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Mesh-Free Methods with Special Focus on EFGM

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Advanced Computational Methods and Geomechanics

Part of the book series: Springer Tracts in Civil Engineering ((SPRTRCIENG))

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Abstract

TO undertake a successful computation task w.r.t. the construction and operation process of engineering structures, one of the mostly concerned obstacles is the limited or incomplete capability to automatically generate regular grid or to re-mesh retorted grid for complex structure domain containing structural planes and undergoing finite deformation. This chapter presents the principle and basic algorithm of the “element free Galerkin method (EFGM)” in structural dynamics that belongs to the family of “mesh-free methods (MFMs)”. In EFGM, the basis functions no longer belong to standard PU (e.g. the shape functions of fundamental FEM), instead, they are created from the neighborhood field nodes in an “influence or support domain” of any shape by the technique of “moving least squares (MLS)” approximation. The nodal variables in the piecewise trial function may be solved from the algebraic equation set according to the virtual work principle or variational principle (weak form). In this manner, no rigorous restraint is imposed on the generation of scattered field nodes (points), which allows for a great simplification in the pre-process work of complex engineering structure. Although it has not outperformed FEMs in the routine problems of geotechnical and hydraulic structures, yet EFGM exhibits great expectation due to its flexibility in handling structural planes, crack growth, and other large deformation issues.

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Authors and Affiliations

  1. School of Water Resources and Hydropower Engineering, Wuhan University, Wuhan, China

    Shenghong Chen

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Chen, S. (2023). Mesh-Free Methods with Special Focus on EFGM. In: Advanced Computational Methods and Geomechanics. Springer Tracts in Civil Engineering . Springer, Singapore. https://doi.org/10.1007/978-981-19-7427-4_9

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  • DOI: https://doi.org/10.1007/978-981-19-7427-4_9

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