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THE UNIVERSITY OF NEWCASTLE SCHOOL OF ENGINEERING DISCIPLINE OF MECHANICAL ENGINEERING MECH4400 COMPUTATIONAL MECHANICS ASSIGNMENT 1 Issued: Wednesday 3rd September 2014 Due: Wednesday 24th September 2014 1. a. To elevate the end of a cantilever cantilever beam without rotating it, as shown in the figure below, forces and moments are required. From the information shown, fill in as many values as you can into the stiffness matrix that operates on the nodal d.o.f. d=[v1,θ1z,v2,θ2z], where v1 and v2 are measured in millimetres. Do not use beam deflection formula but instead rely on given data, physical argument, statics and symmetry of k. Ignore transverse shear deformation.
b. The figure below shows a planar structure structure consisting of lightweight members members and springs. Spring k A resists translation and kB resists relative rotation between bars AB and BC. Each bar is of length 5L and and sliders without friction on the horizontal horizontal surface. Determine the stiffness matrix that operates on the two d.o.f, u A and uC.
2.
Let the structure shown below have two-node elements and one d.o.f. per per node. Number the nodes so that there are as few coefficients as possible between the skyline and the diagonal of K.
3.
For a given displacement matrix, D, why does the form DTKD/2 represent strain energy in a structure? Hint: consider work done by applied loads.
4.
The figure below shows a two-dimensional pin-jointed truss loaded as shown. Crosssectional areas in mm2 are shown in parenthesis next to each of the truss elements. Consider symmetry and model one-half of the truss shown. (HINT: think carefully about how you model the vertical truss under the applied load and the effect of boundary conditions). Determine all displacements and element stresses. Use E = 200GPa.
5.
The two-element structure shown below is built of standard beam elements with two degrees of freedom per node (a vertical translation and a rotation). By an error, the boundary conditions given by the computer program are: w 1 = 1 = 2 = 3 = 0. The expected result of w3 = PL3/3EI is not computed. Determine: a. The value of w3 computed by the program, and b. Sketch the predicted deformed shape of the structure.
