The effect of out-of-plane restraint on plane-stress solutions near straight boundaries

Abstract

The existence of out-of-plane displacement restraint where thin photoelastic plates are bonded to relaively rigid boundaries or inclusions will induce transverse stress components whose presence can cause the in-plane stresses to deviate significantly from the plane-stress solution. The extended generalized planestress formulation, which was developed in a previous paper to study the effect of out-of-plane restraint on the through-the-thickness averages of the in-plane stresses and displacements in thin plates, is applied here to obtain correction factors by which the photoelastically determined in-plane stress components at a straight restrained boundary can be multiplied to recover the desired twodimensional solution. Cases of mechanical and thermal loadings which vary sinusoidally in the direction parallel to the restrained boundary are treated.

The stress-field alterations due to out-of-lane restraint are shown to depend strongly on Poisson's ratiov and the ratioL/H of the half-wavelength of the load variation to the plate thickness, and can be minimized by choosing a photoelastic material with the smallest values ofv andH possible. The simple asymptotic form of the stress-field alterations for large values ofL/H has enabled us to prescribe simple correction factors in this range. Finally, it is observed that, although the normal stress component which is parallel to the restrained boundary is altered to a greater degree than are the other in-plane stress components, the effect on this stress component penetrates into the plate a distance of only about one plate thickness, whereas the effect on the other components penetrates a distance of approximately one half-wavelength of the load variation.