Truss design using Finite element method

Learning outcomes that are assessed by this coursework are:

1. To demonstrate an understanding of the concepts and principles associated with FEA.

2. To be able to generate problem-specific FEA codes using MATLAB software.

3. To apply FEA and MATLAB to obtain solution of the problems in Engineering/product design.

1 Objectives

1. To investigate the axial forces, stresses and strains in the structural frame- work by experiments;

2. To develop a finite element model using MATLAB software to calculate the nodal displacements, axial force, strain and stress in each member and their validation with experimental results;

3. To compare some aspect of the performance of structures fabricated from welded steel, extruded aluminium and Carbon Fibre Reinforced Plastics (CFRP).

Experimental Apparatus

The structural framework made from stainless steel member is available at the Solid Mechanics Lab QB 1.05a. A sketch of the configuration, boundary condi- tions and loading is shown in Figure 1. Laboratory technical staff will be avail- able during each session to assist you for performing experiments. At the end of the lab session, you should have measured strains in each structural member for the applied load of 5 00 N.

Compile your experimental results in tabulated form, refer lab sheet. You should submit the signed lab sheet along with the final report. Failure to submit the signed lab sheet will result in losing the marks correspond to the experimen- tal section of this coursework. Refer manufacture guide, available in the lab, to learn more about the structural assembly, strain and force measuring system.

Finite element modelling

You should model the structural framework by using the finite element method. For this, you will use MATLAB software to write code to predict the axial forces, stresses and strains in the structural framework as shown in Figure 1. This will allow you to compare the experimental results.

You will also submit the MATLAB code (as an Appendix to the report) used to model the structural framework.

The prime characteristics of the MATLAB program should be:
1. The MATLAB code should show clearly the inputs and outputs.
2. It should include su?cient comments to explain each steps.
3. Clarity on each step involved from elemental stiffness matrix.
4. Assembly of elemental stiffness matrix.
5. Solve for nodal displacements, elemental stress & strains and forces.

Figure 1: Truss members are made from stainless steel material having Young's modulus E = 210GPa and the diameter of each member is d = 5.98mm. Use this for calculating axial strain, stress and force in each truss member for the applied load of 5 00N.

4 Performance Index

Having validated your finite element program, you should be able to use the same to compare some aspect of the performance of structures fabricated from the material listed in the Table 1. Consider the following questions to rank the materials according to the performance metric.

• What is the minimum diameter that will withstand the 10kN load if you fabricate the structural members made from the materials listed in the Table 1?

• Considering the factor of safety 3, which material you will choose for min- imum weight design? You will need to estimate the mass of the structural member for chosen cross-section details.

• What material you will choose for the minimum cost design?

Table 1: Properties of the 3 different materials for performance index compari- son for the Truss configuration shown in Figure 1.

Report format

The report should be concisely written and not more than 10 pages. An ideal report contains the following sections.

1. The Title page including your name, P-number. The Summary should con- tain a very brief resume of what you have done, why you have done it and what you have concluded - all in not much more than 100 words.

2. An Introduction and Objectives in which you briefly explain the background to the work to be described and justify why the investigation is worth car- rying out. Your statement of the objectives of the experiments can be based on the those given in the course work sheet.

3. Experimental section - there is no need to repeat all the details of the Apparatus and experimental method, however, you should give a brief account of the procedure that you are used to measure the axial strains in each structural member. You should include the signed copy of the lab sheet as a proof that you have carried out the experiments in the lab.

4. The best way to present the numerical data in the section on Results is in tabular form- think about the form of the table it would be best to use: tables, like diagrams, should be numbered and have caption to explain what they are.

5. It is good practice to separate the presentation of results from their Discussion: this section should include a comparison between the what you have ob- served in the experiments, compared to what you have predicted using the finite element method. Any significant variation should be the subject of the comments.

6. Consider the following questions to rank the materials;

• What is the minimum diameter that will withstand the 1 0kN load if you fabricate the structural members made from the materials listed in the Table 1?

• Considering the factor of safety 3, which material you will choose for minimum weight design? Clue - You will need to estimate the mass of the structural member for chosen cross-section details.

• What material you will choose for the minimum cost design?