A LOCAL RADIAL POINT INTERPOLATION METHOD (LRPIM) FOR FREE VIBRATION ANALYSES OF 2-D SOLIDS

By Guirong Liu, Yuantong T. Gu. 2001

543 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/d20bf3e3997eff6ab97ab872932893ddafce55df

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. A. J. Ferreira
2. C. Roque
3. Erasmo Carrera
4. R. N. Jorge
5. M. Cinefra
6. Guirong Liu
7. Romesh C. Batra
8. Hung Nguyen-Xuan

In Computational Mechanics

1. Guirong Liu
2. Guiyong Zhang
3. Trung Nguyen-Thoi
4. Hung Nguyen-Xuan
5. Guangyao Li
6. Z. Zhong
7. Khin Yong Lam
8. K. Y. Dai

In Mechanics of Materials

1. Guirong Liu
2. Hung Nguyen-Xuan
3. Trung Nguyen-Thoi
4. A. J. Ferreira
5. Erasmo Carrera
6. R. N. Jorge
7. C. Roque
8. Guiyong Zhang

Citations in the corpus

• Free vibration analysis of functionally graded shells by a higher-order shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations (2013, unknown): “The use of radial basis function for the analysis of structures and materials has been previously studied [15–29].”
• On the convergence analysis, stability, and implementation of meshless local radial point interpolation on a class of three‐dimensional wave equations (2016, methodology): “In order to avoid the singularity difficulty in the polynomial PIM, the RBF is used to develop the RPIM for meshless weak form techniques [58, 60, 61].”
• Comparisons of two meshfree local point interpolation methods for structural analyses (2002, methodology): “G. R. Liu (&), Y. T. Gu Singapore-MIT alliance (SMA), Centre for Advanced Computations in Engineering Science (ACES), Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260 E-mail: mpeliugr@nus.edu.sg et al., 2001; Liu and Gu, 2001c ).”
• Solving high order ordinary differential equations with radial basis function networks (2005, methodology): “The case of using the integration formulations (weakform/inverse statement) with the direct RBF interpolation schemes can be found in, for example, Liu and Gu [23], Wang and Liu [24,25], Wang et al [26], Gu and Liu [27] and Wu and Liu [28].”
• A LINEARLY CONFORMING POINT INTERPOLATION METHOD (LC-PIM) FOR 2D SOLID MECHANICS PROBLEMS (2005, methodology): “, polynomial basis functions [Liu and Gu, 2001a; Liu, 2002] and radial basis functions [Wang and Liu, 2002a; Liu and Gu, 2001b].”
• A meshfree radial point interpolation method (RPIM) for three-dimensional solids (2005, methodology): “The RPIM has been successfully applied to 1D and 2D solid mechanics (Gu and Liu, 2001; Liu and Gu, 2001b; Liu and Yan, et al. 2002), plate and shell structures (Liu and Chen, 2001; Liu and Liu, et al. 2002), problems of smart materials (Liu and Dai, et al. 2002), geometrically nonlinear problems (”