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| A review of numerical integration approaches for Galerkin meshfree methods |
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Abstract Meshfree methods are capable of constructing arbitrary order smoothing and compatible shape functions only through unstructured nodes and do not reply on elements with specific connectivity. Compared with the conventional finite element methods, meshfree methods show obvious advantages in modeling large deformation, moving boundary and higher order problems. Galerkin meshfree methods are one class of most widely used meshfree methods. Although no elements are required for the shape function construction, Galerkin meshfree methods do need some kind of background cells to perform the weak form integration. Due to the rational nature and overlapping characteristics of meshfree shape functions, commonly higher order Gauss quadrature is necessary for the numerical integration of Galerkin meshfree methods, which leads to low computational efficiency and considerable difficulty to model large scale practical problems. Consequently, the development of efficient and robust integration algorithms has been an important topic for Galerkin meshfree methods. This paper first briefly discusses the imposition of essential boundary conditions, and then presents a detailed review on some typical numerical integration approaches for Galerkin meshfree methods, where the characteristics for various integration algorithms are outlined.
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Received: 02 February 2016
Published: 21 June 2016
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2016, Vol. 37 
