Using the results of Exercise 13.22, solve the problem of a stress-free spherical cavity in an infinite
Question:
Using the results of Exercise 13.22, solve the problem of a stress-free spherical cavity in an infinite elastic medium under uniform far-field stress σ∞x =σ∞y = σ∞z = S. Explicitly show that the stress concentration factor for this case is K = 1.5 and compare this value with the corresponding two-dimensional case. Explain why we would expect such a difference between these two concentration factors.
Data from exercise 13.22
Using the basic field equations for spherical coordinates given in Appendix A, formulate the elasticity problem for the spherically symmetric case, where uR = u(R), u∅ = uθ = 0. In particular, show that the governing equilibrium equation with zero body forces becomes:
Step by Step Answer:
Elasticity Theory Applications And Numerics
ISBN: 9780128159873
4th Edition
Authors: Martin H. Sadd Ph.D.