A Meshless Local Petrov-Galerkin Method for Solving the Bending Problem of a Thin Plate

By S. Long, Satya N. Atluri. 2002

167 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/744b9e97af7d359ceeaf6db341b06c1b953ddfae

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. Zhenting Lin
2. Vladimír Sládek
3. Ján Sládek
4. Dong-dong Wang
5. Satya N. Atluri
6. H. Ching
7. L. Qian
8. S. Shen

In Computational Mechanics

1. Zhenting Lin
2. S. Shen
3. Dong-dong Wang
4. Vladimír Sládek
5. Ján Sládek
6. H. Ching
7. L. Qian
8. Pihua Wen

In Mechanics of Materials

1. Zhenting Lin
2. Vladimír Sládek
3. Ján Sládek
4. Satya N. Atluri
5. Pihua Wen
6. L. Qian
7. Dong-dong Wang
8. S. Shen

Citations in the corpus

• Static and dynamic analysis of 2‐D functionally graded elasticity by using meshless local petrov‐galerkin method (2004, background): “The bending of a thin plate has been studied by Gu and Liu (2001b) and Long and Atluri (2002).”
• Thermal Analysis of Reissner-Mindlin Shallow Shells with FGM Properties by the MLPG (2008, methodology): “Similar approach has been successfully applied to a thin Kirchhoff plate [Long and Atluri, 2002; Sladek et al., 2002, 2003].”
• Bending analyses of 1D orthorhombic quasicrystal plates (2013, methodology): “The MLPG method has attracted much attention in the past decade and it has been successfully applied also to plate problems (Long and Atluri, 2002; Sladek et al., 2006, 2007; Soric et al., 2004).”
• Meshfree Methods: Progress Made after 20 Years (2017, unknown): “…order di ff erentiation in the PDE, such as thin plate and shell problems (Chen and Wang 2006; Krysl and Belytschko 1995, 1996; Liu and Chen 2001; Long and Atluri 2001; Wang and Chen 2008; Wang and Peng 2013) where meshfree approximation functions with higher order continuity can be employed…”
• The Meshless Local Petrov-Galerkin (MLPG) Method: A Simple \& Less-costly Alternative to the Finite Element and Boundary Element Methods (2002, methodology): “…of the MLPG method have been reported in solving the convection-diffusion problems [Lin & Atluri (2000)]; fracture mechanics problems [Kim & Atluri (2000), Ching & Batra (2001)]; Navier-Stokes flows [Lin & Atluri (2001)]; and plate bending problems [Gu & Liu (2001), and Long & Atluri (2002)].”
• Free vibration analysis of thin plates using Hermite reproducing kernel Galerkin meshfree method with sub-domain stabilized conforming integration (2010, methodology): “Long and Atluri [21] also proposed a meshless local Petrov Galerkin method for thin plate problems.”
• Dispersion and transient analyses of Hermite reproducing kernel Galerkin meshfree method with sub-domain stabilized conforming integration for thin beam and plate structures (2011, methodology): “A meshless local Petrov Galerkin method was introduced by Long and Atluri [18] for thin plate bending analysis.”