By Nicholas P. Cheremisinoff, Paul N. Cheremisinoff

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20) EI dx 4 Again the continuous variable, w in this case, is approximated in terms of discrete nodal values, but we introduce the idea that not only w itself but also its derivatives θ can be used in the approximation. 21) w˜ = [N1 N2 N3 N4 ] w2 ⎪ ⎪ ⎪ ⎪ ⎩θ ⎭ 2 where θ1 = d w/dx at node 1 and so on. 22) 30 Programming the Finite Element Method Note that the shape functions have the property that they, or their derivatives in this case, equal one at a specific node and zero at all others. 26) which recovers the standard ‘slope–deflection’ equations for beam elements.

To view the undeformed mesh, click on the Representation dropdown box at the bottom of the Properties tab and select Surface with Edges. There is also a dropdown box that performs the same action in the toolbars that appear at the top of the ParaView display. The model can be rotated by clicking, holding and dragging the mouse. Zooming in and out is done by holding down the control (ctrl) button on the keyboard and the left mouse button at the same time. x, where x, y and z are either 1 – the node is constrained in that axis, or 0 – the node is free to move in that axis (note this is the opposite of the convention used in the book).

Org). 11 Visualisation It is good practice to inspect finite element models before analysis using a visualisation tool in order to check the quality of the mesh and ensure that the loading and boundary conditions have been correctly applied. The same tool can be used after the analysis to plot, for example, the deformed mesh and contours of derived quantities such as stress and strain. Two visualisation strategies are adopted here. The first uses subroutines to conveniently generate PostScript images as direct output from the programs: SUBROUTINE SUBROUTINE SUBROUTINE SUBROUTINE mesh dismsh vecmsh contour !

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