Application of the network method to simulate elastostatic problems defined by potential functions. Applications to axisymmetrical hollow bodies

Abstract

The direct application of the network method for the numerical solution of 2D linear elastostatic problems formulated by potential functions has demonstrated to be a powerful tool that provides accurate solutions with small computational times. The method is used for solving axisymmetrical problems formulated by two (Boussinesq and Timpe) or three (Papkovich–Neuber) displacement potentials. The network method makes most of the potent computational algorithms implemented in electrical simulation codes and allows an easy implementation of the complex boundary conditions inherent to this potential formulation in comparison with other classical numerical methods. The application to a hollow cylinder subjected to general load boundary conditions is presented by comparing the elastic solution with those provided by other formulations.

Keywords:

• Papkovich–Neuber representation
• numerical simulation
• linear elasticity
• axisymmetrical
• network method

2010 AMS Subject Classifications :

• 65E05
• 74S30
• 31A99