Numerical realization of the geometrical immersion based on Castigliano variational principle

A variant of the geometric embedding method based on the Castigliano variational principle, the basic procedure that uses a finite element method in terms of stresses is considered. The results of comparing this approach with the analytical solution for thick-walled pipe under internal pressure and the numerical solution of plane problem of elasticity for noncanonical regions, demonstrating the practical convergence of the iterative procedure of immersion, quality of the natural boundary conditions and the distribution of the stress tensor components in the field is presented. Method achieves high accuracy solutions in terms of stresses for a sufficiently small number of elements, to effectively solve problems for the construction of noncanonical form of voltages.