受扭椭圆截面直杆的弹塑性理论分析  

Elastoplastic Theoretical Analysis of StraightBars with Torsional Elliptic Cross Section

作　　者：陈彦 孙云[2] 陈允 CHEN Yan;SUN Yun;CHEN Yun(School of Civil Engineering,Yangzhou Polytechnic College,Yangzhou 225000,China;College of Architectural Science and Engineering,Yangzhou University,Yangzhou 225000,China)

机构地区：[1]扬州市职业大学土木工程学院,江苏扬州225000 [2]扬州大学建筑科学与工程学院,江苏扬州225000

出　　处：《常州工学院学报》2024年第5期8-17,共10页Journal of Changzhou Institute of Technology

基　　金：国家自然科学基金(12102380)。

摘　　要：在理想弹塑性力学模型下,从计算受扭椭圆截面直杆的屈服扭矩开始,分析截面弹性区与塑性区分界线的变化情况,根据平面点到直线距离的计算公式,用解析法推导计算椭圆截面扭矩的二重积分表达式,并运用广义极坐标变换将椭圆区域的积分转化为对单位圆区域的积分,得到两类弹塑性状态和塑性极限状态下扭矩的计算式。根据第一类完全椭圆积分在不同离心率下的数值分析受扭椭圆截面直杆极限扭矩与屈服扭矩的比值关系,计算直杆在两类弹塑性状态和塑性极限状态下卸载后横截面的残余应力,并编程给出相应残余应力在广义极坐标下的函数图像,最后计算出受扭椭圆截面直杆在弹塑性状态下卸载后的残余扭转角。Under the ideal elastic-plastic mechanics model,the variation of the elastic region and the plastic boundary of the section is analyzed from the calculation of the yield torque of a straight bar with torsional elliptic section.According to the calculation formula of the distance between the plane point and the straight line,the double integral expression of the elliptic section torque is derived by the analytical method.The integral of the elliptic region is transformed into the integral of the unit circle region by the generalized polar coordinate transformation,and the formula of torque in two kinds of elastic-plastic state and plastic limit state is obtained.According to the numerical analysis of the ratio relationship between the ultimate torque and yield torque of the torsional elliptic cross section of the straight bar under different eccentricity of the first kind of complete elliptic integral,the residual stress of the cross section after the straight bar is unloaded under two kinds of elastic-plastic state and the limit state is calculated,and the function image of the corresponding residual stress under generalized polar coordinates is programmed.Finally,the residual torsion angle of the torsional elliptic straight bar after unloading under elastoplastic condition is calculated.

关 键 词：屈服扭矩 广义极坐标变换 极限扭矩 第一类完全椭圆积分 残余应力 残余扭转角 

分 类 号：O344.3[理学—固体力学]