圓管在循環彎曲負載下力學行為之理論研究

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

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為（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為。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為。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。

The purpose of this paper is to use the endochronic theory combinedwith the principle of virtual work to simulate the mechanical behavior (therelationship of bending moment, curvature and ovalization) of two differentcircular tubes, namely a SAE-4130 low-alloy steel tube and a 7075-T6aluminum alloy tube, subjected to cyclic bending. In this study, based onthe uniaxial stress-strain relationship of these two materials (known experimentaldata), the corresponding material constants of the endochronictheory is determined. By substituting the constants into the calculationstructure of the endochronic theory, combined with the principle of virtualwork, the mechanical behavior of circular tubes can be obtained. Next, twotypes of FEM analysis software, ANSYS and ABAQUS are used to simulatethe mechanical behavior of the materials under the same loadingconditions. It is found that the simulation results are very close to thosepredicted by the endochronic method presented in this work.