彈性板受集中載重之分析

Abstract

本文的目的在於探討二維正向性無限平板受到集中力作用所產生應力情形。其內容有無限板受到 方向集中力作用，無限板受到 方向集中力作用，無限板受到兩點集中力模擬純彎矩，無限板受到三點集中力模擬彎曲四種不同情形。其中無限板受到 方向集中力作用，無限板受到 方向集中力作用為基本解，且無限板受到兩點集中力模擬純彎矩，無限板受到三點集中力模擬彎曲可由基本解疊加後得到結果。 本文將上面四種模型的應力分成兩部份，第一個部份為材料力學部份產生支應力，第二個部份為在集中力附近所產生的應力分佈，稱之為西華德-逢卡門修正項(Seewald-von Karman correction)，本文稱其為局部區域效應(Local effect)。此兩部分的應力相加為無限板受集中力作用之完整解。材料力學解的部份有使用到尤拉-伯努利樑理論以及受到 方向集中力作用的理論。局部區域效應部份的應力使用到非奇異性的二維異向性材料之邊界積分方程式來計算。

The objective of this thesis is to discuss the stress distribution of concentrated forces acting on a two-dimensional infinite plate made of an elastic orthotropic material. The loading cases considered include: (a.) a horizontal concentrated force at the center of the plate; (b.) a vertical concentrated force on the plate surface; (c.) two non-collinear concentrated forces on the top and bottom plate surfaces simulating pure bending; and (d.) three concentrated forces on the plate surfaces simulating three-point bending. In this study the elasticity solutions are separated into two parts. The first part is the solution obtained by the mechanics-of-materials approach, while the second part is a correction term called Seewald-von Karman correction. The Seewald-von Karman correction is calculated using nonsingular boundary integral equations.