HW#10 Assigned 11-9-06; Due 11-14-06

(a) A hollow steel sphere with a 1.0 inch inner radius and a 3.0 inch outer radius has an internal pressure of 10,000 psi. The external pressure is zero. Use axisymmetric modeling to find the maximum hoop stress developed in the sphere. Compare your result with the theoretical solution

Sigma = 0.5p (b^3 + 2a^3)/(b^3 - a^3)

where p = the internal pressure, a, b = inner and outer radii

(b) Use solid elements to solve the problem described in (a) above.

Make use of symmetry. An octant of the sphere can be created in ANSYS by first creating an annular area (as for the problem above) and then sweeping that area through a 90 degree rotation about the Y axis.

Preprocessor -> Operate -> Extrude/Sweep -> Areas -> About Axis

Use both 10 node tet (free mesh) and 20 node brick (mapped mesh) models and compare your results with the theoretical solution. The large tet models can take a while to compute. Optional solution methods can speed things up; See ANSYS Tutorial Lesson 4.

Note: In problem (b) you can apply bc and pressures to areas. Review Lessons 3 and 4 before working these problems.