Finite Element Modelling

Abstract

The work described in this paper represents an effort to demonstrate the validity of the hybrid approach to the analysis of structural deformation. Mathematical modelling was incorporated into the process of reducing data from a digital correlation analysis of a speckled surface. The experimental data was collected both by directly imaging the surface onto a digitizing vidicon system and by transmitting the image through a coherent optical fiber bundle. Considerable savings of time and resources can be realized through the hybrid approach and the strengths of the theoretical and experimental procedures complement each other beautifully. The final results agreed within a few percent of each other and with values obtained by another independent method (high frequency moire), demonstrating the accuracy of the procedure. Hybrid approach The idea of a hybrid approach to structural analysis is not new(1,2,3,4). Although a long history of development can be traced for engineering studies based on mathematical models (finite-difference equations, boundary value integrals, finite element models) and on experimentally obtained data (gaging, optical or acoustical metrology), each method has well known limitations. Mathematical studies depend on the correspondence between some abstract model undergoing specified affects and a real structure subjected to a complex of interacting forces. A detailed model quickly becomes very large and mathematically complex, placing large burdens on the computational and financial resources of the designer. Also, the validity of the results depends on how well boundary conditions have been incorporated into the model. On the other hand, direct experimental methods of analysis often depend on only a few data values, measured at isolated points on the structure. The obtaining of this data for certain critical regions may be difficult or dangerous (complex structures, inaccessible locations, hazardous environments). In such cases, the surface can be illuminated by an incoherent fiber optic bundle and the image transmitted back through a coherent fiber optic bundle to a remote analyzing system. The hybrid method is an attempt to take advantage of the strengths of these two approaches, while minimizing their weaknesses. Basically, the idea is to drastically reduce the finite element mesh required and to incorporate real measured values instead of generalized boundary conditions. Speckle metrology