Open AccessThe Point Interpolation Method for Static Analysis Using Quadratically Consistent Three-Point Integration Scheme
Author(s) -
Huihui Chen,
Cheng Jia,
Y. T. Gu,
Yujie Zhou,
Ziyu Ge
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1600/1/012019
Subject(s) - interpolation (computer graphics) , galerkin method , mathematics , numerical integration , basis function , mathematical optimization , quadratic equation , kronecker delta , node (physics) , quadratic growth , consistency (knowledge bases) , algorithm , computer science , finite element method , mathematical analysis , geometry , animation , physics , computer graphics (images) , structural engineering , quantum mechanics , engineering , thermodynamics
The element free Galerkin method (EFG) is much interest in recent years due to its merits of only node information needed in constructing shape functions and high precision. However, its low computational efficiency becomes a technical issue in the simulation of realistic problems. To develop a more efficient and accurate method, the point interpolation method using quadratically consistent three-point integration scheme (PIM-QC3) is proposed, based on consistency framework for meshfree nodal shape function and its derivatives. And the shape functions along with corrected nodal derivatives at integration points, adopt quadratic basis, meet the differentiation of the approximation consistency (DAC) and the discrete divergence consistency (DDC). In addition, they possess Kronecker delta property and could enforce displacement boundary conditions simply. The T6-Scheme is utilized for node selection in constructing approximation, to avoid the singular moment matrix and make the computation of shape functions simple. Numerical results show the excellence of the proposed method in accuracy and efficiency of all tested methods. Specially, it is more efficient than three-point integration scheme based on element-free Galerkin method. The research in this paper could provide an efficient and reliable tool for analysis of engineering structure.