彈性基礎上之尤拉梁的一般勁度矩陣

Abstract

本文係利用結構矩陣法推導彈性基礎上之梁的受力與變位的關係，也就是 求出其勁度矩陣。吾人於推導過程中，係假設土壤為互不影響的線性彈簧 以簡化數學運算。而由於形狀函數採用控制方程式之理論解，故所導出之 勁度矩陣精確度相當高。除了推導勁度矩陣，本文並且利用此矩陣作了一 些常見問題的分析，如剛架結構的分析、固定端彎矩及彈性穩定問題的研 究等等。另外，本文亦對以上問題加以討論，並提出建議。 This paper presents the relations between forces and displacements of beams on the elastic foundation, that is, the stiffness matrix. The approach to the formulation of the stiffness matrix is using the method of structural matrix, which is frequently used for analyzing many structures. The process of formulation is on the assumption that the soil medium is simulated as the uncoupled linear springs such that it simplifies the mathematical calculations. Except for the formulation of previous matrix, presented also analyze some problems about the frame structure, the fixed-end moment, and the elastic stability. Furthermore, presented discusses some topics about above problems and makes suggestions about them.