A DIFFERENTIAL QUADRATURE FINITE ELEMENT METHOD

International Journal of Applied Mechanics - Tập 02 Số 01 - Trang 207-227 - 2010
Yufeng Xing1, Bo Liu1, Liu Guang1
1The Solid Mechanics Research Center, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

Tóm tắt

This paper studies the differential quadrature finite element method (DQFEM) systematically, as a combination of differential quadrature method (DQM) and standard finite element method (FEM), and formulates one- to three-dimensional (1-D to 3-D) element matrices of DQFEM. It is shown that the mass matrices of C 0 finite element in DQFEM are diagonal, which can reduce the computational cost for dynamic problems. The Lagrange polynomials are used as the trial functions for both C 0 and C 1 differential quadrature finite elements (DQFE) with regular and/or irregular shapes, this unifies the selection of trial functions of FEM. The DQFE matrices are simply computed by algebraic operations of the given weighting coefficient matrices of the differential quadrature (DQ) rules and Gauss-Lobatto quadrature rules, which greatly simplifies the constructions of higher order finite elements. The inter-element compatibility requirements for problems with C 1 continuity are implemented through modifying the nodal parameters using DQ rules. The reformulated DQ rules for curvilinear quadrilateral domain and its implementation are also presented due to the requirements of application. Numerical comparison studies of 2-D and 3-D static and dynamic problems demonstrate the high accuracy and rapid convergence of the DQFEM.

Từ khóa


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Thông tin xuất bản

International Journal of Applied Mechanics

Tập 02 Số 01

207-227

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