彈性矩形板受任意載重之研究

Abstract

本文主要乃推導矩形板承受任意分佈荷重下之外力變形關係式,其中荷重 假設為分段平滑,以一形狀函數表之,且以一無限級數展開,並利用級數基 底函數之正交性,求得假設外力模型與一般彈性薄板理論之關係,進而利用 彈性薄板理論推導出其外力變形關係式,最後將此一關係式應用於土壤結 構互制課題中,求得考慮基礎柔性下之動力反力矩陣.本文針對翻轉及垂直 擾動,並考慮四周簡支及四周固定兩種邊界條件,經由上述方法推導其外力 變形關係式. This paper is a procedure to generate the relationship between the arbitrary loading and the displacement caused by it. First, the arbitrary loading is assumed to be piecewise constant and then expressed in terms of infinite series. We can find that the base functions of the infinite series are orthogonal to each other. By this, there is obtained the relationship between the assumed loading model and the classical plate theory model. Then use the classical plate theory, the relationship between arbitrary loading and the displacement is generated. Because of the assumption of the loading, this numerical solution is useful not only for the simple loading which the classical theory can solve, but also the complex loading which the classical theory can't solve. Finally, the impedance functions for flexible foundation is generated. This paper considers the rocking and vertical motions with simple supported and fixed boundary conditions.