辛方法在弹性圆板屈曲问题中的应用  

Symplectic Method with Application to Circular Elastic Plate Buckling

作　　者：徐新生[1] 邱文彪[1] 付月[1] 周震寰[1] 褚洪杰[1] 

机构地区：[1]大连理工大学,大连116024

出　　处：《应用力学学报》2009年第3期530-534,共5页Chinese Journal of Applied Mechanics

基　　金：国家973项目(10672031);博士学科点基金(20060141008)

摘　　要：在辛几何空间中将临界载荷和屈曲模态归结为辛本征值和本征解问题,从而形成一种辛方法。研究和讨论了轴对称屈曲和非轴对称屈曲问题,它们分别属于零本征值问题和非零本征值问题。以弹性圆板屈曲问题作为研究对象,借助于系统的能量构造出哈密顿体系,得到了该体系下的所有的本征解。数值结果给出了圆板和圆环板问题的临界载荷和屈曲模态。数值结果表明:对应低阶屈曲模态的临界载荷相对较小且屈曲模态在周向的波纹数也较少,说明在屈曲过程中低阶屈曲模态容易出现,特别是轴对称屈曲更容易发生;对应较大分支数的临界载荷,其值相对较大且屈曲模态在径向的波纹更加复杂;同时物理常数和几何参数也会直接影响临界载荷的大小。A Hamiltonian system is presented for buckling of elastic circular plates with the aid of the energy of the structure. In the symplectic space, critical loads and buckling modes are reduced to find eigenvalues and eigensolutions. All eigensolutions are obtained. The axisymmetric buckling and non-axisymmetric buckling arediscussed and classified into the problems of zero-eigenvalue and non-zero-eigenvalues respectively. The numerical examples show critical loads and buckling modes of circular plates and annular plates. And the critical load, which the buckling mode of the lower order corresponds with, is the smaller and the mode appears easily, especially the axisymmetric mode. Contrarily, for the higher branch, the critical load is increased and the buckling mode is complex. Besides, physical constants and geometric parameters influence critical loads directly.

关 键 词：弹性圆板 屈曲 哈密顿体系 辛方法 

分 类 号：O343.9[理学—固体力学]