APPLICATIONS OF A GENERAL FINITE-DIFFERENCE METHOD FOR CALCULATING BENDING DEFORMATIONS OF SOLID PLATES

摘要

This paper reports the findings of an investigation of a finite-difference method directly applicable to calculating static or simple harmonic flexures of solid plates and potentially useful in other prob¬lems of structural analysis. The method, which was proposed in a doc-toral thesis by John C. Houbolt, is based on linear theory and incorpo-rates the principle of minimum potential energy. Full realization of its advantages requires use of high-speed computing equipment. After a review of Houbolt's method, results of some applications are presented and discussed. The applications consisted of calculations of the natural modes and frequencies of several uniform-thickness cantilever plates and, as a special case of interest, calculations of the modes and frequencies of the uniform free-free beam. Computed frequencies and nodal patterns . for the first five or six modes of each plate are compared with existing1-experiments, and those for one plate are compared with another approxi¬mate theory. Beam computations are compared with exact theory. On the basis of the comparisons it is concluded that the method is accurate and general in predicting plate flexures, and additional applications are suggested. An appendix is devoted to computing procedures which evolved in the progress of the applications and which facilitate use of the method in conjunction with high-speed computing equipment.