Extended comparison of the Hilber-Hughes-Taylor α-method and the

Hoff, Claus; Hughes, Thomas J.R.; Hulbert, Gregory M.; Pahl, Peter Jan

doi:10.1016/0045-7825(89)90142-4

Cited by 29 publications

(8 citation statements)

References 5 publications

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“…Alternatively, the ordinary differential equations may be discretized usingjnite elements in time. For example, in Argyris and Scharpf,' Bazzi and Anderheggen,' Hoff and Pah1,3*4 Hoff et aE., 5 Kawahara and Hasegawa,6 Kujawski and Desai' and Zienkiewicz and co-workers,8-12 continuous functions in time are substituted into the ordinary differential equations emanating from semidiscretizations, multiplied by weighting functions and integrated over time intervals. Many traditional ordinary differential equation algorithms were rederived in this manner as well as useful new algorithms for structural dynamics.…”

Section: Introductionmentioning

confidence: 99%

Time finite element methods for structural dynamics

Hulbert

1992

Numerical Meth Engineering

160

100

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Time finite element methods are developed for the equations of structural dynamics. The approach employs the time-discontinuous Galerkin method and incorporates stabilizing terms having least-squares form. These enable a general convergence theorem to be proved in a norm stronger than the energy norm. Results are presented from finite difference analyses of the time-discontinuous Galerkin and least-squares methods with various temporal interpolations and commonly used finite difference methods for structural dynamics. These results show that, for particular interpolations, the time finite element method exhibits improved accuracy and stability.

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Section: Introductionmentioning

confidence: 99%

Time finite element methods for structural dynamics

Hulbert

1992

Numerical Meth Engineering

160

100

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“…The resolution of this problem needs a space -time discretisation. The finite element method is frequently used [11] for the space domain and most of the numerical scheme can be written in the Newmark algorithm way [5,9]. In three-dimensional cases, the size of the problem to solve is not proportional to the number of degree of freedom (d.o.f.…”

Section: Reference Problemmentioning

confidence: 99%

A 3D shock computational strategy for real assembly and shock attenuator

Lemoussu

Boucard

2002

Advances in Engineering Software

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The extension of an approach, suitable for bolting structures impact computation with a large number of unilateral friction contact surfaces, and with local plasticity of the bolts, is presented. It is a modular approach based on a mixed domain decomposition method and the LATIN method. This iterative resolution process operates over the entire time-space domain. A 3D Finite-Element code is presented and dedicated to applications concerning connection refined models for which the structure components are assumed elastic. Several examples are analysed to show the method's capability of describing shocks throw real three-dimensional assembly. Comparisons between classical dynamic code LS-DYNA3D are presented.

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“…For time FEMs established by the weighted residual method, the trial functions commonly used involve Lagrange interpolation polynomials [26], linear/quadratic polynomials [27,28], Taylor expansion [29,30], or Taylor formulae [31,32]. Zienkiewicz has developed a framework for constructing a direct integration method based on weighted residuals of the governing equations [33].…”

Section: Introductionmentioning

confidence: 99%

“…Xianghua Xing [34] has proposed a direct integration method based on Galerkin weak form for linear dynamics, named the GW method. Hoff and Pahl have formed a one-step time FEM by setting acceleration, velocity, and displacement to be linear, quadratic, and cubic Taylor polynomials, respectively, which has been applied to both linear [29] and nonlinear [35] structural dynamic problems. Betsch P has proposed a time FEM with inherent energy conservation based on Hamilton's canonical equations combined with the continuous Galerkin (cG) method [36], which has been successfully applied to nonlinear elastodynamics [37].…”

Section: Introductionmentioning

confidence: 99%

A Time Integration Method Based on Galerkin Weak Form for Nonlinear Structural Dynamics

Xing¹,

Yang²,

Wang³

2019

Applied Sciences

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This paper presents a step-by-step time integration method for transient solutions of nonlinear structural dynamic problems. Taking the second-order nonlinear dynamic equations as the model problem, this self-starting one-step algorithm is constructed using the Galerkin finite element method (FEM) and Newton–Raphson iteration, in which it is recommended to adopt time elements of degree m = 1,2,3. Based on the mathematical and numerical analysis, it is found that the method can gain a convergence order of 2m for both displacement and velocity results when an ordinary Gauss integral is implemented. Meanwhile, with reduced Gauss integration, the method achieves unconditional stability. Furthermore, a feasible integration scheme with controllable numerical damping has been established by modifying the test function and introducing a special integral rule. Representative numerical examples show that the proposed method performs well in stability with controllable numerical dissipation, and its computational efficiency is superior as well.

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Extended comparison of the Hilber-Hughes-Taylor α-method and the

Cited by 29 publications

References 5 publications

Time finite element methods for structural dynamics

Time finite element methods for structural dynamics

A 3D shock computational strategy for real assembly and shock attenuator

A Time Integration Method Based on Galerkin Weak Form for Nonlinear Structural Dynamics

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