(* ::Package:: *)

(************************************************************************)
(* This file was generated automatically by the Mathematica front end.  *)
(* It contains Initialization cells from a Notebook file, which         *)
(* typically will have the same name as this file except ending in      *)
(* ".nb" instead of ".m".                                               *)
(*                                                                      *)
(* This file is intended to be loaded into the Mathematica kernel using *)
(* the package loading commands Get or Needs.  Doing so is equivalent   *)
(* to using the Evaluate Initialization Cells menu command in the front *)
(* end.                                                                 *)
(*                                                                      *)
(* DO NOT EDIT THIS FILE.  This entire file is regenerated              *)
(* automatically each time the parent Notebook file is saved in the     *)
(* Mathematica front end.  Any changes you make to this file will be    *)
(* overwritten.                                                         *)
(************************************************************************)



(* ::Input::Initialization:: *)

(* Definitions of the displacement functions. *)
uR=Simplify[(D[\[Phi],R]+R*Cos[\[Beta]]*D[\[Omega],R]-(3-4*\[Nu]\.13)*Cos[\[Beta]]*\[Omega]+(2/R)*D[\[Psi],\[Theta]])/(2*\[Mu])]


(* ::Input::Initialization:: *)
u\[Theta]=Simplify[((1/R*Sin[\[Beta]])*D[\[Phi],\[Theta]]+Cot[\[Beta]]*D[\[Omega],\[Theta]]-2*Sin[\[Beta]]*D[\[Psi],R]-(2*Cos[\[Beta]]/R)*D[\[Psi],\[Beta]])/(2*\[Mu])]



(* ::Input::Initialization:: *)
u\[Beta]=Simplify[((1/R)*D[\[Phi],\[Beta]]+Cos[\[Beta]]*D[\[Omega],\[Beta]]+(3-4*\[Nu])*Sin[\[Beta]]*\[Omega]+(2*Cot[\[Beta]]/R)*D[\[Psi],\[Theta]])/(2*\[Mu])]

(* The stress functions. *)


(* ::Input::Initialization:: *)
\[Sigma]RR=Simplify[D[\[Phi],R,R]+R*Cos[\[Beta]]*D[\[Omega],R,R]-2*(1-\[Nu])*Cos[\[Beta]]*D[\[Omega],R]+(2*\[Nu]/R)*Sin[\[Beta]]*D[\[Omega],\[Beta]]+(2/R)*D[\[Psi],R,\[Theta]]-(2/R^2)*D[\[Psi],\[Theta]]]


(* ::Input::Initialization:: *)
\[Sigma]\[Theta]\[Theta]=Simplify[(1/R)*D[\[Phi],R]+(Cot[\[Beta]]/R^2)*D[\[Phi],\[Beta]]+(1/(R*Sin[\[Beta]])^2)*D[\[Phi],\[Theta],\[Theta]]+(1-2*\[Nu])*Cos[\[Beta]]*D[\[Omega],R]+(2*\[Nu]/R)*Sin[\[Beta]]*D[\[Omega],\[Beta]]+(Cos[\[Beta]]^2/(R*Sin[\[Beta]]))*D[\[Omega],\[Beta]]+(Cot[\[Beta]]/(R*Sin[\[Beta]]))*D[\[Omega],\[Theta],\[Theta]]+(2/(R*Sin[\[Beta]])^2)*D[\[Psi],\[Theta]]-(2/R)*D[\[Psi],R,\[Theta]]-(2*Cot[\[Beta]]/R^2)*D[\[Psi],\[Beta],\[Theta]]]


(* ::Input::Initialization:: *)
\[Sigma]\[Beta]\[Beta]=Simplify[(1/R)*D[\[Phi],R]+(1/R^2)*D[\[Phi],\[Beta],\[Beta]]+(Cos[\[Beta]]/R)*D[\[Omega],\[Beta],\[Beta]]+(1-2*\[Nu])*Cos[\[Beta]]*D[\[Omega],R]+(2*(1-\[Nu])*Sin[\[Beta]]/R)*D[\[Omega],\[Beta]]+(2*Cot[\[Beta]]/R^2)*D[\[Psi],\[Theta],\[Beta]]-2*(\.13Cot[\[Beta]]/R)^2*D[\[Psi],\[Theta]]]


(* ::Input::Initialization:: *)
\[Sigma]\[Theta]\[Beta]=Simplify[(1/(R^2*Sin[\[Beta]]))*D[\[Phi],\[Theta],\[Beta]]-(Cot[\[Beta]]/(R^2*Sin[\[Beta]]))*D[\[Phi],\[Theta]]+(Cot[\[Beta]]/R)*D[\[Omega],\[Beta],\[Theta]]+(2*(1-\[Nu])/R)*D[\[Omega],\[Theta]]-(1/(R*Sin[\[Beta]]^2))*D[\[Omega],\[Theta]]+(Cot[\[Beta]]/(R^2*Sin[\[Beta]]))*D[\[Psi],\[Theta],\[Theta]]-(Sin[\[Beta]]/R)*D[\[Psi],R,\[Beta]]-(Cos[\[Beta]]/R^2)*D[\[Psi],\[Beta],\[Beta]]+(1/(R^2*Sin[\[Beta]]))*D[\[Psi],\[Beta]]]


(* ::Input::Initialization:: *)
\[Sigma]\[Beta]R=Simplify[(1/R)*D[\[Phi],\[Beta],R]-(1/R^2)*D[\[Phi],\[Beta]]+(1-2*\[Nu])*Sin[\[Beta]]*D[\[Omega],R]+Cos[\[Beta]]*D[\[Omega],\[Beta],R]-(2*(1-\[Nu])*Cos[\[Beta]]/R)*D[\[Omega],\[Beta]]+(1/R^2)*D[\[Psi],\[Theta],\[Beta]]+(Cot[\[Beta]]/R)*D[\[Psi],\[Theta],R]-(2*Cot[\[Beta]]/R^2)*D[\[Psi],\[Theta]]]


(* ::Input::Initialization:: *)
\[Sigma]R\[Theta]=Simplify[(1/(R*Sin[\[Beta]]))*D[\[Phi],R,\[Theta]]-(1/(R^2*Sin[\[Beta]]))*D[\[Phi],\[Theta]]+Cot[\[Beta]]*D[\[Omega],R,\[Theta]]-(2*(1-\[Nu])*Cot[\[Beta]]/R)*D[\[Omega],\[Theta]]+(1/(R^2*Sin[\[Beta]]))*D[\[Psi],\[Theta],\[Theta]]-Sin[\[Beta]]*D[\[Psi],R,R]-(Cos[\[Beta]]/R)*D[\[Psi],R,\[Beta]]+(2*Cos[\[Beta]]/R^2)*D[\[Psi],\[Beta]]+(Sin[\[Beta]]/R)*D[\[Psi],R]] 
