Journal ArticleDOI
Galerkin meshless methods based on partition of unity quadrature
Zeng Qing-hong,Lu Detang +1 more
Reads0
Chats0
TLDR
In this article, a new numerical quadrature technique, partition of unity quadratures (PUQ), for Galerkin meshless methods is presented. But it is not a meshless method based on finite covering.Abstract:
Numerical quadrature is an important ingredient of Galerkin meshless methods. A new numerical quadrature technique, partition of unity quadrature (PUQ), for Galerkin meshless methods was presented. The technique is based on finite covering and partition of unity. There is no need to decompose the physical domain into small cell. It possesses remarkable integration accuracy. Using Element-free Galerkin methods as example, Galerkin meshless methods based on PUQ were studied in detail. Meshing is always not required in the procedure of constitution of approximate function or numerical quadrature, so Galerkin meshless methods based on PUQ are “truly” meshless methods.read more
Citations
More filters
Journal ArticleDOI
Maximum-entropy meshfree method for compressible and near-incompressible elasticity
TL;DR: A modified Gaussian integration scheme on background cells for meshfree methods that alleviates errors in numerical integration and ensures patch test satisfaction to machine precision is presented and a lockingfree small-strain elasticity formulation for mesh free methods is proposed.
Maximum-Entropy Meshfree Method for Compressible and Near-Incompressible Elasticity
TL;DR: In this article, a modified Gaussian integration scheme on background cells for mesh-free methods is presented, which alleviates errors in numerical integration and ensures patch test satisfaction to machine precision.
Journal ArticleDOI
Analytical and numerical modeling of resonant piezoelectric devices in China-A review
TL;DR: The results on theoretical and numerical modeling of resonant piezoelectric devices in China are reviewed in this paper, where solutions to dynamic problems of the propagation of bulk acoustic waves, surface acoustic waves (SAW), vibrations of finite bodies, and analyses of specific devices are discussed.
Journal ArticleDOI
Global interpolating meshless shape function based on generalized moving least-square for structural dynamic analysis
Dan Xie,Kailin Jian,Weibin Wen +2 more
TL;DR: In this paper, a global interpolating meshless shape function based on the generalized moving least square (GMLS) is formulated by the transformation technique, and an improved element-free Galerkin (EFG) method is proposed for the structural dynamic analysis.
Journal ArticleDOI
Modeling vibration behavior of delaminated composite laminates using meshfree method in Hamilton system
Jie Chen,Hai Wang,Guanghui Qing +2 more
TL;DR: In this article, free vibration analysis of composite laminates with delaminations is performed based on a three-dimensional semi-analytical model established by introducing the local radial point interpolation method (LRPIM) into a Hamilton system.
References
More filters
Journal ArticleDOI
Element‐free Galerkin methods
Ted Belytschko,Y. Y. Lu,L. Gu +2 more
TL;DR: In this article, an element-free Galerkin method which is applicable to arbitrary shapes but requires only nodal data is applied to elasticity and heat conduction problems, where moving least-squares interpolants are used to construct the trial and test functions for the variational principle.
Journal ArticleDOI
Meshless methods: An overview and recent developments
TL;DR: Meshless approximations based on moving least-squares, kernels, and partitions of unity are examined and it is shown that the three methods are in most cases identical except for the important fact that partitions ofunity enable p-adaptivity to be achieved.
Journal ArticleDOI
A stabilized conforming nodal integration for Galerkin mesh-free methods
TL;DR: In this paper, a strain smoothing stabilization for nodal integration is proposed to eliminate spatial instability in nodal integrations, where an integration constraint is introduced as a necessary condition for a linear exactness in the mesh-free Galerkin approximation.
Journal ArticleDOI
A new implementation of the element free Galerkin method
Y. Y. Lu,Ted Belytschko,L. Gu +2 more
TL;DR: In this paper, a modified variational principle is used to replace the Lagrange multipliers at the outset by their physical meaning so that the discrete equations are banded, and weighted orthogonal basis functions are constructed so the need for solving equations at each quadrature point is eliminated.
Journal ArticleDOI
Nodal integration of the element-free Galerkin method
Stephen Beissel,Ted Belytschko +1 more
TL;DR: In this paper, it is shown that nodal integration, like SPH, suffers from spurious singular modes and is treated by the addition to the potential energy functional of a stabilization term which contains the square of the residual of the equilibrium equation.
Related Papers (5)
Exact imposition of essential boundary condition and material interface continuity in Galerkin-based meshless methods
Hong Zheng,Wei Li,Xiuli Du +2 more