Development of an implicit method with numerical dissipation from a generalized single-step algorithm for structural dynamics

Hoff, Claus; Pahl, Peter Jan

doi:10.1016/0045-7825(88)90053-9

Cited by 157 publications

(80 citation statements)

References 15 publications

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“…The plate equation is integrated using an implicit finite difference method for structural dynamics developed by Hoff and Pahl [33]. The calculation of N. was done using At first, we consider the case of small amplitude forcing (E* = 0.0025) leading to an essentially linear response.…”

Section: Methods Of Solutionmentioning

confidence: 99%

Coupling Between Plate Vibration And Acoustic Radiation

Frendi

Maestrello

Bayliss

1994

Journal of Sound and Vibration

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Section: Methods Of Solutionmentioning

confidence: 99%

Coupling Between Plate Vibration And Acoustic Radiation

Frendi

Maestrello

Bayliss

1994

Journal of Sound and Vibration

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“…The methods typically employ temporal finite differences, with a variety of different schemes used to interpolate the solution over the time step. Most classical methods can now be cast into unified multi-parameter integration schemes where an adjustment in the parameters leads to one of several different methods with different numerical properties (e.g., [44,100,102]). Thomas [90] studied the three "classic" methods (Newmark, Houbolt, and Wilson-θ) and their applicability to the mooring dynamics problem.…”

Section: Temporal Discretizationmentioning

confidence: 99%

“…44 In this appendix we use the classical von Neumann method [48,82] to analyze the stability of the box method as a pure finite difference method. This contrasts with the amplification matrix method of stability analysis which operates on the semi-discrete equation of motion.…”

Section: A8 Static Governing Equationsmentioning

confidence: 99%

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The dynamics of geometrically compliant mooring systems

Gobat¹

2000

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Geometrically compliant mooring systems that change their shape to accommodate deformations are common in oceanographic and offshore energy production applications. Because of the inherent geometric nonlinearities, analyses of such systems typically require the use of a sophisticated numerical model. This thesis describes one such model and uses that model along with experimental results to develop simpler forms for understanding the dynamic response of geometrically compliant moorings.The numerical program combines the box method spatial discretization with the generalized-α method for temporal integration. Compared to other schemes commonly employed for the temporal integration of the cable dynamics equations, including box method, trapezoidal rule, backward differences, and Newmark's method, the generalized-α algorithm has the advantages of second-order accuracy, controllable numerical dissipation, and improved stability when applied to the nonlinear problem. The numerical program is validated using results from laboratory and field experiments.Field experiment and numerical results are used to develop a simple model for dynamic tension response to vertical motion in geometrically compliant moorings. As part of that development, the role of inertia, drag, and stiffness in the tension response are explored. For most moorings, the response is dominated by inertial and drag effects. The simple model uses just two terms to accurately capture these effects, including the coupling between inertia and drag. The separability of the responses to vertical and horizontal motions is demonstrated and a preliminary model for the response to horizontal motions is presented.The interaction of the mooring line with the sea floor in catenary moorings is considered. Using video and tension data from laboratory experiments, the tension shock condition at the touchdown point and its implications are observed for the first time. The lateral motion of line along the bottom associated with a shock during unloading may be a significant cause of chain wear in the touchdown region. Results from the laboratory experiments are also used to demonstrate the suitability of the elastic foundation approach to modeling sea floor interaction in numerical programs.

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“…Bathe and co-workers proposed this scheme for structural dynamic problems and presented research results on the behaviour of the scheme ( [Bathe and Baig(2005)], [Bathe(2007)], [Bathe and Noh(2012)]). Typically, the authors have used the analysis of the amplification matrix, see [Hoff and Pahl(1988)], [Hoff and Pahl(1988-2)], [Hughes(2000)]. In the upcoming study, we will pick up these evaluations, describe the main essentials and extend them with several further aspects.…”

Section: Introductionmentioning

confidence: 99%