Question 1: Plate and shell elements (25 marks)
As one of benchmarking problems for shell elements, a hollow cylinder with a (600 + 2 Ã— 0.q)-mm length, a (300 + 0.q)-mm radius and a thickness of (3 + 0.q) mm is closed on both ends by a diaphragm and loaded by a pair of opposite forces, F = (1.0 + 0.q) ï‚´ 105 N, on the top surface in the middle of the hollow cylinder as shown below.
You are required to a) establish an appropriate finite element model for this cylinder fully taking advantage of the symmetry boundary conditions; b) apply the proper boundary conditions including support constraints and loadings; and c) run at least 4 finite element simulations with different mesh size to determine the maximum resultant deflection as well as the maximum von Mises stress in the model considering mesh refinement for convergence.
Question 2: Practical Considerations on FEA (25 marks)
A pulley with 8 bolt holes of a (1+ 0.q)-cm diameter, made of steel, have material properties of E = 207 GPa and ï® = 0.29, and a mass density ï² of 7850 kg/m3 as shown below and the right figure shows its axisymmetric cross-section with dimensions in cm. The pulley will rotate at a speed of 3,000 + q rpm in its daily working.
You are required to conduct a structural static FEA fully using cyclic symmetry to create a small FE model to determine the maximum von Mises stress and max resultant displacement under such a situation. The number of replications about the axis should be determined reasonably.
Question 3: FEA on Dynamic Analysis and Vibration (50 marks)
Assume the bar has a length of (1 + 0.q) m, a modulus of elasticity E of 70 GPa, a mass density ï² of 2700 kg/m3. It has a square cross-section of (50 + 0.q) ï‚´ (50 + 0.q) mm
You are required to determine the first two natural frequencies for the bar: a) using a theoretical procedure with 2 two-node bar elements; b) using a Modal Analysis available in ANSYS WB; and c) comparing the results from a) and b) for a discussion.