(* ::Package:: *)

(* THE MICHELL SOLUTION

The terms in each block of Table 8.1 are listed separately in the following cells. *)


\[Phi]0=C01*r^2+C02*r^2*Log[r]+C03*Log[r]+C04*\[Theta]


\[Phi]1c=C11*r^3*Cos[\[Theta]]+C12*r*\[Theta]*Sin[\[Theta]]+C13*r*Log[r]*Cos[\[Theta]]+C14*Cos[\[Theta]]/r


\[Phi]1s=C15*r^3*Sin[\[Theta]]+C16*r*\[Theta]*Cos[\[Theta]]+C17*r*Log[r]*Sin[\[Theta]]+C18*Sin[\[Theta]]/r


\[Phi]nc=Cn1*r^(n+2)*Cos[n*\[Theta]]+Cn2*r^(-n+2)*Cos[n*\[Theta]]+Cn3*r^n*Cos[n*\[Theta]]+Cn4*r^(-n)*Cos[n*\[Theta]]


\[Phi]ns=Cn5*r^(n+2)*Sin[n*\[Theta]]+Cn6*r^(-n+2)*Sin[n*\[Theta]]+Cn7*r^n*Sin[n*\[Theta]]+Cn8*r^(-n)*Sin[n*\[Theta]]


(* Notice that the last two cells can be used to generate expressions for any value of n, using commands such as *)

\[Phi]3c=\[Phi]nc/.n->3


(* The required function can now be assembled by combining appropriate terms from the above terms. For example,if we require terms varying with Cos[2*\[Theta]] and \[Theta]-independent terms, we would write *)

\[Phi]2c=\[Phi]nc/.n->2
\[Phi]=\[Phi]0+\[Phi]2c



(* The stress components are then given by *)

\[Sigma]rr:=(1/r)*D[\[Phi],r]+(1/r^2)*D[\[Phi],\[Theta],\[Theta]];
\[Sigma]r\[Theta]:=(1/r^2)*D[\[Phi],\[Theta]]-(1/r)*D[\[Phi],r,\[Theta]];
\[Sigma]\[Theta]\[Theta]:=D[\[Phi],r,r];



(* To obtain the corresponding displacements (Table 9.1),we use the file `urt.m'---i.e. *)

<<urt.m
