The two-dimensional frame model of the differential quadrature element method

Chen, Chang New

doi:10.1016/s0045-7949(96)00230-1

Cited by 15 publications

(6 citation statements)

References 7 publications

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“…Although some interrelated methods have been developed in Refs. [8][9][10][11][12], there are limitations when the methods are applied to analyze nonlinear problems with the discontinuity conditions of multi-variables. In the present paper, an effective and general method for dealing with nonlinear problems with discontinuity conditions of multi-variables is presented.…”

Section: Disposal For Continuity and Discontinuity Conditions At The mentioning

confidence: 99%

“…Matrix A = diag{mθ, mλ 1 , mλ 2 , mλ 3 , mŨ , mW } collecting the coefficients for the derivative term of all the unknowns with regard to time T , in which, mŨ , mW are the identity matrixes as all the coefficients forÜ ,Ẅ are 1, while the sub-matrixes associated with mθ, mλ 1 , mλ 2 , mλ 3 are all zero as there are no derivative terms of the variables with regard to time T (see (11), also see (2)), so A is a singular matrix. H is a vector collecting all the algebraic functions resulting from spatial discretization for the associated unknowns.…”

Section: Solution Of Nonlinear Differential-algebraic Equationsmentioning

confidence: 99%

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Differential-algebraic approach to large deformation analysis of frame structures subjected to dynamic loads

Duan

Yuanlin

Chang-jun

2008

Appl. Math. Mech.-Engl. Ed.

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A nonlinear mathematical model for the analysis of large deformation of frame structures with discontinuity conditions and initial displacements, subject to dynamic loads is formulated with arc-coordinates. The differential quadrature element method (DQEM) is then applied to discretize the nonlinear mathematical model in the spatial domain, An effective method is presented to deal with discontinuity conditions of multivariables in the application of DQEM. A set of DQEM discretization equations are obtained, which are a set of nonlinear differential-algebraic equations with singularity in the time domain. This paper also presents a method to solve nonlinear differential-algebra equations. As application, static and dynamical analyses of large deformation of frames and combined frame structures, subjected to concentrated and distributed forces, are presented. The obtained results are compared with those in the literatures. Numerical results show that the proposed method is general, and effective in dealing with discontinuity conditions of multi-variables and solving differential-algebraic equations. It requires only a small number of nodes and has low computation complexity with high precision and a good convergence property.

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Section: Disposal For Continuity and Discontinuity Conditions At The mentioning

confidence: 99%

Section: Solution Of Nonlinear Differential-algebraic Equationsmentioning

confidence: 99%

Differential-algebraic approach to large deformation analysis of frame structures subjected to dynamic loads

Duan

Yuanlin

Chang-jun

2008

Appl. Math. Mech.-Engl. Ed.

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show abstract

“…Therefore, the displacement at every point is obtained from equation (33). The velocity and acceleration can be obtained from equation (22).…”

Section: Applicationsmentioning

confidence: 99%

“…Utilizing di!erent test functions, many terms have been coined; to cite only a few, they are harmonic di!erential quadrature (HDQ) [26,28], Fourier expansion-based di!erential quadrature (FDQ) [27], generalized di!erential quadrature (GDQ) [30], and generalized di!erential quadrature method (GDQM) [31]. Some terms are coined from the &&element'' concept: quadrature element method (QEM) [16,32], and di!erential quadrature element method (DQEM) [18,20,33,34].…”

Section: Introductionmentioning

confidence: 99%

The Generalized Differential Quadrature Rule for Initial-Value Differential Equations

Liu

2000

Journal of Sound and Vibration

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“…Articles of following works involving DQEM with the stated characteristics have also been published [8][9][10][11][12]. As the flexural deformation problems of frame members have the governing equation with fourth-order, other fourth-order differential equations can straitly be solved [13].…”

Section: Introductionmentioning

confidence: 99%