Dynamic And Thermal Buckling Of Cylindrical Shells In Hamiltonian System

Cylindrical shell is a basic structure of solid mechanics. Its buckling problem is important in the theories of structural stability and much attention has focused on the problem in industrial production and daily life. Many research of instability has been carried out and applied to many practical problems. Because of different characters of thermal load and impact load, the buckling phenomena of cylindrical shells are different. Therefore, it is necessary to study dynamic buckling of shells under combined action of both thermal load and mechanical impact load.In the Lagrangian system, the research of dynamic pre-buckling is so difficult, because there are not appropriate methods to solve the high-order partial differential equations and the solution space is not complete. On the basis of structural mechanics theory, the Hamiltonian system is introduced to research the pre-buckling of cylindrical shell. The research of pre-buckling problem is transited from Euclidean space to Symplectic space. Then higher-order partial differential equation and numerical method are solved.With the aid of stress wave and bifurcation theory, this paper deals with pre-buckling of cylindrical shells subjected to thermal load, mechanical impact load, or thermal-mechanical impact coupling loads. The Hamiltonian system is established by energy function. In the Simplistic space, eigenvalues and eigensolutions are equal to the critical buckling loads and buckling modes of the problem. By solving the disturbed equations, the bifurcation condition of the dynamic buckling, critical buckling load and buckling mode were obtained.The critical buckling loads and buckling modes of shells under thermal, mechanical impact or thermal-mechanical coupling loads are presented. The main influential factors of dynamic buckling in shells are analyzed. Numerical results show that local buckling depends on the local effects of stress waves when shells are impacted. Shells in fixed or simple support appear different buckling modes and loads. Thermal load and mechanical loads influence each other, and both of them determine the dynamic buckling of shells. The more kings of loads, the more complex of buckling process. Physical constants and geometric parameters also have effects on the laws of critical buckling loads and modes. The conclusions provide important data and theoretical basis for prediction of heat-durability and thermal-mechanical inflection capacity and structure stability design of cylindrical shells. The innovation points are that the superposition of thermal load and mechanics loads is carried out by mean of linear thermal stress theory. The Hamiltonian system separately is introduced to research the pre-buckling of cylindrical shells under thermal load and thermal-mechanics coupling loads.