SYMPLECTIC METHOD FOR DYNAMIC BUCKLING OF CYLINDRICAL SHELLS UNDER COMBINED LOADINGS

2013 ◽  
Vol 05 (04) ◽  
pp. 1350042 ◽  
Author(s):  
JIABIN SUN ◽  
XINSHENG XU ◽  
C. W. LIM
Keyword(s):  
Boundary Conditions ◽  
Impact Load ◽  
Cylindrical Shells ◽  
Dynamic Buckling ◽  
Plane Boundary ◽  
Symplectic Method ◽  
Buckling Modes ◽  
Dual Variables ◽  
Combined Action ◽  
Symplectic System

A symplectic system is developed for dynamic buckling of cylindrical shells subjected to the combined action of axial impact load, torsion and pressure. By introducing the dual variables, higher-order stability governing equations are transformed into the lower-order Hamiltonian canonical equations. Critical loads and buckling modes are converted to solving for the symplectic eigenvalues and eigensolutions, respectively. Analytical solutions are presented under various combinations of the in-plane and transverse boundary conditions. The results indicated that in-plane boundary conditions have a significant influence on this problem, especially for the simply supported shells. For the shell with a free impact end, buckling loads should become much lower than others. And the corresponding buckling modes appear as a "bell" shape at the free end. In addition, it is much easier to lose stability for the external pressurized shell. The effect of the shell thickness on buckling results is also discussed in detail.

Dynamic Buckling of Cylindrical Shells under Axial Impact in Hamiltonian System

2012 ◽  
Vol 13 (1) ◽  
Author(s):  
Jia-Bin Sun ◽  
Xin-Sheng Xu ◽  
Chee-Wah Lim
Keyword(s):  
Hamiltonian System ◽  
Critical Load ◽  
Impact Load ◽  
Dynamic Buckling ◽  
Inertia Force ◽  
Elastic Cylindrical Shell ◽  
Symplectic Method ◽  
Buckling Mode ◽  
Axial Impact ◽  
Dual Variables

AbstractIn this paper, the dynamic buckling of an elastic cylindrical shell subjected to an axial impact load is analyzed in Hamiltonian system. By employing a symplectic method, the traditional governing equations are transformed into Hamiltonian canonical equations in dual variables. In this system, the critical load and buckling mode are reduced to solving symplectic eigenvalues and eigensolutions respectively. The result shows that the critical load relates with boundary conditions, thickness of the shell and radial inertia force. And the corresponding buckling modes present some local shapes. Besides, the process of dynamic buckling is related to the stress wave, the critical load and buckling mode depend upon the impacted time. This paper gives analytically and numerically some new rules of the buckling problem, which is useful for designing shell structures.

Dynamic Buckling of Cylindrical Shells under Axial Impact in Hamiltonian System

2012 ◽  
Vol 13 (1) ◽  
Author(s):  
Jia-Bin Sun ◽  
Xin-Sheng Xu ◽  
Chee-Wah Lim
Keyword(s):  
Hamiltonian System ◽  
Critical Load ◽  
Impact Load ◽  
Dynamic Buckling ◽  
Inertia Force ◽  
Elastic Cylindrical Shell ◽  
Symplectic Method ◽  
Buckling Mode ◽  
Axial Impact ◽  
Dual Variables

AbstractIn this paper, the dynamic buckling of an elastic cylindrical shell subjected to an axial impact load is analyzed in Hamiltonian system. By employing a symplectic method, the traditional governing equations are transformed into Hamiltonian canonical equations in dual variables. In this system, the critical load and buckling mode are reduced to solving symplectic eigenvalues and eigensolutions respectively. The result shows that the critical load relates with boundary conditions, thickness of the shell and radial inertia force. And the corresponding buckling modes present some local shapes. Besides, the process of dynamic buckling is related to the stress wave, the critical load and buckling mode depend upon the impacted time. This paper gives analytically and numerically some new rules of the buckling problem, which is useful for designing shell structures.

An Analytical Symplecticity Method for Axial Compression Plastic Buckling of Cylindrical Shells

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Xinsheng Xu ◽  
Jiabin Sun ◽  
C. W. Lim
Keyword(s):  
Cylindrical Shells ◽  
Compressive Load ◽  
Symplectic Method ◽  
Proportional Loading ◽  
Plastic Buckling ◽  
Buckling Modes ◽  
Rigorous Approach ◽  
Hamilton Variational Principle ◽  
Buckling Behavior ◽  
Bifurcation Buckling

This study is mainly concerned with the analytical solutions of plastic bifurcation buckling of cylindrical shells under compressive load. The analysis is based on the J2 deformation theory with a linear hardening and proportional loading is adopted in the calculation. A symplectic solution system is established and Hamilton's governing equations are derived from the Hamilton variational principle. The basic problem in plastic buckling is converted into solving for the symplectic eigenvalues and eigensolutions, respectively. The obtained results reveal that boundary conditions have a very limited influence on bucking loads but its influence on buckling modes and plastic borders cannot be neglected. Meanwhile, it is demonstrated that the shell material properties significantly affect the plastic buckling behavior. This proposed symplectic method is shown to be a rigorous approach. It also provides a uniform and systematic way to any other similar problems.

Computer Simulation on the Dynamic Buckling of Initial-Defect Plates under Axial Step Load

2015 ◽  
Vol 1094 ◽  
pp. 482-486
Author(s):  
Yu Peng Zong ◽  
Zhi Jun Han ◽  
Guo Yun Lu
Keyword(s):  
Computer Simulation ◽  
Boundary Conditions ◽  
Impact Load ◽  
Time History ◽  
Lower Surface ◽  
Dynamic Buckling ◽  
Axial Impact ◽  
Different Boundary Conditions ◽  
Initial Defect ◽  
Symmetric Point

Computer simulation on the dynamic buckling of different forms of initial-defect and different boundary conditions plates under axial impact load was carried out by using ABAQUS /Standard.The strain-time history curve of the symmetric point of upper and lower surface is give,they are coincidence before the buckling and suddenly separate when the buckling occur which is called be bifurcation,and the critical buckling time is also acquired. The results indicate that the influence of different initial-defect locations and amplitudes on the dynamic buckling is very great.

A SYMPLECTIC HAMILTONIAN APPROACH FOR THERMAL BUCKLING OF CYLINDRICAL SHELLS

2010 ◽  
Vol 10 (02) ◽  
pp. 273-286 ◽  
Author(s):  
XINSHENG XU ◽  
HONGJIE CHU ◽  
C. W. LIM
Keyword(s):  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Thermal Buckling ◽  
Symplectic Space ◽  
Critical Temperatures ◽  
Buckling Modes ◽  
Uniform Temperature Field ◽  
Geometric Boundary ◽  
Natural Boundary Conditions ◽  
Symplectic Eigenvalue

The paper deals with the thermal buckling of cylindrical shells in a uniform temperature field based on the Hamiltonian principle in a symplectic space. In the system, the buckling problem is reduced to an eigenvalue problem which corresponds to the critical temperatures and buckling modes. Unlike the classical approach where a predetermined trial shape function satisfying the geometric boundary conditions is required at the outset, the symplectic eigenvalue approach is completely rational where solutions satisfying both geometric and natural boundary conditions are solved with complete reasoning. The results reveal distinct axisymmetric buckling and nonaxisymmetric buckling modes under thermal loads. Besides, the influence for different boundary conditions is discussed.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

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