2017
DOI: 10.3390/app7020138
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A Time Finite Element Method Based on the Differential Quadrature Rule and Hamilton’s Variational Principle

Abstract: An accurate and efficient Differential Quadrature Time Finite Element Method (DQTFEM) was proposed in this paper to solve structural dynamic ordinary differential equations. This DQTFEM was developed based on the differential quadrature rule, the Gauss-Lobatto quadrature rule, and the Hamilton variational principle. The proposed DQTFEM has significant benefits including the high accuracy of differential quadrature method and the generality of standard finite element formulation, and it is also a highly accurat… Show more

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Cited by 12 publications
(11 citation statements)
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“…2. The method of storing incremental matrix Equation (19) indicates that A(h N ) can be expressed as…”
Section: M Algorithmmentioning
confidence: 99%
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“…2. The method of storing incremental matrix Equation (19) indicates that A(h N ) can be expressed as…”
Section: M Algorithmmentioning
confidence: 99%
“…However, excessive single‐step calculations limit the use of this type of methods. The second type is the use of the higher‐order differential quadrature time element . Nevertheless, this approach expands system size and has unavoidable numerical difficulty in calculating higher‐order interpolation polynomials.…”
Section: Introductionmentioning
confidence: 99%
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“…Besides of the finite difference method, this is one of the main numerical methods for initial value problems (IVPs). In recent years, many alternative finite element methods (FEMs) for IVPs have been developed [16], which are as well-known as time FEM. According to the different ways of construction, the time FEM can be roughly classified into three kinds: (1) Constructed by Gurtin variational principle, which transforms the initial-boundary value problem into the equivalent boundary value problem (BVP) by means of Laplace positive and inverse transformation [17,18]; (2) Constructed by Hamilton's variational principle or Hamilton's law of variation [19][20][21], in which Bailey [22,23], Simikins [24], and Borri [25] have made important achievements successively and; (3) Constructed by the weighted residual method, and is what we use in the present paper.…”
Section: Introductionmentioning
confidence: 99%
“…Bathe and Wilson [39] presented a perfect and underlying process for the accuracy and stability analysis of time integration methods. By referencing to predecessors' procedure, this paper makes comprehensive researches on the improved DQTEM which is different from the Differential Quadrature Time Finite Element Method (DQTFEM) [40] proposed recently by the authors. DQTFEM solved the weak form of ordinary differential equations of motion based on the general form of Hamiltonian Variational Principle, the spatial domain was discretized by the standard FEM, and the Gauss-Lobatto-Legendre integration points were used in the calculation of the time derivatives through DQ rule.…”
Section: Introductionmentioning
confidence: 99%