By David Johnson
In recent times an expanding emphasis has been put on numerically dependent tools of structural research. This has been mirrored within the construction of structural mechanics texts which are oriented in the direction of specific numerical methodologies, in particular the finite point procedure. while this procedure serves the desires of strength study engineers, a focus at the numerical research features of structural mechanics is of much less relevance to specialist engineers, who're more likely to be anxious with the use and interpretation of numerical analyses, yet now not within the improvement of the methodologies.
It is to this crew that complicated Structural Mechanics is mainly addressed.
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Extra info for Advanced Structural Mechanics
The structure stiffness equations relate the total nodal force components for the complete structure to the nodal displacement components for the complete structure. Since there are nine nodes in the present analysis and each node has two force (or displacement) components, there will be a total of 18 stiffness equations. 40). Since these sub-matrices are 2 ¥ 2, the structure stiffness matrix, so formed, will be 9 ¥ 9. 41) where ÏFx1 ¸ F1 = Ì ˝ ÓÔFy1 ˛Ô the total force components at node 1. To construct the structure stiffness matrix in terms of the element stiffness sub-matrices, each node in turn is considered and the sum is obtained of the force contributions made at the node by the elements which the node interconnects.
53)). 59) and y = α9 + α10ξ + α11η + α12ξ 2 + α13ξη + α14 η 2 + α15ξ 2 η + α16ξη 2 Just as the displacement components are made to coincide exactly with the nodal components, so the nodal geometric components are made to coincide exactly with the nodal coordinate positions. 57). 61)), a fairly complex function of ξ and η. 66 will obviously reflect [B] and be an even more complicated function of ξ and η than [B] itself. 66), and Gaussian integration is normally employed for this purpose. The Gauss method (Zienkiewicz and Taylor, 1989) requires the function to be integrated to be evaluated at a number of Gauss points.
These conditions imply that there is no horizontal displacement along the vertical centre-line (although vertical displacement can occur along this line) and, similarly, that vertical movements cannot take place along the horizontal centre-line (but horizontal movements can). 48) Restraining boundary displacement components implies that, at the relevant boundary points, there are restraint forces which physically represent the reactions from the adjacent portions of the block. 49) (page 31). 48)) have been set to zero.
Advanced Structural Mechanics by David Johnson