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

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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:

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

Data from appendix a

Cylindrical coordinates ero  - = = = ur r 1 = +/- (  ur ue +  ar + 1/due 1 uz - 2 dz  1/ur duz + 2 dz ar ur +

Spherical coordinates eR eg = eRo -  JUR R 1 R sin COR = = R  30 UR + 1/1 dur u - - - + sin our + cos ud + 2R

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