圓管在循環彎曲負載下力學行爲之理論研究

Theoretical Analysis on Mechanical Behavior of Circular Tubes Subjected to Cyclic Bending

徐日豐(Ri-Fong Shie) ； 徐建民(Chien-Min Hsu) ； 潘文峰(Wen-Fung Pan)

《技術學刊》 20卷3期 (2005/09) Pp. 305-314

https://doi.org/10.29507/JT.200509.0010

摘要

本文是將內涵時間理論結合虛功原理延伸去描述兩種圓管，SAE-4130低合金鋼管及7075-T6鋁合金管，在循環彎曲負載下所呈現的力學行爲（彎矩、曲度及橢圓化關係）。本文分析流程是先根據兩種材料的單軸應力－應變關係（已知的實驗數據），來求得內涵時間理論所對應的材料常數，再將該常數代入內涵時間理論結合虛功原理的運算架構中，來求得圓管在循環彎曲負載下的力學行爲。接著，本文以兩種有限元素分析軟體，ANSYS及ABAQUS，來分析相同的兩種材料在相同的負載狀況的力學行爲。結果顯示，兩種分析軟體所描述的結果和內涵時間方法所描述的結果相當接近。

關鍵字

內涵時間理論 ； 虛功原理 ； 圓管 ； 循環彎曲 ； 力學行爲 ； 有限元素分析軟體ANSYS ； 有限元素分析軟體ABAQUS

並列摘要

The purpose of this paper is to use the endochronic theory combined with the principle of virtual work to simulate the mechanical behavior (the relationship of bending moment, curvature and ovalization) of two different circular tubes, namely a SAE-4130 low-alloy steel tube and a 7075-T6 aluminum alloy tube, subjected to cyclic bending. In this study, based on the uniaxial stress-strain relationship of these two materials (known experimental data), the corresponding material constants of the endochronic theory is determined. By substituting the constants into the calculation structure of the endochronic theory, combined with the principle of virtual work, the mechanical behavior of circular tubes can be obtained. Next, two types of FEM analysis software, ANSYS and ABAQUS are used to simulate the mechanical behavior of the materials under the same loading conditions. It is found that the simulation results are very close to those predicted by the endochronic method presented in this work.

並列關鍵字

endochronic theory ； principle of virtual work ； circular tubes ； cyclic bending ； mechanical behavior ； FEM analysis software ANSYS ； FEM analysis software ABAQUS