ENGT5258 Course Work II: Truss design using Finite element method Dr K KandanFaculty of Technology - Course work Specification 2016/17 Module name Advanced Solid Mechanics Module code ENGT5258/ENGD5258 Module leader/tutor name Dr Karthikeyan Kandan Contact details [email protected] Title of the Assignment FEA Truss analysis This coursework item is Summative This summative coursework will be marked anonymously: Yes The 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. This coursework is Individual assignment This coursework constitutes 30% to the overall module mark. Date Set 21/10/2016 Date & Time Due 16/12/2016 Your marked coursework and feedback will be available to you on 09/01/2017 If for any reason this is not forthcoming by the due date your module leader will let you know why and when it can be expected. The Head of Studies should be informed of any issues relating to the return of marked coursework and feedback. Note that you should normally receive feedback on your coursework by no later than four working weeks after the formal hand-in date, provided that you met the submission deadline. When completed you are required to submit your coursework to: Dr Karthikeyan Kandan Via FOTAC. Late submission of coursework policy: Late submissions will be processed in accordance with current University regulations which state: "the time period during which a student may submit a piece of work late without authorisation and have the work capped at 40% (50% PG level) if passed is 14 calendar days. Work submitted unauthorised more than 14 calendar days after the original submission date will receive a mark of 0%. These regulations apply to a student's first attempt at coursework. Work submitted late without authorisation which constitutes reassessment of a previously failed piece of coursework will always receive a mark of 0%." Academic Offences and Bad Academic Practices: These include plagiarism, cheating, collusion, copying work and reuse of your own work, poor referencing or the passing off of somebody else's ideas as your own. If you are in any doubt about what constitutes an academic offence or bad academic practice you must check with your tutor. Further information and details of how DSU can support you, if needed, is available at: http://www.dmu.ac.uk/dmu-students/the-student-gateway/academic-support-office/academic-offences.aspx http://www.dmu.ac.uk/dmu-students/the-student-gateway/academic-support-office/bad-academic-practice.aspx Tasks to be undertaken: Explain and answer the questions attached to this form. Deliverables to be submitted for assessment: Hard copy report. How the work will be marked: According to the attached sheet. 21 Problem Statement A local engineering consulting firm approaches you with their typical problem. They designed a truss-like structure which is subjected to a load as shown in Figure 1 and Figure 2. Since this structure is planned to be mounted overhead in undisclosed factory, they want to reduce the weight, hence the cross-sectional area of the truss-members. Dimensions, load conditions are given in Figure 1 and Figure 2. The company also would appreciate the rationale for selection of area, and factor of safety from engineering point of view. The material is mild steel, and you are advised to use mechanical properties of standard mild steel: Young's Modulus, E = 210 GPa and Yield Stregnth, σY = 250 MPa. 2 Deliverable • Your task is to evaluate a suitable cross section, using standard box section sizes that are widely available in the U.K. • Also you should suggest the best configuration based on the advantage and limitation from engineering point of view. You will be assessed on both the quality of the decisions made and the methods used to make the decisions. You will also need to make a judgement on what constitutes good performance (e.g. the safety factor used). While performing calculations use consistent SI units. 3 Selection Criteria The company proposed the following selection criteria: 1. The material definition and area are reasonable from engineering design point of view. (10%) 2. All loading conditions are considered, proper factor of safety is chosen. (20%) 3. Analyses of the whole structure performed and nodal displacements are determined. (20%) 4. Stress and strain at each element is determined, the structure is strong enough for the loading condition. (20%) 35. The MATLAB program is easy to read, with all appropriate comments and inputs and output results clearly labelled and shown. (10%) 6. The course work report is presented in a professional manner with clear content, introduction and all relevant sections as per the guidelines stated in this document. (20%) 45˚ C A B D G E F L= 800 mm 10 kN 0.75 L sliding support pinned support Figure 1: Truss for overhead loading pulley configuration 1 10 kN pinned support sliding support L= 800 mm 0.75 L 45˚ C A B D G E F Figure 2: Truss for overhead loading pulley configuration 2 44 Report format The report should be concisely written and not more than 20 pages. An ideal report contains the following sections. 4.1 Introduction Brief summary of the problem and justification to the chosen box section. 4.2 Description of Elemental stiffness matrix Clearly tabulate discretisation plan for the two configuration, for example, see Table 1. State elemental stiffness matrix that you have used. Write down an individual stiffness matrix for each truss members for both Truss configuration in Figure 1 and Figure 2. Truss Member Node 1 Node 2 xi, yi xj, yj θ c s ℓ A 1 2 B 2 3 C 3 4 D 4 1 E 4 2 F 4 5 G 5 1 Table 1: A sample table to present the discretisation plan for Truss configuration in Figure 1. 4.3 Assembly of global stiffness matrix Assembly of individual stiffness matrix for both Truss configuration in Figure 1 and Figure 2. Write down the global stiffness matrix after assembly for each configuration. 54.4 Boundary conditions and loads Write down prescribed boundary conditions and applied loads for each configuration. Also, clearly state active Degrees of Freedom for each truss member for both Truss configuration. 4.5 Governing equation The final governing equation to solve displacement by using global stiffness matrix and prescribed boundary conditions and external loads. 4.6 Results Primarily, the following three items should be calculated from the MATLAB program that you have written for both Truss configuration. • Nodal displacements • Elemental strains • Elemental stresses Configuration 1 Configuration 2 Truss Nodal Displacement Nodal Displacement Member Node 1 Node 2 Node 1 Node 2 A B C D E F G Table 2: A sample table to present the nodal displacements for Truss configuration in Figure 1 and Figure 2. 6The nodal displacements results should be summarised in tabular format as shown in Table 2 for Truss configuration in Figure 1 and Figure 2. You should include the expression for calculating the elemental stress and strains, by considering factor of safety. The elemental strains and stresses should be summarised in the following tabular format, see Table 3, for both Truss configuration in Figure 1 and Figure 2. Truss Configuration 1 Configuration 2 Member Elemental Strain Elemental Stress A B C D E F G Table 3: A sample table to present the elemental strains and stresses for Truss configuration in Figure 1 and Figure 2. You will use these results to justify your choices, for example, chosen box-section as well as the truss configuration to 'safely' withstand the applied load by considering appropriate factor of safety. 4.7 MATLAB Programming You will also submit the MATLAB code (as an Appendix to the report) used to create the chosen configuration FEA model. The prime characteristics of the MATLAB program should be: 1. The MATLAB code should show clearly the inputs and outputs. 2. It should include sufficient comments for engineers in the company to understand it. 3. Clarity on each steps involved from elemental stiffness matrix 74. Assembly of elemental stiffness matrix 5. Solve for nodal displacements, elemental stress & strains 4.8 Recommendations 1. The suitable configuration from Figure 1 and Figure 2 for given loading. 2. The standard box section to safely withstand the applied load for suitable truss configuration from Figure 1 and Figure 2. 5 Assessment Criteria The final assessment will be a report written in the format of a • Description of how the two configurations (Figure 1 and Figure 2) have been set up • A comparative analysis,in terms of nodal displacements, elemental stress and strains, for the two configurations. • Discussion about the results, weighing up the advantages/disadvantages of each configuration. • Conclusions about the appropriate cross section and the efficacy of Finite Element Analysis approach 8