The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics

By Satya N. Atluri, T. Zhu. 2000

369 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/09c692ea4d43a1aec64a8e741e7cba466f6b7df6

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

1. Timon Rabczuk
2. Stéphane P.A. Bordas
3. Ted Belytschko
4. Xiaoying Zhuang
5. Pedro Areias
6. Sheng-Wei Chi
7. Jiun-Shyan Chen
8. Wing Kam Liu

In Mechanics of Materials

1. Timon Rabczuk
2. Stéphane P.A. Bordas
3. Ted Belytschko
4. Jiun-Shyan Chen
5. Xiaoying Zhuang
6. Hung Nguyen-Xuan
7. Guirong Liu
8. Trung Nguyen-Thoi

Citations in the corpus

• A LOCAL RADIAL POINT INTERPOLATION METHOD (LRPIM) FOR FREE VIBRATION ANALYSES OF 2-D SOLIDS (2001, neutral): “Two &&truly'' meshless methods, called the meshless local Petrov}Galerkin (MLPG) method and the local point interpolation method (LPIM), have been developed based on local weak forms.”
• Subdomain radial basis collocation method for heterogeneous media (2009, methodology): “Meshfree methods can be classified into two types, one based on Galerkin weak form integrated by quadrature rules [1–6] and the other based on strong form with direct collocation [7–12].”
• Geometrically Nonlinear Analysis of Reissner-Mindlin Plate by Meshless Computation (2007, neutral): “The radial basis function selected multiquadrics [ Atluri and Zhu (1999) ] as”
• A Meshfree Thin Shell for Arbitrary Evolving Cracks Based on An Extrinsic Basis (2006, methodology): “Li, Soric, Jarak, and Atluri (2005) recently developed a locking-free thin and thick plate within the framework of the Meshless local Petrov Galerkin (MLPG) method, Atluri and Shen (2002); Atluri and Zhu (1998, 2000) .”
• Implicit boundary method for finite element analysis using non‐conforming mesh or grid (2008, methodology): “The meshless local Petrov–Galerkin (MLPG) method by Atluri and Zhu [5] uses MLS approximation and a local symmetric weak form derived from weighted residual method confined to a small local subdomain of a node.”
• Meshless methods: A review and computer implementation aspects (2008, methodology): “The most popular method is the meshless local Petrov–Galerkin (MLPG) method [2] [3] [4].”
• Static and dynamic analysis of 2‐D functionally graded elasticity by using meshless local petrov‐galerkin method (2004, methodology): “The recent developments in the MLPG method include the following: Atluri and Zhu (2000) solved elastostatic problems, Lin and Atluri (2000) introduced the upwinding scheme to analyze steady state convectiondiffusion problems, and Liu and Gu (2000) coupled the MLPG method with either the finite…”
• Exponential basis functions in solution of static and time harmonic elastic problems in a meshless style (2010, methodology): “This is in contrast with the cases in which the governing equations and the boundary conditions are approximately satisfied during the solution process, for example meshless methods based on collocation [6–8, 23, 28, 29].”
• A meshfree contact-detection algorithm (2001, methodology): “…moment matrix; these include the element-free Galerkin (EFG) method by Belytschko et al. [5] [6], the reproducing kernel particle method (RKPM) by Liu et al. [20±27], h-p Cloud method by Duarte and Oden [12] [13], and the meshfree local Petrov±Galerkin (MLPG) method by Atluri and Zhu [1] [2].”