Computational and Applied Mathematics

, Volume 37, Issue 1, pp 135–159 | Cite as

Boundary node Petrov–Galerkin method in solid structures

  • M. Li
  • F. F. Dou
  • T. Korakianitis
  • C. Shi
  • P. H. Wen


Based on the interpolation of the Lagrange series and the Finite Block Method (FBM), the formulations of the Boundary Node Petrov–Galerkin Method (BNPGM) are presented in the weak form in this paper and their applications are demonstrated to the elasticity of functionally graded materials, subjected to static and dynamic loads. By introducing the mapping technique, a block of quadratic type is transformed from the Cartesian coordinate to the normalized coordinate with 8 seeds for two-dimensional problems. The first-order partial differential matrices of boundary nodes are obtained in terms of the nodal values of the boundary node, which can be utilized to determine the tractions on the boundary. Time-dependent partial differential equations are analyzed in the Laplace transformed domain and the Durbin’s inversion method is applied to determine the physical values in the time domain. Illustrative numerical examples are given and comparison has been made with the analytical solutions, the Boundary Element Method (BEM) and the Finite Element Method (FEM).


Meshless Local Petrov–Galerkin method Partial differential matrix Mapping Lagrange interpolation Functionally graded media Laplace transform 



The work of this paper was partially supported by a Grant from the National Youth Science Foundation of China (Grant No. 11401423).


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2016

Authors and Affiliations

  • M. Li
    • 1
  • F. F. Dou
    • 2
  • T. Korakianitis
    • 3
  • C. Shi
    • 4
  • P. H. Wen
    • 4
  1. 1.College of MathematicsTaiyuan University of TechnologyTaiyuanChina
  2. 2.School of Mathematical SciencesUniversity of Electronic Science and Technology of ChinaChengduChina
  3. 3.Parks College of Engineering, Aviation and TechnologySaint Louis UniversitySt. LouisUSA
  4. 4.School of Engineering and Materials Science, Queen MaryUniversity of LondonLondonUK

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