Finite element analysis of the statics of and vibrations in axisymmetric shells

  • Wajih Shahla

Student thesis: Doctoral ThesisDoctor of Philosophy


The finite element process is now used almost routinely as a tool of engineering analysis. From early days, a significant effort has been devoted to developing
simple, cost effective elements which adequately fulfill accuracy requirements.
In this thesis we describe the development and application of one of the simplest elements available for the statics and dynamics of axisymmetric shells . A semi analytic truncated cone stiffness element has been formulated and implemented in a computer code: it has two nodes with five degrees of freedom at each node,
circumferential variations in displacement field are described in terms of trigonometric series, transverse shear is accommodated by means of a penalty function and rotary inertia is allowed for.
The element has been tested in a variety of applications in the statics and dynamics of axisymmetric shells subjected to a variety of boundary conditions.
Good results have been obtained for thin and thick shell cases .
Date of AwardAug 1985
Original languageEnglish


  • axisymmetric shell
  • semi-analytic finite element method penalty function
  • transverse shear
  • rotary inertia

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