The Boundary Element Method in Thermoelastic Stress Separation — II: A General Hybrid Numerical/Experimental Technique

Abstract

The background to thermoelastic stress analysis (TSA) is given in [1]. In this paper the extension of the thermoelastic stress separation method to arbitrarily shaped two-dimensional domains is described. The stress separation method developed here is based on the second-order form of the equilibrium equations expressed as two Poisson differential equations with coupled boundary conditions [2]. A pure equilibrium technique for stress separation is possible with known traction vector (free surface or specified load on surface) and stress sum data over the complete boundary. Otherwise a hybrid method must be employed using results of an independent stress analysis method. The Finite Element Method (FEM) or the Boundary Element Method (BEM) are best suited to solutions of the Poisson equations over arbitrarily shaped structures. Commercial FEM codes can be employed [3], however this has been found to be restrictive for this application; BEM is therefore employed here. Algorithms using either the cell integration method (CIM) or the dual reciprocity method (DRM) have been developed since the Monte Carlo integration method has shown to be unnecessary [1]; the relative merits of each method is discussed in detail. An algorithm based on the FEM [4] is first developed [5,6] for the smooth representation and differentiation of TSA data. A method of data smoothing is required since experimental TSA data contain a degree of noise. Edge error removal and multiple TSA scan sampling techniques improve data representation. A benchmark problem with simulated noisy experimental TSA scan data is used to test the general stress separation method.