兩個垂直集中力分別作用在矩形立方體和細長矩形柱子頂部及底部表面中心之解析解的探討

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Title:	兩個垂直集中力分別作用在矩形立方體和細長矩形柱子頂部及底部表面中心之解析解的探討
Other Titles:	The Discussion on the Analytical Solutions of Two Concentrated Normal Forces Acting at the Centers of the Top and Bottom Surfaces of a Rectangular Block and a Slender Rectangular Column
Authors:	邵德文;曾長偉;陳冠宏
Contributors:	淡江大學機械與機電工程系
Keywords:	格林-邵函數;拍伯克維支-紐伯-布斯尼斯克函數;Green-Shaw function;Papkovitch-Neuber-Boussinesq function;Mathematica;COSMOS/M
Date:	2001-12
Issue Date:	2014-03-07 11:45:44 (UTC+8)
Abstract:	本文引用矩形立方體空間固體的格林-邵函數，因為共有六個邊界面，所以取2/sup 6/項，即六十四項。利用積分形式的格林公式，以及根據Eubanks和Sternberg、對三度空間任意凸形體僅需要三個獨立拍伯克維支-紐伯-布斯尼斯克函數的證明結果，故選用Bx、Bz、β三個函數。解出Bx、Bz及β函數後，得出其解析解，再利用電腦繪圖軟體Mathematica繪出解析解之位移與應力的分佈圖。並利用有限元素法軟體COSMOS/M作分析，得到數值解。再將兩者相互作比較。經由本文探討所知，我們發現，藉由繪出位移、應力的分佈圖與物理意義均非常相似。因此解得的解析解是相近且準確度可以接受的。利用本文所求到的結果，在實際的工程應用上，可提供一可靠確切的計算方法。 The main topic of this paper is to use Green-Shaw functions for a rectangular block, then take 2/sup 6/ terms (64 terms).Then solve the Papkovitch-Neuber-Boussinesq functions with the Green;s function in integral form. Another reason is that according to proof of Eubanks and Sternberg, any three independent Papkovitch-Neuber-Boussinesq functions are required for any geometrical shaped convex domain in 3D space, so the selction of the three functions Bx,Bz,beta are justified. Then, solve the Bx, Bz, beta. After that we use plot software of Mathematica to draw the displacement and stress distribution digrams, and we use FEM software of COSMOS/M to get the numerical solution. Then, we compared the solutions by the analytical solution methods and the finite element solution. We find that results of displacement components and stress components have similar graphs and similar physical similarity. We get similar answers with an accuracy that may be acceptable. The results of this paper may provide some important information for future engineering works.
Relation:	中國民國力學學會90年度年會暨第25屆全國力學會議=Proceedings of 25 National Conference of Theoretical and Applied Mechanics，12頁
Appears in Collections:	[Graduate Institute & Department of Mechanical and Electro-Mechanical Engineering] Proceeding

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