固有関数を用いた有限要素による補強平板の曲げ及び座屈解析

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The formulation of a long quadrilateral finite element for plate bending is described herein. This method is a development of the finite strip method to the finite element procedure. It is well known that comparatively accurate solutions can be obtained with a few degrees of freedom by the finite strip descretization, because the displacement interpolation functions in the longitudinal direction are selected as eigenfunctions. It imposes, however, a significant geometric limitation because of its rectangular shape and the incapability to connect adjacent elements along the shorter sides. By modifying the finite strip method the authors were able to obtain the versatility contained in the finite element method. The nodal displacements are taken in this method as generalized coordinates which are amplitudes of the eigenfunctions in the finite strip method. A general quadrilateral element is mapped into the standard square element in the local coordinates for the derivation of the stiffness. The long quadrilateral element satisfies all the continuity requirements except the slope along the shorter sides. The element stiffness derivation is outlined and numerical results are presented to evaluate the accuracy and demonstrate the effectiveness of the element. As a practical example the buckling analysis is performed with respect to the corner connection of the trans. ring of an ore carrier. The results show this method to be potent especially for stiffened plates such as those of ship structures.
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固有関数を用いた有限要素による補強平板の曲げ及び座屈解析

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