Question 1: General FEA

A key part of the FEM and any FEA model are the appropriate assignment of boundary conditions. Explain why it is necessary to set the appropriate boundary conditions in FEA simulations. What happens if you don't assign boundary conditions or assign them incorrectly? Explain your answer according to the impact on the FEM and the real-world application of a FEA model.

Question 2: Spring Elements

For the assembly of springs shown in the figure below, given k1 = 15 N/mm and k2 = 10 N/mm.

Determine:

1) the force F3 required to displace node 2 as δ = 0.25 mm to the right;

2) the displacement at node 3;

3) the reaction force at node 1.

Question 3: Bar Element

Material properties are an essential part of any structural design or analysis. The most common material test is a uniaxial tensile test. The basic finite element model of this test is shown in the figure below.

It consists of two bar elements with circular cross-section as shown.

The material is steel with a Youngs Modulus, E, of 210 GPa. The specimen is displaced by δ = 0.13 mm.

Determine:

1) the nodal displacement at node 2;

2) the reaction at node 1;

3) the force at node 3 required to displace node 3 as δ;

4) the axial stress in each element.

Question 4: Truss Structure-Update

The finite element model of a plane truss structure is shown in the following figure is composed of members having a square 25 mm × 25 mm cross section and is aluminium with a modulus of elasticity E = 71 GPa.

Determine:

1) the nodal displacements in the global coordinate system for the loads shown;

2) all the reactions at each support;

3) the internal force at each member;

4) the axial stress in each member.

Finally,

5) Use ANSYS Mechanical APDL to repeat this finite element analysis and compare the results with the solutions obtained by hand calculations or using MS EXCEL spreadsheet.