Sciences 7: 69–83
Hardy RL (1990) Theory and applications of the multiquadrics-biharmonic method (20 years of discovery 1968–1988). Computers and Mathematics with Application 19: 163–208
Sladek V, Sladek J, Zhang Ch (2006) A meshless Point Interpolation Method for Local Integral Equations in elasticity of non-homogeneous media. In: Sladek J, Sladek V (eds.) Advances in the Meshless Method. Tech Science Press, Forsyth, pp 263–290
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Sladek, V., Sladek, J., Zhang, C. (2008). The Use of Finite Elements for Approximation of Field Variables on Local Sub-Domains in a Mesh-Free Way. In: Composites with Micro- and Nano-Structure. Computational Methods in Applied Sciences, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6975-8_6
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DOI: https://doi.org/10.1007/978-1-4020-6975-8_6
Publisher Name: Springer, Dordrecht
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Online ISBN: 978-1-4020-6975-8
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