Stress Analysis by Combination of Holographic Interferometry and Boundary-integral Method Surface displacements obtained by double-aperture speckle interferometry are used in the boundary-integral method for the calculation of stresses over the region of the studied model by J. Balas, J. Sl .dek and M. Drz,k ABSTRACT--The paper describes a hybrid experimental and numerical method analysis of bodies. It consists of the experi- mental method of doubfe-aperture speckie interferometry and the boundary-integral method. The interference patterns allowing evaluation of the displacement vector are obtained by the speckle interferometry. The boundary displacements obtained experimentally are conveniently used for the calcula- tion of stresses in the body by the boundary-integral method. Some examples bear witness of the effectiveness and accuracy of the hybrid technique. Introduction Methods of experimental stress analysis allow one to determine stress components in the interior and on the surface of solids by the evaluation of measurements, It is, however, not possible always to obtain the displace- ment and stress field by experiments alone. It becomes necessary to utilize numerical methods to supplement experimental methods. The combination of the finite- element method for determination of bending moments of a plate and the experimentally obtained deflections is described in Ref. 1. The boundary-integral-equation (BIE) method is ver~ convenient for combinations with a number of experi- mental methods. The BIE method for stress analysis is based on the numerical solution of integral equations2 '3 The method is very well suited to solve two- and three- dimensional problems as it reduces them to boundary Solutions, i.e., only elements on the boundary need to be defined. Depending on the completeness of the experi- mental data, we first study the unknown reactions and/or displacements on the boundary of the studied region or we proceed immediately to the calculation of the stress and strain field at the internal points of the region. The hybrid numerical and experimental method for the analysis of three-dimensional problems permits the deter- mination of stress components at interior points non- destructively. The presented method has another advantage in comparison with a purely' numerical approach by allowing a reduction of the initial complicated problem to a problem with simple boundary conditions. For example, let us study the problem of vertical plate with a hole taking into account the friction between the plate and the J. BalaYl (SESA Member) is Head and J. Sl~dek and M. Dr~fk are Scientific Workers, Department of Theoretical and Experimental Mechanics, Institute of Construction and Architecture, Slovak Academy o f Sciences, 842 20 Bratsilava, Czechoslovakia. Original manuscript submitted: October 7, 1981. Authors notified of acceptance: June 8, 1982. Final version received: August 27, 1982. base. The determination of the boundary conditions on the lower edge of the plate would be very complicated. By specifying the values of displacements on the boundary of the region a simple problem is obtained. The displace- ment values on the boundary have been found by speckle interferometry. Another case used as illustration of the numerical-experimental method is a three-point flexure of a beam including a crack. Procedure for three-dimen- sional problems is similar. Measurement of Displacements by Double.aperture Speckle lnterferometry Optical methods using the property of coherent light to form laser speckle belong to the promising methods of experimental stress analysis. Their use for the analysis of deformable bodies allows measurements of displacements of individual points on a diffused surface. To these methods belongs the double-aperture speckle interferometry (DASI) method, the principle of which has been described by Duffy. ''~ The basic element of an interferometer is a lens with a double-aperture diaphragm~ The lens is placed so as to project the image of a diffuse surface illuminated by coherent light on a holographic plate. The double-exposure specklegrams present lines of equal values of components of displacement vector in the surface plane, A wider use of this method in experimental practice has hitherto been prevented by a number of problems, particularly the problem of very long exposure times due to the small apertures and a generally poor quality of the fringe pattern. If the DASI method is used with transparent models with one ground screen, the ex- posure time may be substantially reduced. The ground screen scatters the coherent light passing through it (Fig. 1). In the given case it was shown as advantageous to use a spherical illuminating wavefront converging to a point in the plane of the image-forming lens. This is how equal luminous flow through both diaphragm apertures is secured with a view to the symmetry of the light scatter due to the ground screen and a maximum depth of modulation Of the laser speckles by the grid. A high diffraction effectivity of the specklegram is reached as well. The use of the transmission technique and a He-Ne laser with 10-roW output allowed us to reduce the exposure times to as little as 10 - 20 s. (Agfa Gevaert 10E75 photographic plates were used.) The interference fringe patterns were recorded by the generally used double-exposure procedure involving the deformation of the body between the first and the second exposure. The simplified relationships for the interpreta- 196 9 June 1983