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.

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.

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.

Analyses of Frame Problems by DQEM Using EDQ

1999 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Algebraic System ◽  
Frame Analysis ◽  
Differential Quadrature ◽  
Rigorous Solution ◽  
Element Analysis ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Domain Boundaries

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 differential quadrature element analysis of the frame problems. The element can be a nonprismatic beam. The EDQ technique is used to discretize the element-based governing differential equations, the transition conditions at joints and the boundary conditions on domain boundaries. An overall algebraic system can be obtained by assembling all of the discretized equations. A numerically rigorous solution can be obtained by solving the global algebraic system. Mathematical formulations for the EDQ-based DQEM frame analysis are carried out. By using this DQEM model, accurate results of frame problems can efficiently be obtained. Numerical results demonstrate this DQEM model.

Out-of-Plane Deflection of Nonprismatic Curved Beam Structures Considering the Effect of Shear Deformation Solved by DQEM

2004 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Shear Deformation ◽  
Differential Quadrature ◽  
Analysis Model ◽  
Beam Structures ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Out Of Plane ◽  
Deflection Analysis ◽  
Governing Differential Equation ◽  
Element Boundary

The development of differential quadrature element method out-of-plane deflection analysis model of curved nonprismatic beam structures considering the effect of shear deformation was carried out. The DQEM uses the differential quadrature to discretize the governing differential equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. The convergence of the developed DQEM analysis model is efficient.

Influence of Axial Force on the Vibration of Euler-Bernoulli Beam Structures Solved by DQEM Using EDQ

2006 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Boundary Conditions ◽  
Axial Force ◽  
Differential Quadrature ◽  
Analysis Model ◽  
Bernoulli Beam ◽  
Beam Structures ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Euler Bernoulli Beam ◽  
Element Boundary

The influence of axial force on the vibration of Euler-Bernoulli beam structures is analyzed by differential quadrature element method (DQEM) using extended differential quadrature (EDQ). The DQEM uses the differential quadrature to discretize the governing differential eigenvalue equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. The convergence of the developed DQEM analysis model is efficient.

Influence of Axially Distributed Force on the Vibration of Euler-Bernoulli Beam Structures Solved by DQEM Using EDQ

2007 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Boundary Conditions ◽  
Numerical Algorithm ◽  
Differential Quadrature ◽  
Analysis Model ◽  
Bernoulli Beam ◽  
Beam Structures ◽  
Differential Quadrature Element Method ◽  
Quadrature Element Method ◽  
Euler Bernoulli Beam ◽  
Element Boundary

The influence of axially distributed force on the vibration of Euler-Bernoulli beam structures is analyzed by differential quadrature element method (DQEM) using extended differential quadrature (EDQ). The DQEM uses the differential quadrature to discretize the governing differential eigenvalue equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. The convergence of the developed DQEM analysis model is efficient.

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