阶梯圆柱壳屈曲问题的哈密顿方法

Hamiltonian method for stepped cylindrical shell buckling

为研究工程中常见阶梯圆柱壳结构的屈曲行为,利用对偶变量关系建立了哈密顿体系下的屈曲模型.基于阶梯区域的连续性条件及端部条件,将圆柱壳临界载荷和屈曲模态归结为哈密顿体系下的广义辛本征值和辛本征解表述.利用该模型研究了阶梯区域的深度、宽度和中心位置对圆柱壳临界荷载和屈曲模态的影响.研究结果表明:临界荷载和屈曲模态对阶梯区域的深度和宽度较为敏感,当阶梯区域尺寸大于一定程度后,壳体会发生局部屈曲现象.该研究方法具有显式和简捷的特点,可为阶梯圆柱壳的精确屈曲评估提供理论依据.

In order to analyze the buckling behavior of stepped cylindrical shell which is common in engineering,a buckling model under the Hamiltonian system is established by using the dual variable relationship.Based on the continuity condition of the step position and boundary condition of the end,the critical loads and buckling modes are reduced to generalized symplectic eigenvalue and symplectic eigensolution under the Hamiltonian system.The influence of the depth,width and center position of the stepped region on critical load and buckling mode of cylindrical shell is investigated.The research results show that the critical load and buckling mode are sensitive to the depth and width of the stepped region,and when the size of the stepped area is larger than a certain value,local buckling will occur.The proposed method is of explicitness and simplicity,which can provide theoretical bassis for the accurate buckling evaluation of stepped cylindrical shells.