Problem 4.37: Turbine disks are often thick near their hub and taper down to a smaller thi...

Problem 4.37: Turbine disks are often thick near their hub and taper down to a smaller thickness at the periphery. The equation governing a variable-thickness disk is

where is the angular speed of the disk and

(a) Construct the weak integral form of the governing equation such that the bilinear form is symmetric and the natural boundary condition involves specifying the quantity

(b) Develop the finite element model associated with the weak form derived in part (a).