Abstract
A one-point integration scheme which analytically integrates the element volume and the gradients of linear fields for general quadrilaterals in an axisymmetric geometry is described. A method for isolating proper hourglass modes is presented. The procedure for the control of hourglass modes has been developed from an algebraic and from a variational viewpoint. The hourglass control obtained satisfies the patch test. Bounds on the quadrilateral eigenvalues, that provide stable time step for explicit time integration algorithms, are evaluated considering the influence of hourglass control. Several linear numerical examples demonstrate the effectiveness of the developed technique for finite element codes.
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