Static Analysis of Reissner-Mindlin Plates by Differential Quadrature Element Method

1998 ◽  
Vol 65 (3) ◽  
pp. 705-710 ◽  
Author(s):  
F.-L. Liu ◽  
K. M. Liew
Keyword(s):  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Two Dimensional ◽  
Quadrature Method ◽  
The Finite Element Method ◽  
Compatibility Conditions ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Bending Problems ◽  
Element Method

In this paper, a new numerical method, the differential quadrature element method has been developed for two-dimensional analysis of bending problems of Reissner-Mindlin plates. The basic idea of the differential quadrature element method is to divide the whole variable domain into several subdomains (elements) and to apply the differential quadrature method for each element. The detailed formulations for the differential quadrature element method and compatibility conditions between elements are presented. The convergent characteristics and accuracy of the differential quadrature element method are carefully investigated for the solution of the two-dimensional bending problems of Reissner-Mindlin plates. Finally, the differential quadrature element method is applied to analyze several bending problems of two-dimensional Reissner-Mindlin plates with different discontinuities including the discontinuous loading conditions, the mixed boundaries, and the plates with cutout. The accuracy and applicability of this method have been examined by comparing the differential quadrature element method solutions with the existing solutions obtained by other numerical methods and the finite element method solutions generated using ANSYS 5.3.

Vibration Analysis of Discontinuous Mindlin Plates by Differential Quadrature Element Method

1999 ◽  
Vol 121 (2) ◽  
pp. 204-208 ◽  
Author(s):  
F.-L. Liu ◽  
K. M. Liew
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Differential Quadrature ◽  
Mindlin Plate ◽  
Quadrature Method ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Element Method

A new numerical technique, the differential quadrature element method (DQEM), has been developed for solving the free vibration of the discontinuous Mindlin plate in this paper. By the DQEM, the complex plate domain is decomposed into small simple continuous subdomains (elements) and the differential quadrature method (DQM) is applied to each continuous subdomain to solve the problems. The detailed formulations for the DQEM and the connection conditions between each element are presented. Several numerical examples are analyzed to demonstrate the accuracy and applicability of this new method to the free vibration analysis of the Mindlin plate with various discontinuities which are not solvable directly using the differential quadrature method.

Differential Quadrature Element Method for the Analysis of Vibration of Frame Structures Having Nonprismatic Members Considering Warping Torsion

2000 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Vibration Analysis ◽  
Differential Quadrature ◽  
Frame Structures ◽  
Rigorous Solution ◽  
Discrete Eigenvalue ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Domain Boundaries ◽  
Eigenvalue System ◽  
Element Method

Abstract The differential quadrature element method (DQEM) and the extended differential quadrature (EDQ) have been proposed by the author. The EDQ is used to the DQEM vibration analysis frame structures. The element can be a nonprismatic beam considering the warping due to torsion. The EDQ technique is used to discretize the element-based differential eigenvalue equations, the transition conditions at joints and the boundary conditions on domain boundaries. An overall discrete eigenvalue system can be obtained by assembling all of the discretized equations. A numerically rigorous solution can be obtained by solving the overall discrete eigenvalue system. Mathematical formulations for the EDQ-based DQEM vibration analysis of nonprismatic structures considering the effect of warping torsion are carried out. By using this DQEM model, accurate results of frame problems can efficiently be obtained.

Structural Analysis by the Differential Quadrature Method Using Modified Weighting Matrices

1998 ◽  
Author(s):  
Siu-Tong Choi ◽  
Yu-Tuan Chou
Keyword(s):  
Boundary Conditions ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Sampling Point ◽  
Order Partial Differential Equation ◽  
Quadrature Method ◽  
The Finite Element Method ◽  
Computationally Efficient ◽  
Base Points ◽  
Sampling Points

Abstract The differential quadrature method has lately been more and more often used for analysis of engineering problems as an alternative for the finite element method or finite difference method. In this paper, static, dynamic and buckling analyses of structural components are performed by the differential quadrature method. To improve the accuracy of this method, an approach is proposed for selecting the sampling points which include base points and conditional points. The base points are taken as the roots of the Legendre polynomials. Accuracy of the problems analyzed will be increased by using the base points. The conditional points are determined according to boundary conditions and specified conditions of external load. A modified algorithm is proposed for applying two or more boundary conditions in a sampling point at boundary of domain, such that the higher-order partial differential equation can be solved without adding new sampling points. By applying this approach to variety problems, such as deflections of beam under nonuniformly distributed loading, vibration and buckling analyses of beam and plate, it is found that numerical results of the present approach are more accurate than those obtained by the equally-spaced differential quadrature method and is computationally efficient.

Truss Analyses by DQEM

1999 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Algebraic Equation ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Equation System ◽  
Numerical Approach ◽  
Differential Quadrature ◽  
Two Dimensional ◽  
Rigorous Solution ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method

Abstract A new numerical approach for solving generic three-dimensional truss problems having nonprismatic members is developed. This approach employs the differential quadrature (DQ) technique to discretize the element-based governing differential equations, the transition conditions at joints and the boundary conditions on the domain boundary. A global algebraic equation system can be obtained by assembling all of the discretized equations. A numerically rigorous solution can be obtained by solving the global algebraic equation system. Mathematical formulations for two-dimensional differential quadrature element method (DQEM) truss model are carried out. By using this DQEM model, accurate results of two-dimensional truss problems can efficiently be obtained. Numerical results demonstrate this DQEM model.

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