2.31 Assignment 6 Due Mon, Oct 15 at 9:30 am A cylindrical steel tank of inside diameter d=2m and length L=5m is subjected to an internal pressure P=200 MPa. There is no external pressure. The cylindrical tank is closed at both ends by hemispherical caps. The material elastic properties are E=200 GPa, and ν=0.3. The material yield stress is 1.5 GPa. For safety reasons, we want to limit the maximum tangential stress (σθθ) in the component to 1.0 GPa. Our task is to determine the minimum (uniform) thickness of the tank, tmin , necessary to meet this design requirement. 1) Pen and paper work (no FE) Idealize the tank as a thin-walled pressure vessel. Based on this idealization, obtain a first estimate for the wall thickness, t1, which satisfies the design requirement. Obtain estimates for the three components of stress σrr, σθθ, σzz at the cylindrical wall. Does thin-wall theory apply for this component? For a tank of thickness t1, calculate the stress distributions, σrr, σθθ, σzz through the tank thickness using the thick-cylinder formulation. (A quick review of the theory to obtain σrr and σθθ is attached at the end of this assignment; σzz can be considered uniform through the thickness). Does your design satisfy the requirement? Using the thick-wall solution, obtain an improved estimate for the wall thickness, t2, which should satisfy the design requirement. 2) FE model Create an axisymmetric FE model of the tank of thickness t2 using quadratic full integration quadrilateral elements. You can take advantage of the symmetry of the problem and model only half of the component. Be careful when you impose the boundary conditions: the entire edge along the z axis must be constrained in r, and the entire edge along the r axis must be constrained in z. Things to keep in mind as you set up the model: dL tmin r z PPROPERTY : In section property you want to create a solid homogeneous section of thickness 1. In material properties you have to input only the Mechanical props (E, ν). MESH : Seed the assembly with a global element size of 0.1. In the mesh dialog choose standard quadratic quads, and make sure you click off the reduced integration option. (you should have CAX8 as element type). Look at the results in the VISUALIZATION module of ABAQUS/CAE: Plot and print the contours of s11, s22, s33 (= σrr, σzz , σθθ) over the tank Æ attach the plots to your assignment. Create a node path along the edge on the horizontal axis of symmetry (r-axis), and obtain and plot the profiles of σrr, σzz and σθθ as a function of r Æ attach the plots to your assignment. How does the FE prediction compare w/ your thick-wall theory estimate? How does it compare with a thin wall estimate? Comments? Repeat the whole simulation with a more refined mesh (seed with 0.05). Compare the stress profiles between the two models and compare them to the theoretical estimate. What is your final choice for