EXPERIMENTAL, ANALYTICAL AND NUMERICAL ANALYSIS

OF STRESS FIELD

WITH UNKNOWN PRESCRIBED BOUNDARY CONDITIONS

A. Bilek1*, A. Khennane2

1IGM University Mouloud Mammeri,Tizi-Ouzou, Algeria

2 IGC University Mouloud Mammeri,Tizi-Ouzou, Algeria

* Corresponding author. E-mail : alibilek2000@yahoo.fr

Received 20 November 2000; revised version accepted 06 April 2001

Abstract

A numerical, analytical and experimental analysis of a stress field subject to prescribed but unknown essential boundary conditions is presented. This kind of problem is generally encountered when fitting machinery components by forcing one into another. The numerical analysis is based on the displacement approach of the finite element method. The unknown prescribed boundary conditions are treated with an original approach. Starting from assumed initial conditions, the equilibrium of the two components is sought after by iterating on the displacements. This process has proved to be very efficient since it converged to the correct solution in no more than nine iterations. The analytical solution is derived from the theory of linear elasticity. The equilibrium equations are integrated analytically. As to the experimental analysis, it is carried out by means of the photoelastic method. The analytical and experimental solutions are used to validate the finite element approach by comparing the obtained results.

Keywords: Unknown boundary conditions; Prescribed boundary conditions; Finite element method; Photoelasticity; Analytical theory of elasticity.

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