Aspects of the use of orthogonal basis functions in the element‐free Galerkin method

By Xiaoying Zhuang, Charles E. Augarde. 2009

74 citations recorded by the source corpus.

The element‐free Galerkin (EFG) method is probably the most widely used meshless method at present. In the EFG method, shape functions are derived from a moving least‐squares approximation using a polynomial basis, a calculation involving the inversion of a small matrix. A new implementation of the EFG method was published soon after the original where an alternative approach using an orthogonal basis was proposed to avoid matrix inversion in the formulation of the shape functions. In this paper we revisit this topic and show that the difficulties associated with the use of a polynomial basis remain present in the orthogonal case. We also show that certain terms in the derivative expressions are omitted in the new implementation of the EFG, which can lead to errors. Finally, we propose a new approach that avoids inversion while maintaining accuracy. Copyright © 2009 John Wiley & Sons, Ltd.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/94e8b8059ee0f67338ec77f60cb7e36604c5c39a

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Citations in the corpus

Fracture modeling using meshless methods and level sets in 3D: Framework and modeling (2012, background): “xI / is a discontinuous weight function with respect to the crack location, Q pj is the orthogonal basis function, and m is the number of bases [33].”
An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function (2014, methodology): “In [19], the use of the orthogonal basis function in the element-free Galerkin (EFG) method is investigated in terms of the solution accuracy and nodal arrangement.”
Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling (2011, unknown): “[6, 22, 23]) and no repetition is necessary here.”