Bearing brackets are widely used in machinery to connect rotating parts, such as shafts, wheels, idler gears, etc., to stationary parts - an example of a ball bearing bracket is shown in Figure 1. A simplified two-dimensional (2D) schematic of a bearing bracket with dimensions is shown in Figure 2. The bracket is rigidly fixed to the base and a load of P = [-150, 100]T kN is applied.
The bracket is made of aluminium with a modulus of elasticity (Young’s modulus) of E = 70 GPa and a Poisson’s ratio of n = 0.33. The bracket’s thickness is 0.1 m.
1- Plot, in a single graph, the relationship between the von Mises stress at points A, B and C (see Figure 2), and the number of elements for different levels of mesh refinement corresponding to global seed sizes of 0.028, 0.014, and 0.007. Would further mesh refinement be required for results that are sufficiently accurate for engineering purposes – when justifying your answer, you might need to perform additional simulations. 
2- To investigate the computational expense associated with increasing the number of element as you refine the mesh, create a graph of the number of elements (x-axis) versus the TOTAL CPU TIME (TCT) (y-axis). Briefly explain the trend displayed in the graph. TCT is the CPU time required to solve the problem. It can be obtained from the job monitor after completing the analysis of each refinement case. Note: you should run this comparison on the same machine under similar conditions. 
3- Plot the contours of the von Mises stress and the displacement magnitude distributions over the deformed bracket geometry for the various refinement levels investigated in Q1. Comment on the variation in the plots as the mesh gets finer. Note: images should be produced using the print command in Abaqus and not by using a screenshot, as the latter will produce poor quality images. You are advised to hide the mesh from the model to obtain better quality images. Ensure the legend is legible. 
The 2D plane stress model was an efficient way to begin the engineering design process. Now create a three-dimensional (3D) model as shown in Figure 3 and undertake a static stress analysis using standard, 3D stress 10-noded quadratic tetrahedron elements (C3D10). 4- As in Q1, repeat the analysis using the different level of mesh refinement and create a single graph of the relationship between the number of elements and the maximum von Mises stress at points A, B and C. In addition, compare the results of the 2D and 3D models and comment on the differences between the solutions.  5- The bracket will now be fixed to the stationary component using bolts. In order to choose a suitable bolt size, calculate the optimum hole radius when (a) only a vertical load of 100 kN is applied, (b) only a horizontal load of -150kN is applied. Consider a bolt design tensile strength of 48 MPa and a design shear strength of 39 MPa. 
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