FEA - Simple Analysis example
- 1. Michael Davis 1000781532 9-26-2014 Homework #3 Problem Statement: Develop and ANSYS model to generate a chart for stress concentration factor in a notched rectangular bar. Set (w/d)=3, Poisson’s ratio = 0.3. Formulation: The model is symmetric about two axes. When dividing the model symmetrically it is important to account for half of the force on the area as well as using (d/2) in the model design to calculate the maximum normal stress in ANSYS. 𝜎𝑎𝑣𝑒𝑟𝑎𝑔𝑒 = 𝐹𝑜𝑟𝑐𝑒 𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑅𝑒𝑑𝑢𝑐𝑒𝑑 𝑎𝑟𝑒𝑎 𝑤ℎ𝑒𝑟𝑒 𝑅𝑒𝑑𝑢𝑐𝑒𝑑 𝐴𝑟𝑒𝑎 = 𝑑 ∗ 𝑡 𝑑 = 𝑟𝑒𝑑𝑢𝑐𝑒𝑑 𝑑𝑖𝑚𝑒𝑛𝑡𝑖𝑜𝑛 𝑑𝑢𝑒 𝑡𝑜 𝑛𝑜𝑡𝑐ℎ = 𝑤 3 𝑤 = 𝑑𝑖𝑚𝑒𝑛𝑡𝑖𝑜𝑛 𝑏𝑒𝑓𝑜𝑟𝑒 𝑛𝑜𝑡𝑐ℎ 𝑤𝑎𝑠 𝑎𝑑𝑑𝑒𝑑 𝑡 = 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝜎 𝑚𝑎𝑥 = 𝑣𝑎𝑙𝑢𝑒 𝑜𝑏𝑡𝑎𝑖𝑛𝑒𝑑 𝑓𝑟𝑜𝑚 𝐴𝑁𝑆𝑌𝑆 𝐾𝑡 = 𝑠𝑡𝑟𝑒𝑠𝑠 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 = 𝜎 𝑚𝑎𝑥 𝜎𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝐹𝑜𝑟𝑐𝑒 𝐴𝑝𝑝𝑙𝑖𝑒𝑑 = 𝜎𝑎𝑝𝑝𝑙𝑖𝑒𝑑 ∗ 𝑤 ∗ 𝑡 The parameters used in evaluation of the stress concentration factor consist of using the default ANSYS material (steel) because it already has assigned the Poisson’s ratio of 0.3. There will be only one curve due to the constant (w/d) = 3. The stress concentration factor will be found by finding different values of K by varying the notch radius ‘r’ then plotting Kt vs (r/d). The scenario will be evaluated by solving plane stress and assuming the steel material is linearly elastic and isotropic.
- 2. ANSYS (Numerical) Model: d = 1 mm w= 3 mm L = 6 mm E = 2E11 Pascal ν = 0.3 Pressure Applied =-1 MPa FrictionlessSupportsappliedtotwofaceslocadedat(d*t) and (L*t) Prssure addedat face (w*t) Figure 1 – Displays the symmetrical model in ANSYS, radius R11 is variable for this assignment.
- 3. Figure 2-Details of Boundary Conditions Placed in ANSYS for pressure loading and symmetrical surfaces.
- 4. MeshUsed: Figure 3 – Course Mesh Figure 4 – Fine Meash From the coarse to the fine mesh,the predictednormal stresschangedby2.4%. This is consideredtobe reasonable convergence. The findmeshwill be usedinthe followingsimulations.
- 5. Results: Figure 5 – Typical Deformed Shape Figure 6 – Typical Contour Plot of σx.
- 6. Figure 7 – Plot of SCF Kt vs (r/d) with fixed (w/d)