The bifurcation phenomenon occurring in twisted square plates with free edges subject to contrary self-equilibrating corner loading was examined. In order to eliminate lateral deflection of the test plates due to their own weight, a special loading apparatus was constructed which held the plates in a vertical plane. The complete strain field occurring at the plate centre was measured using two strain gauge rosettes mounted on opposing sides of the plate at the centre. Principal curvatures were calculated and related to corner load for several plates with differing edge length/thickness ratios. A Southwell plot was used relating mean curvature to the ratio mean curvature/Gaussian curvature, from which the Gaussian curvature occurring at bifurcation was determined. The critical dimensionless twist ka was then calculated for each plate size. It was found that there is a linear relation between the critical dimensionless twist ka occurring at bifurcation, and the thickness to edge length ratio h/a ratio, specifically: ka = 10.8h/a. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

An experimental study is presented on the non-linear twisting of plates with free edges, through the application of self-equilibrating corner loads. A simple apparatus was designed and various sizes of plates were twisted while measuring the surface strains on both sides at the centre. Initial difficulty was encountered due to unwanted deflection of the plate under its own weight. The Rayleigh-Ritz method is used to determine an analytical relationship between midsurface strains and curvatures in the pre- and post-bifurcation regions of twisting. In both the experimental and analytical results, the midsurface strains are found to vary linearly with the Gaussian curvature. Non-dimensional groups are identified which collapse the experimental load-strain, load-curvature and midsurface strain-Gaussian curvature relationships. These non-dimensional groups collapse the results in both the linear and non-linear regions. The curvature at the point of bifurcation is identified as a function of plate dimensional parameters. Also shown are the expressions for critical surface strain and corner load at which bifurcation occurs. The experimental load-curvature relationship and point of bifurcation are compared with analytical results found in the literature. A large discrepancy in the literature is resolved for the theoretical point of bifurcation. The present results form a basis for verification of future analytical results, and are important in the measurement of constitutive relationships using the twisted plate test. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate