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Title: Boundary node Petrov–Galerkin method in solid structures

Abstract

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).

Authors:
 [1];  [2];  [3]; ;  [4]
  1. Taiyuan University of Technology, College of Mathematics (China)
  2. University of Electronic Science and Technology of China, School of Mathematical Sciences (China)
  3. Saint Louis University, Parks College of Engineering, Aviation and Technology (United States)
  4. University of London, School of Engineering and Materials Science, Queen Mary (United Kingdom)
Publication Date:
OSTI Identifier:
22769393
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 1; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; ANALYTICAL SOLUTION; BOUNDARY ELEMENT METHOD; INTERPOLATION; LAPLACE TRANSFORMATION; MATRICES; PARTIAL DIFFERENTIAL EQUATIONS; TIME DEPENDENCE

Citation Formats

Li, M., E-mail: liming04@gmail.com, Dou, F. F., Korakianitis, T., Shi, C., and Wen, P. H., E-mail: p.h.wen@qmul.ac.uk. Boundary node Petrov–Galerkin method in solid structures. United States: N. p., 2018. Web. doi:10.1007/S40314-016-0335-7.
Li, M., E-mail: liming04@gmail.com, Dou, F. F., Korakianitis, T., Shi, C., & Wen, P. H., E-mail: p.h.wen@qmul.ac.uk. Boundary node Petrov–Galerkin method in solid structures. United States. doi:10.1007/S40314-016-0335-7.
Li, M., E-mail: liming04@gmail.com, Dou, F. F., Korakianitis, T., Shi, C., and Wen, P. H., E-mail: p.h.wen@qmul.ac.uk. Thu . "Boundary node Petrov–Galerkin method in solid structures". United States. doi:10.1007/S40314-016-0335-7.
@article{osti_22769393,
title = {Boundary node Petrov–Galerkin method in solid structures},
author = {Li, M., E-mail: liming04@gmail.com and Dou, F. F. and Korakianitis, T. and Shi, C. and Wen, P. H., E-mail: p.h.wen@qmul.ac.uk},
abstractNote = {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).},
doi = {10.1007/S40314-016-0335-7},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 1,
volume = 37,
place = {United States},
year = {2018},
month = {3}
}