Postbuckling behavior of rectangular plates

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Virginia Polytechnic Institute

Unlike simple columns, rectangular plates which are supported on all edges may carry considerable load beyond their buckling load. Under some conditions it may be advantageous to utilize this additional load-carrying capacity. Von Karman has presented the basic nonlinear differential equations for a plate element undergoing large deflections. In this dissertation the nonlinear equations of von Karman are converted into a s~t of linear equations by expanding the displacements into a prn,er series in terms of an arbitrary parameter. The first few equations of the set can be identified as the usual (linear) small deflection equations. Solution of these and then some of the succeeding equations permits a study of the behavior of the plate at buckling and then beyond into the large deflection range. At present it seems that only plates without initial eccentricities subject to in-plane loading may be solved by the present method. The advantage of the present method is the simplicity of solution.

The elastic postbuckling behavior of simply supported rectangular plates subjected to longitudinal compression and subjected to a unIform temperature rise is investigated in detail by solving the first few of the equations. Results are presented for these problems in the form of equations and curves. Load-shortening curves for the compression problem and similar curves for one of the temperature problems solved indicate that changes in buckle pattern will occur. Because of the incompleteness and the inconsistencies of the treatment of the phenomenon of change in buckle pattern in the literature, a study of this phenomenon is made. In order to analyze change in buckle pattern in a rigorous fashion the postbuckling behavior of a symmetric three element column on a nonlinear elastic foundation is determined. It is indicated how the principles learned from the column analysis may be applied qualitatively to plate problems.

The results for the plate in compression are compared to previous theoretical results and to experiment. For a square plate the present results agree with previous exact results. For an infinitely long plate the present thesis gives more accurate (lower) loads than previous results. Experimental results which have not been reported previously are described in this thesis, and results from these and other experiment are compared with the present theory. Comparisons are made for total shortening and local strains and deflections which indicate good agreement between experimental results and theoretical results.