Dispersion-based guidance for the temporal and spatial discretization of the one- and two-dimensional finite element solutions to the transient heat equation

2003 ◽  
Vol 192 (22-24) ◽  
pp. 2617-2631 ◽  
Author(s):  
W. Dauksher ◽  
A.F. Emery
1999 ◽  
Vol 36 (02) ◽  
pp. 102-112
Author(s):  
Michael D. A. Mackney ◽  
Carl T. F. Ross

Computational studies of hull-superstructure interaction were carried out using one-, two-and three-dimensional finite element analyses. Simplification of the original three-dimensional cases to one- and two-dimensional ones was undertaken to reduce the data preparation and computer solution times in an extensive parametric study. Both the one- and two-dimensional models were evaluated from numerical and experimental studies of the three-dimensional arrangements of hull and superstructure. One-dimensional analysis used a simple beam finite element with appropriately changed sections properties at stations where superstructures existed. Two-dimensional analysis used a four node, first order quadrilateral, isoparametric plane elasticity finite element, with a corresponding increase in the grid domain where the superstructure existed. Changes in the thickness property reflected deck stiffness. This model was essentially a multi-flanged beam with the shear webs representing the hull and superstructure sides, and the flanges representing the decks One-dimensional models consistently and uniformly underestimated the three-dimensional behaviour, but were fast to create and run. Two-dimensional models were also consistent in their assessment, and considerably closer in predicting the actual behaviours. These models took longer to create than the one-dimensional, but ran in very much less time than the refined three-dimensional finite element models Parametric insights were accomplished quickly and effectively with the simplest model and processor, but two-dimensional analyses achieved closer absolute measure of the displacement behaviours. Although only static analysis with simple loading and support conditions were presented, it is believed that similar benefits would be found for other loadings and support conditions. Other engineering components and structures may benefit from similarly judged simplification using one- and two-dimensional models to reduce the time and cost of preliminary design.


Author(s):  
W. Dauksher ◽  
A. F. Emery

The dispersive errors in the finite element solution to the one- and two-dimensional heat equations are examined as a function of element type and size, capacitance matrix formulation, time stepping scheme and time step size.


Author(s):  
L F Campanile ◽  
R Jähne ◽  
A Hasse

Classical beam models do not account for partial restraint of anticlastic bending and are therefore inherently inaccurate. This article proposes a modification of the exact Bernoulli–Euler equation which allows for an exact prediction of the beam's deflection without the need of two-dimensional finite element calculations. This approach offers a substantial reduction in the computational effort, especially when coupled with a fast-solving schema like the circle-arc method. Besides the description of the new method and its validation, this article offers an insight into the somewhat disregarded topic of anticlastic bending by a short review of the published theories and a selection of representative numerical results.


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