Dynamic Buckling Of Elastic Cylindrical Shells In Hamiltonian System

The stability of structure is an important research subject in solid mechanics, and much attention is focused on the problem in industry equipments, especially in aerospace now. Since cylindrical shell is a basal structure, its buckling problem is playing an important role in the theories of structural stability. The research of instability has achieved a lot of results and solved a lot of practical problems. But the solution and mechanism for dynamic buckling of cylindrical shells in the effect of coupling stress wave is very hard to research, especially for non-axisymmetric buckling in symmetric structure and load. So it is necessary to present a new research method.Impact load is a familiar dynamic load. It propagates and reflects as a stress wave in structure under the affect of inertia and transform of structures and time effect. The speeds of different kinds of stress waves(such as compressed stress wave and torsional stress wave) are unequal under coupled impact load. So the internal forces in structure are different between different areas, and the boundaries of these areas are changing with time. It is a characteristic of this paper that dynamic buckling of cylindrical shells at complicated stress is researched.The research of dynamic buckling is so difficult because the high-order partial differential equations are very hard to be solved. The traditional method for high-order partial differential equations is limited. It does not fit universal problems, and the solution space is not complete. When the Hamiltonian system is introduced into the research of dynamic buckling in cylindrical shells, the problem uses dual variables in Symplectic space instead of variables in traditional Euclidean space. The symplectic eigenfunction expansion method gives out an exact solution space. So many problems are solved, which can not find the solution in traditional methods.In this paper, the fundamental problems of the dynamic buckling in cylindrical shells are axial impact, torsion impact and coupling impact. The dual variables in symplectic space are gotten from energy function, and the Hamiltonian system is established. The critical buckling loads and buckling modes are described by eigenvalues and eigensolutions in symplectic space. The zero-eigensolutions describe axisymmetric buckling and non-zero eigensolutions describe non-axisymmetric buckling. The bifurcation condition of front buckling is obtained from the boundary and continuous conditions of dual variables, and partial differential equation is converted to linear equations. The eigenvalues and eigensolutions are given out to describe the critical buckling loads and buckling modes.Numerical results show the critical buckling loads and buckling modes of cylindrical shells under axial impact, torsion impact and coupling impact. The pictures show that the critical buckling loads and buckling modes of cylindrical shells are affected by boundary conditions. The form of coupled impact load decides the critical buckling load curves and critical buckling modes. The critical buckling modes have special forms that according to characteristics of propagation and reflection of stress wave. Material constants and geometry parameters also have effects on the rule of critical buckling load.The symplectic eigensolutions are conjugated and orthogonal in Hamiltonian system and the solution space is complete. So all buckling forms can be assembled by symplectic eigensolutions and their conjugated eigensolutions. The symplectic method and its results are useful for post-buckling questions that are non-linear and large-deformation. This method can also be extended to other research fields.