Isoparametric finite point method in computational mechanics

Wenxue Wang, Y. Takao

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

In this paper, a new meshless method, the isoparametric finite point method (IFPM) in computational mechanics is presented. The present IFPM is a truly meshless method and developed based on the concepts of meshless discretization and local isoparametric interpolation. In IFPM, the unknown functions, their derivatives, and the sub-domain and its boundaries of an arbitrary point are described by the same shape functions. Two kinds of shape functions that satisfy the Kronecker-Delta property are developed for the scattered points in the domain and on the boundaries, respectively. Conventional point collocation method is employed for the discretization of the governing equation and the boundary conditions. The essential (Dirichlet) and natural (Neumann) boundary conditions can be directly enforced at the boundary points. Several numerical examples are presented together with the results obtained by the exact solution and the finite element method. The numerical results show that the present IFPM is a simple and efficient method in computational mechanics.

Original languageEnglish
Pages (from-to)481-490
Number of pages10
JournalComputational Mechanics
Volume33
Issue number6
DOIs
Publication statusPublished - Jan 1 2004

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Computational mechanics
Computational Mechanics
Boundary conditions
Meshless Method
Interpolation
Shape Function
Derivatives
Finite element method
Discretization
Kronecker Delta
Meshless
Collocation Method
Neumann Boundary Conditions
Dirichlet
Governing equation
Exact Solution
Finite Element Method
Interpolate
Derivative
Unknown

All Science Journal Classification (ASJC) codes

  • Ocean Engineering
  • Mechanical Engineering
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Cite this

Isoparametric finite point method in computational mechanics. / Wang, Wenxue; Takao, Y.

In: Computational Mechanics, Vol. 33, No. 6, 01.01.2004, p. 481-490.

Research output: Contribution to journalArticle

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