Hybrid method for stress analysis of finite three-dimensional elastic components

Abstract

A new hybrid experimental–analytical/numerical method for stress analysis of a finite three-dimensional elastic component is developed in this paper. It uses the experimentally measured surface stresses and a Green's function method to determine the displacement field (and thus strain and stress fields) in the interior of the component. The method is based on a displacement formulation in three-dimensional elasticity. It is first demonstrated that solving the elasticity problem can be reduced to solving two kinds of Dirichlet problems of Laplace and Poisson equations when the surface stresses become known. These Dirichlet problems are then solved by using Green's function method in potential theory. The solutions are derived in integral forms in terms of the Green function, which is unique for given shape of the engineering component. Green's functions for three typical shapes of a rectangular prism, a solid cylinder and a solid sphere are provided. A sample problem is analyzed to demonstrate applications of the new method. The present method differs from the known boundary integral equation method in elasticity theory. In addition, it can be directly applied to actual engineering components, unlike the model-based photoelasticity method.