Finite Element Methods in Engineering Practice Assessment

Question 1

Figure Q1 shows a six-bladed Smith Turbine. The engineer wishes to determine the stresses that develop within the structure when it rotates through a viscous fluid. The resulting pressure distribution on each part of the turbine is known and can be applied directly to the system. Describe some of the pre- processing steps you would employ in the analysis. You should discuss, amongst others, features such as dimension of the study, symmetry, boundary conditions, meshing concerns.          

Any 7 marks from

• Three-dimensional analysis [1]
• Cyclic symmetry [1]
• Only need to use 60 degrees of the system. [1]
• Need to have roller conditions on the boundary. [1]
• Figure of roller conditions [1]
•  
• Expect some stress concentration at the connection between the cup and the disk [1]

• o so use smaller (transition) elements there. [1]

• Use larger elements away from the connection. [1]
• Use a static analysis; [1]
• Pressure differential on the inside and outside of the cup applied as boundary (surface) loads. [1]

Question 2The rod element shown in Figure Q2 is subjected to a temperature rise of ????????^???????? and a distributed load of ????(????) = ???????????????? ????????/????, where ???? is measured from local node 1 of the element. The physical and geometric properties of the element are as follows: E= 100 GPa , A= 200 mm² , L= 500 mm, a = 12.5 x 10^-6 /^oC.

a)Determine the equivalent force due to the thermal load.

b)What is the equivalent nodal force vector due to the distributed load?

C)What is the deflection at a point 300 mm from the left?

d)Calculate the stress in the element.

Question 3

Consider the truss system shown in Figure Q3. Let E = 200 GPa, and A = 150 mm² for each truss. The element numbers are circled, while the node numbers are not. The magnitude of P is 30 kN.

1. Create a suitable connectivity table for the system.                                                                                                                                     [1]