轴向拉伸细长杆的非线性力学模型  

A Nonlinear Mechanical Model for Extensible Slender Rods

作　　者：马刚[1] 孙丽萍[1] 艾尚茂[1] 王宏伟[1] 

机构地区：[1]哈尔滨工程大学船舶工程学院,哈尔滨150001

出　　处：《应用数学和力学》2015年第4期371-377,共7页Applied Mathematics and Mechanics

基　　金：黑龙江省科学基金(QC2014C049);中央高校基本科研业务费专项资金(HEUCFD1402;HEUCFD1424);高等学校博士学科点专项科研基金新教师类资助课题(20132304120008);高等学校学科创新引智计划(B07019)

摘　　要：聚酯系泊缆是深海工程中具备一定抗弯刚度、易拉伸变形的细长杆件结构.聚酯缆的轴向变形属大拉伸范畴,分析中应当区分变形前后状态,特别是缆索长度的改变使得基于小拉伸假设的细长杆模型需要予以改进.因此,基于Garrett细长杆模型,应用总体坐标和斜率取代Euler-Bernoulli(欧拉-伯努利)梁元的转角,解决缆索在空间中大转动变形的几何非线性问题;使用轴向拉伸变形前后物质点对应的方法,借助单元两个节点和一个中点,以及3个二次多项式形函数描述轴向拉伸变形下细长杆元的运动微分方程.通过与轴向拉伸悬臂梁的对比分析,验证了该拉伸杆元的收敛性和准确性.The polyester mooring line is a flexible rod liable to axial extension and bending de- formation. Due to its large axial deformation in tension, the polyester line＇ s deformed configu- rations shall be distinguished from the undeformed ones, and the slender rod model based on the small extension hypothesis shall be improved in view of its nonnegligible length change. The global coordinates and slopes were used to replace the rotation angles in the Euler-Bernoulli beam to deal with the geometrically nonlinear problem of large spatial rotation based on Gar- rett＇ s slender rod theory. Then the point-to-point mapping method was proposed to correlate the 2 configurations before and after axial extension in the slender rod theory, with 2 element nodes, 1 intermediate point and 3 quadratic polynomial combined to derive the differential equations of motion for the slender rod element in tension. Through comparison between the numer- ical results and the analytical solution Of an extensible cantilever beam example, convergence and accuracy of the proposed model are proved.

关 键 词：轴向拉伸 细长杆 非线性 聚酯缆 大转动 

分 类 号：O342[理学—固体力学]