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An introduction to programming the meshless Element F reeGalerkin method

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Summary

A detailed description of the Element Free Galerkin (EFG) method and its numerical implementation is presented with the goal of familiarizing scientists and engineers with the new computational technique. In this spirit, an in-depth explanation of the essential concepts which comprise the method is given with specific emphasis on the one-dimensional formulation. First, the EFG algorithm for a one-dimensional problem in linear elastostatics is given; the results are compared to those achievable with standard finite element techniques. A step by step explanation of the MATLAB program used to solve the problem is given with specific references to the EFG method in one-dimension. Next, a simplified two-dimensional implementation to linear elastostatics is described. Results are calculated with the method and the aid of a two-dimensional MATLAB EFG program, and conclusions are drawn about the method and its capabilities. The source programs used to solve both the one-dimensional and two-dimensional problems are provided in the Appendices and are available on the web.

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Authors and Affiliations

  1. Department of Civil Engineering, Northwestern University, 2145 Sheridan Road, 60208-3109, Evanston, IL, USA

    J. Dolbow & T. Belytschko

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  1. J. Dolbow
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  2. T. Belytschko
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Dolbow, J., Belytschko, T. An introduction to programming the meshless Element F reeGalerkin method. Arch Computat Methods Eng 5, 207–241 (1998). https://doi.org/10.1007/BF02897874

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