Application of the geometric immersion method based on the Castigliano variational principle for the axisymmetric problems of elasticity theory

摘要

The fundamentals of the geometric immersion stress method for axisymmetric problems of elasticity theory have been stated. The geometric immersion method involves reduction of the initial problem for Clapeyron's free form elastic body to an iteration sequence of elasticity theory problems on some canonical domain. The iteration procedure for the variational equation of the geometric immersion method has been stated, as well as its discrete analog construction technique suggested with the finite-element stress method for the axisymmetric problem of the elasticity theory in the cylindrical coordinates. A practical application of the method has been demonstrated by a test problem. A reasonably good fit between the stress fields definition and the numerical solution by the traditional finite-element displacement method has been obtained.