Using the basic field equations for spherical coordinates given in Appendix A, formulate the elasticity problem for the spherically symmetric case, where u R u(R), u u 0 In particular, show that the governing equilibrium equation with zero body forces becomes Data from appendix a 2 du 2 du dR R dR ...

For the spherically symmetric case U uRu U 0 and relation A12 reduces to du 2 du 2 211 R dR2 ...

Using the basic field equations for spherical coordinates given in Appendix A, formulate the elasticity problem for

Question:

Using the basic field equations for spherical coordinates given in Appendix A, formulate the elasticity problem for the spherically symmetric case, where u_R = u(R), u_∅ = u_θ = 0. In particular, show that the governing equilibrium equation with zero body forces becomes:

2 du 2 du + dR R dR R2 Next solve this equation and show that the general solution can be expressed as C