Abstract
A one-point integration scheme which analytically integrates element volume and uniform strain modes for general isoparametric quadrilateral in axisymmetric geometry is described. A method for isolating proper hourglass modes is presented. It is shown that these modes rather differ from hourglass modes in plane Cartesian geometry, especially near the axis of symmetry. A simple elastic and viscous hourglass control scheme is presented and discussed. Bounds on the quadrilateral eigenvalues that provide stable time steps for explicit time integration algorithms are obtained considering isotropic hypoelastic material. Numerical examples demonstrate the effectiveness of the developed technique for finite element code.
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