新しい長方形板曲げ要素による平板のハイブリッド型有限要素解析

抄録

In this paper, four new rectangular plate bending models for the finite element method based on the modified principle of potential or complementary energy are proposed. These models have special features as follows. 1) The displacement parameter on a node of the structural system in the analysis is only the nodal deflection. 2) The displacement fields of a element and its boundary are expressed as a function of the displacement parameters of the nodes, not only in its element but also in the adjacent elements, so that they could have the higher order displacement functions without increasing the total number of displacement parameters. 3) The displacement functions of the elements and their boundaries are obtained in the explicit expression. 4) The continuity requirements on inter-elements are satisfied by using the modified variational principle. The deflections and resultant stresses of rectangular thin plates are calculated in order to examine the convergencies and accuracies of the present models. Also, the behavior of flat slabs under uniformly distributed load is investigated as a practical example. As a result of the analyses, it may be concluded that these present models are very useful for reducing the total number of the unknown displacement parameters.