For the general displacement formulation with no body forces, show that Naviers equations (5.4.3) reduce to the

Question:

For the general displacement formulation with no body forces, show that Navier’s equations

(5.4.3) reduce to the form:

Ui, kk + 1 1 - 2v Uk, ki = 0

and thus, the field equation formulation will now only depend on the single elastic constant, Poisson’s ratio. For the case with only displacement boundary conditions, this fact would imply that the solution would also only depend on Poisson’s ratio. Determine the reduction in this Navier equation for the case of v =0.5.

Equation 5.4.3