A curved axisymmetric shell element with three nodes is developed, Quadratic interpolation is used and as the transverse shearing strain is included only first derivatives arerequired inthecalculation of the strains. The element is found to yield accurate solutions for thick circular plates but a penalty factor must be used when the ratio ofplate radius to thickness is of the order of 100, With appropriate values of the penalty factor, though, thin plate behaviour is reproduced with reasonable accuracy. Further, it is shown thatfor all practical purposes the penalty factor need only be based on the plate thickness, This is a useful conclusion in relation to shell analysis where different penalty factor values would otherwise need to be evaluated on the basis of the radius to thickness ratio. Finally the element is shown to give good results for cylindrical and spherical shells.
w'=-usina+wcosa, cp'=c/J.
(1) U' =Ucos a -w sin a, minimum effort and with reduced integration calculation of the element stiffness matrix will be quite economical.
Taking the local dimensionless coordinates to vary from -I (at node 1) to +I (at node 3) the quadratic interpolation is
Figure shows the general element geometry and the global (at node I) and local (at node 3) freedoms of the element. At any point on the element the orientation of the tangent to the surface is given by the angle a so that transformation to local displacements is given by