Question 1: Application of 2D Solid Elements

Simplification of complex geometry to perform an efficient analysis of a mechanical or structural problem is a critical step the Computer Aided Engineering analyst must make. In particular, simplifying complex 3D problems into 2D can be beneficial, reducing setup, solve times and allowing for rapid design optimisation.

For this task you are required to identify a series of physical problems which lend themselves to being simplified to the use of a 2D solid element.

You are required to:

Describe and discuss the differences of the 2D Solid Element types:

o Plane Stress;
o Plane Strain; and
o Axisymmetric.

Provide 4 realistic case studies in which the simplification from 3D to 2D solid elements can be made for each of the 2D Solid Element types proposed above. You must describe and discuss why the simplification is suitable. Include schematics and support mathematically if able to do so. This should be conducted clearly, with clearly defined boundary conditions etc.

Setup an ANSYS FE model for one of the case studies discussed above for each element type. Therefore, three models: one for the plane stress, plane strain and axisymmetric element assumptions.

Present the FE setup (element selection, mesh, boundary conditions etc.), results and a detailed discussion of the suitability for the 2D assumption in a clear and structured report. Describe and discuss the critical results for the particular analysis?

Question 2: Bar Element

Considering an aluminium rod under compression, its FE model is an assembly of two bar elements as shown in the figure below. The rod has a square cross-section (30 mm x 30 mm) and the Youngs Modulus of the aluminium is 70 GPa.

Determine

1) the nodal displacements at nodes 1-3;
2) the reaction at node 1; and
3) the axial stresses and strains in each element.

Question 3: Truss Structure - Update

Consider the three membered planar truss-structure shown in the figure below. All members of the truss have identical square cross-sectional area (A) of 25 mm x 25 mm, and Youngs Modulus (E) = 210 GPa. The hinged joints, A, B and C allow free rotation of the members about the z-axis.

Determine:

1) the horizontal and vertical displacements at joint C;
2) the reaction forces at each support;
3) the stress and strain of each member.