轴压-扭矩耦合载荷下功能梯度圆柱壳屈曲问题的辛方法  

Symplectic Method for Buckling of Functionally Graded Cylindrical Shells under Combined Axial Compression and Torsion

作　　者：张宏宇 白海峰 左忠义[4] ZHANG Hongyu;BAI Haifeng;ZUO Zhongyi(School of Mechanical Engineering,Dalian Jiaotong University,Dalian 116028,China;Dalian Rail Transit Design Institute Co.,Ltd,Dalian 116021,China;School of Civil Engineering,Dalian Jiaotong University,Dalian 116028,China;School of Traffic and Transportation Engineering,Dalian Jiaotong University,Dalian 116028,China)

机构地区：[1]大连交通大学机械工程学院,辽宁大连116028 [2]大连轨道交通设计院有限公司,辽宁大连116021 [3]大连交通大学土木工程学院,辽宁大连116028 [4]大连交通大学交通运输工程学院,辽宁大连116028

出　　处：《大连交通大学学报》2023年第3期52-57,62,共7页Journal of Dalian Jiaotong University

基　　金：辽宁省科学技术计划项目(2021JH4/10100061)。

摘　　要：为了对功能梯度圆柱壳在轴压-扭矩耦合载荷作用下的屈曲问题进行研究,基于Donnell薄壳理论,建立了屈曲问题的哈密顿求解体系,将问题从传统的欧几里得空间表述转变为辛对偶空间表述。采用分离变量法求解哈密顿正则方程,将原问题的求解归结为求解辛空间下的本征值和本征解,从而获得解析的临界载荷和屈曲模态。数值算例中通过与有限元结果对比,验证了该方法的准确性,并分析了载荷比例、尺寸参数、材料参数以及轴压/扭矩等关键参数对临界载荷和屈曲模态的影响。The buckling of functionally graded cylindrical shells under axial compression-torsion coupling loads is investigated.The Hamiltonian system of buckling problem is established based on Donnell's thin shell theory,and the problem is transformed from the traditional Euclidean space to the symplectic dual space.The Hamiltonian equation is solved by the separated variable method,and the solution of original problem is reduced to solving the eigenvalues and eigensolutions in symplectic space.Thus,the analytical critical loads and buckling modes are obtained.In the numerical example,the accuracy of the proposed method is verified by comparing with the finite element results,and the effects of key parameters such as load ratio,geometric parameters,material parameters and axial compression/torsion on the critical loads and buckling modes are discussed.

关 键 词：圆柱壳 屈曲 耦合载荷 功能梯度材料 辛方法 

分 类 号：TB34[一般工业技术—材料科学与工程]