マトリックス法による平板の曲げ振動の解析

概要

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In recent years, the finite element method (matrix method) has made a significant contribution to the area of structural mechanics, especially in two-dimensional stress problems or in axi-symmetrical shell problems. However this seems to be not the case for plate-bending problems, because of difficulties for developing the shape function of a triangular element which will satisfy displacement compatibility conditions along the boundaries of two neighbouring elements. Authors have made basic study on this problem and as the first step, the shape function of a rectangular plate element proposed by Greene was examined and it was confirmed that his shape function satisfies such compatibility conditions completely. Using his shape function, the stiffness and mass matrices were developed and vibration analysis of rectangular plates supported at several points was made and the results of which were compared with experiment. It was duly proved that the finite element method can be successfully applied at least to the plate bending problems where the rectangular plate element may be used.
社団法人日本船舶海洋工学会の論文
1968-07-29