Assignment 2 MEC4426/MAE3426 Due time and date: 10pm Sunday 24/09/2021 Assignment Three Objectives: 1. Further understand stress concentration. 2. Apply FEA to systematically investigate a problem. 3. Improve FEA skills. Many engineering structures have notches and we often see material failure around these notches. The failure is related to the high stress fields in the neighbourhood of the notches as there is a concentration of stress in these regions. You are required to analyse the stress concentration factor in a thin plate caused by a pair of semi-circular notches in the middle of the plate, as shown in the figure below. Here the stress concentration factor is defined as: (1) where σ is the external tensile stress, see illustration and maxσ is the maximum stress component along the tensile direction. maxσ occurs at the points A and B on the notches in the narrowest cross section. [ ])2/( maxmax raa K ave −×σ σ = σ σ = Assignment 2 MEC4426/MAE3426 Due time and date: 10pm Sunday 24/09/2021 Dimensional analysis finds that the stress concentration factor K is a function of a set of dimensionless parameters: ),,,(1max νσ Π= σ σ = E r b r aK ave (2) where E is the Young’s modulus and v the Poisson’s ratio of the plate material. The plate is considered as a linear elastic isotropic material. If the Poisson’s ratio is fixed as 0.3, which is true for most of the metallic materials, then Eq. (2) can be simplified as ),,(2max σ Π= σ σ = E r b r aK ave (3) Apply the finite element analysis to numerically determine the influence of all the dimensionless factors in Eq. (3) on the stress concentration factor K. Please use symmetrical conditions and create your mesh wisely. A symmetrical model can be the one illustrated below: Assignment 2 MEC4426/MAE3426 Due time and date: 10pm Sunday 24/09/2021 In your report, you need to address the following requirements: (1) You are required to detail one of your FE calculations, including dimensions, mesh, boundary conditions, loading conditions, convergence check and stress results, especially the stress component in the tensile direction along the path AC. (2) You are required to plot at least three diagrams (as there are three dimensionless parameters) to show your final results. (3) Briefly discuss your results through the comparison with your numerical results and results available from literature and draw the conclusions. Assignment 2 MEC4426/MAE3426 Due time and date: 10pm Sunday 24/09/2021 General guides: 1). You may choose the following data for your initial analysis: = 200 GPa = 100 MPa = 100 mm = 200 mm = 10 mm 2). You need to choose the ranges of those three dimensionless factors a/r, b/r and E/σ in your study. Please provide reasons for your choices. 3). To present the influence of the factors for Eq. (3), you need to investigate the influence of the factors one by one. For example, to consider the influence of a/r, you need to change the values of the ratio a/r to do a few (at least 5) FE calculations while keeping the values of other ratios b/r and E/σ as constants. The simple way to change the values of the ratio a/r while keeping b/r constant is to change the value a. For example, a = 80, 100, 120, 140, 200 mm, r= 10 mm, b = 200 mm and E = 200 GPa, σ = 300 MPa. 4). Complete a literature survey to find results from literature to compare with your FE results. In your discussion, you may consider the limitation of your numerical results. For example, the effect of plastic deformation is not considered in the FEA. 5). Dimensional analysis is a powerful tool to systematically examine a physical problem. It has found its application not only in fluid mechanics but also in solid mechanics. To help you understand/revise dimensional analysis and its application in solid mechanics, I uploaded a few pages extracted from Fracture Mechanics --- Fundamentals and Applications by T. L. Andersons (If you have no desire to understand dimensional analysis, you can neglect the attached file, which will not affect you to work on this assignment).