Fundamentals of the Finite Element Method (FEM) and Element Selection - Engineering Assignment

Internal Code : MAS841

Engineering Assignment

You are required to submit an MS Word/PDF document detailing your solution procedure and detailed discussion to each of the following questions in a report style format. If you have used MS Excel to perform the calculations please submit this file in addition to the PDF or MS Word document. Make sure your MS Word, PDF and/or MS Excel files are well structured and clear to follow. You will be assessed on the accuracy of your final solution, the clarity of your solution procedure and the discussion of your answers. Questions : 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: a) Describe and discuss the differences of the 2D Solid Element types: o Plane Stress; o Plane Strain; and o Axisymmetric. b) Provide 6 realistic case studies, in total, in which the simplification from 3D to 2D solid elements above can be made: o 2x plane stress case studies; o 2x plane strain case studies; and o 2x axisymmetric case studies. You must describe and explain why the simplification is suitable for each for them. Include schematics and support mathematically if able to do so. This should be conducted clearly, with clearly defined boundary conditions, etc. c) Setup an ANSYS FE model for one of the case studies discussed above for each element type (3 case studies in total): o 1x plane stress; o 1x plane strain; and o 1x axisymmetric. 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 : Bar Element Considering the composite member below, discretize the problem using the minimum number of bar elements required to solve it. The elastic properties and geometry of sections 1 and 3 are identical: Young’s modulus E1 = E3 = 210 GPa and cross-section area A1 = A3 = 0.1 m2 . For the middle section we have E2 = 170 GPa and A2 = 0.05 m2 . The length L is 0.5 m Determine: a) the nodal displacements at the interfaces of the sections; b) the reaction force at the fixed end; and c) the axial stresses and strains in each section.