Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/18176
標題: 等效系統法於厚度變化矩形板之分析
EQUIVALENT SYSTEMS FOR VARIABLE THICKNESS RECTANGULAR PLATES
作者: 彭及忠
PENG, CHI-CHUNG
關鍵字: EQUIVALENT SYSTEMS;等效系統法;VVARIABLE THICKNESS;RECTANGULAR PLATE;厚度變化;矩形板
出版社: 應用數學系
摘要: 
本文是藉由等效系統法探討沿著二維方向厚度變化之矩形板問題.厚度變
化之矩形板,其原始之平衡方程式因有變系數之柔度,所以無法輕易去解其
撓度, 藉由等效系統法我們可用常係數之柔度代換變系數之柔度, 以降低
厚度變化矩形板之平衡方程式數學上解其微分方程式計算的複雜性,因為
常系數柔度之 等效系統法可用數學式導出和證明.此外 ,等效系統法計算
上會產生高階之無窮級數,我們用誤差比較的方法得到一個近乎精確值的
計算公式命名為簡式等效系統法.於此為了避免材料破壞,我們可使用等效
系統法及簡式等效系統法分析厚度變化矩形板其抵抗負荷應力及變形的能
力而在工程應用上建立一個可用,實際,臨界極限的範圍.

The problem of rectangular plates with variable thickness
along two directions is solved by using the method of
equivalent systems. The original differential equation for
plates with variable thickness is difficult to solve due to the
non-constant flexural rigidity. By using the method of
equivalent systems, we permit the replacement of the original
variable flexural rigidity with uniform flexural rigidity to
reduce the mathematical complexity of the variable thickness
problem. The equivalent systems of uniform flexural rigidity
are derived and proved mathematically. To facilitate the
mathematical computations, an accurate approximation is named
after the simplified equivalent systems by simplifying the
equivalent systems which is developed for eliminating complexity
of the high order series expansion. The variable rectangular
plate can be analyzed in both equivalent systems and simplified
equivalent systems for fear of failure, thus permitting
observation of progressive deterioration of the plate's ability
to resist load, stress, and deformation, and establishing
useful, practical, critical limits in engineering application.
URI: http://hdl.handle.net/11455/18176
Appears in Collections:應用數學系所

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