Analysis of continuous curved girder-slab bridges

1989 ◽  
Vol 16 (6) ◽  
pp. 895-901 ◽  
Author(s):  
Abul K. Azad ◽  
Mohammed H. Baluch ◽  
Aejaz Ali
Keyword(s):  
Structural Analysis ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Static Analysis ◽  
Difference Method ◽  
Series Solution ◽  
Curved Beams ◽  
Radial Line ◽  
Horizontally Curved ◽  
Flexible Supports

A static analysis of horizontally curved, continuous multigirder slab type bridge decks has been proposed using finite difference method in conjunction with the method of consistent deformation. The deck is idealized as a curved thin plate supported by flexible supports having both vertical and rotational flexibility. The proposed Levy-type series solution requires generation of linear equilibrium difference equations only along the central radial line of the deck, thus obviating the need of a large computational molecule. The simple repetitive algorithm for this method of analysis is an advantage in computer programming. Key words: bridges (curved), beams (curved), structural analysis, computation, concrete, steels, moments.

Boundary-layer flow between nodal and saddle points of attachment

1970 ◽  
Vol 41 (4) ◽  
pp. 823-835 ◽  
Author(s):  
J. C. Cooke ◽  
A. J. Robins
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Saddle Point ◽  
Difference Method ◽  
Series Solution ◽  
Nodal Point ◽  
Saddle Points ◽  
The Other ◽  
The Finite Difference Method ◽  
Layer Flow

A simplified example of this type of flow was examined in detail by developing two series, eventually matched, one about the nodal point and the other about the saddle point, and also by finite differences, marching from the nodal point to the saddle point. It was found that the results of marching the two series were in agreement with the finite difference method. The series solution near the saddle point is not unique, but numerical evidence indicates that the correct solution is that which has ‘exponential decay’ at infinity, and that this type of solution, if such exists, automatically emerges when the finite difference method is used.

scholarly journals WO-GRID METHOD OF STRUCTURAL ANALYSIS BASED ON DISCRETE HAAR BASIS. PART 1: ONE-DIMENSIONAL PROBLEMS

2017 ◽  
Vol 13 (4) ◽  
pp. 128-139
Author(s):  
Marina L. Mozgaleva ◽  
Pavel A. Akimov
Keyword(s):  
Structural Analysis ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Grid Method ◽  
Algebraic Equations ◽  
Initial State ◽  
One Dimensional ◽  
Haar Basis ◽  
Linear Algebraic Equations

The distinctive paper is devoted to the two-grid method of structural analysis based on discrete Haar basis (in particular, the simplest one-dimensional problems are under consideration). A brief review of publications of recent years of Russian and foreign specialists devoted to the current trends in the use of wavelet analysis in construction mechanics is given. Approximations of the mesh functions in discrete Haar bases of zero and first levels are described (the mesh function is represented as the sum in which one term is its approximation of the first level, and the second term is so-called complement (up to the initial state) on the grid of the first level). Projectors are constructed for the spaces of vector functions of the original grid to the space of their approximation on the first-level grid and its complement (the detailing component) to the initial state. Basic scheme of the two-grid method is presented. This method allows solution of boundary problems of structural mechanics with the use of matrix operators of significantly smaller dimension. It should be noted that discrete analogue of the initial operator equation (defined on a given interval) is a system of linear algebraic equations (SLAE) constructed within finite difference method (FDM) or the finite element method (FEM). Next, the transition to the resolving SLAE is done. Block Gauss method is used for its direct solution (forward-backward algorithm is realized). We consider a numerical solution of the boundary problem of bending of the Bernoulli beam lying on an elastic foundation (within Winkler model) as a practically important one-dimensional sample. There is good consistency of the results obtained by the proposed method and by standard finite difference method.

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