UBC Theses and Dissertations
Bifurcation of a square plate twisted by corner forces Miya, Raymon
A square plate twisted by corner forces is described by classical linear theory as a saddle surface. In an experiment, as the plate deforms to any noticeable deflection, it appears not as a saddle surface, but as a cylindrical surface. The transformation in mode shapes presents problems in determining material behaviour by shear in a plate twisting experiment. The two mode shapes can be described by either displacement or curvature of the surface. The purpose of this work is to investigate the buckling of a square plate twisted by corner forces by determining the bifurcation point and comparing the present FEA work with the experimental results of Howell and other results found in literature. The problem is examined using nonlinear finite element buckling analysis. The bifurcation point is determined by load-displacement plots. The critical value of Gaussian curvature at the centre of the plate is determined by the Southwell plot method. The critical value of Gaussian curvature is found to occur before the bifurcation point. Gaussian curvature is found to vary by an order of magnitude over the plate at bifurcation.
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