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An accurate model for vibration of a porous magneto-electro-thermo-elastic functionally graded (METE-FG) cylindrical shell made of barium titanate (BaTiO3) and cobalt diiron tetraoxide (CoFe2O4) with magneto-electro-thermal loadings is proposed within the framework of Hamiltonian system. Four types of porosity distribution profiles in the thickness direction are considered. By introducing a new total eigenvector, the higher-order governing differential equations are transformed into a set of lower-order equations. The exact solution for free vibration of METE-FG shells can be expanded in terms of specific symplectic eigenfunctions having seven possible explicit forms. Subsequently, analytical frequency equations and vibration mode shapes for METE-FG shells with various boundary conditions are derived simultaneously. A comparison study is presented to demonstrate the accuracy of the proposed model and very good agreement is observed. The effects of material properties and magneto-electro-thermal loadings on free vibration characteristics of METE-FG cylindrical shells are analyzed and discussed in detail.

By considering the pre-buckling effect and in-plane constraint, an accurate nonlinear buckling analysis of a functionally graded porous graphene platelet reinforced composite cylindrical shells under axial compressive load is performed. The stability equation is established according to a unified shell theory including the classical thin shell theory and the high-order shear deformation theory. Three types of porosity distributions and graphene platelet reinforced patterns are considered, and the modified Halpin–Tsai model and rule of mixtures are employed to determine their effective material properties. Explicit expressions of buckling equations for clamped or simply supported boundary conditions are obtained by the Galerkin's method. Highly accurate critical buckling loads and analytical buckling mode shapes are obtained simultaneously. A comparison between theoretical prediction and experiment is presented to verify the present method and very good agreement is reported. The influences of material properties on the buckling behaviors are also extensively investigated. It is recommended that the symmetric dispersion pattern is the optimal material distributions for both graphene platelets and porous, and the largest possible weight fraction, specific surface area and average thickness of graphene platelets could induce a better anti-buckling performance for the nanocomposite shell.

An accurate nonlinear buckling model for functional graded multilayer hybrid composites cylindrical shells under combined loads is proposed. A two-steps micromechanical approach including Halpin-Tsai and Mori-Tanaka method is employed to obtain the effective material properties of hybrid composites. A unified shell theory including Donnell's shell theory, first-order shear deformation theory and high-order shear deformation theory are adopted to derive the governing buckling equations. The axisymmetric pre-buckling deformation is taken into consideration in the solution procedure. Highly accurate critical buckling loads and analytical buckling mode shapes are obtained by Galerkin's method. The accuracy of the present solutions is validated by comparing with results of existing literature and numerical simulations. Effects of influencing parameters of reinforcements and their interactions on the structural stability of the hybrid composites cylindrical shells are revealed. Keywords: Functionally graded material, Hybrid composite, Cylindrical shell, Buckling, Critical buckling load

Buckling behaviors of shear deformable grid-stiffened functionally graded cylindrical shells are investigated under the combined compressive and thermal loads. The governing equations are established on the basis of Reddy's higher-order shear deformation theory. For the perfect grid-stiffened cylindrical shells, separation of variables is employed to obtain the accurate buckling solutions. Then, according to the derived mode functions, Galerkin's solving procedure is conducted for shells including the initial geometric imperfection. The effects of geometric parameters, properties of FGMs and temperature fields on the anti-buckling performances of grid-stiffened shells are concerned under the clamped boundary condition. Besides, imperfection sensitivities for various reinforced grids are discussed in detail.

This article is mainly focused on accurate solutions for axial impact buckling of functionally graded cylindrical shells in a heated environment. A new analytical methodology is developed, and a rigorous solving procedure is conducted to guarantee the accuracy of the obtained results. Various aspects related to boundary conditions, geometric parameters, material properties and temperature variations are investigated systematically. The numerical results reveal that in-plane boundary conditions have an obvious influence on the shell. If the reflection of stress waves occurs, critical stresses should further decrease with the interaction of incident and reflected waves. The ability of FGCSs in resisting buckling failure can be improved by controlling the material exponent.

The precise estimation of the cutting force coefficients in milling is very important, which has great impact on the precise calculation of the milling forces and the stability lobes of the system. On the basis of the imprecise estimation of cutting force coefficients in milling of thin-walled part using cutter with different tooth radii, the calculation process of actual cutting force coefficients is proposed in this article. First, based on the different amplitudes of milling forces caused by the long and short teeth of cutter, the nominal milling forces and nominal cutting force coefficients are constructed, and the radii error of the long and short teeth of cutter is calculated. Then, actual cutting force coefficients are derived based on radii error of cutter teeth. Finally, an experiment is performed to verify the validity of the calculation process of actual cutting force coefficients proposed in this article, and the results show that the actual cutting force coefficients obtained by consideration of radii error are more effective than theoretical cutting force coefficients obtained without consideration of radii error in the calculation of milling forces.

Exact solutions for the torsional bifurcation buckling of functionally graded (FG) multilayer graphene platelet reinforced composite (GPLRC) cylindrical shells are obtained. Five types of graphene platelets (GPLs) distributions are considered, and a slope factor is introduced to adjust the distribution profile of the GPLs. Within the framework of Donnell’s shell theory and with the aid symplectic mathematics, a set of lower-order Hamiltonian canonical equations are established and solved analytically. Consequently, the critical buckling loads and corresponding buckling mode shapes of the GPLRC shells are obtained. The effects of various factors, including the geometric parameters, boundary conditions and material properties on the torsional buckling behaviors are investigated and discussed in detail.

In this paper, the buckling behaviors of cylindrical shells made of a new kind of carbon fiber reinforced polymer (CFRP) and coated with functionally graded polymeric material (FGPM) are investigated. The fundamental equations of a moderately-thick shell are established within the framework of Reddy’s higher-order shear deformation theory (HSDT). The material model is derived by combining the conventional micro-mechanical CFRP model with the hybrid FGPM model. Micro-crack damage in CFRP core is included via the damage variables. The buckling compressive stresses of the shells exposed to the thermal environment are obtained by the Galerkin’s method. The solutions reveal that the lay-up sequence of the laminas and the thickness ratio of the FGPM coating to CFRP core have significant influence on the computed results. The variation of the buckling loads with respect to the content of carbon fiber and distributed profile of the FGPM components follows some nonlinear laws. The structural instability induced by damages appear to be more remarkable with the increased shell thickness. However, this effect can be reduced by optimizing the ply angles of the stacking laminas. More factors, such as geometric parameters, numbers of fiber layers, lamina stacking sequences, damage, material properties and thermal loads, are also discussed in detail.

This paper derives new analytical solutions for thermal bifurcation buckling of cylindrical shells made of functionally graded materials (FGMs) with temperature-dependent material properties. The Donnell’s shell theory is adopted and a symplectic solution methodology is established through the Hamiltonian variational principle. The fundamental buckling problem is then converted into the solving for the symplectic eigenvalues and eigenvectors. The solutions reveal that boundary conditions and temperature-dependent FGM properties have significant influence on thermal buckling behavior. It is also concluded that temperature field conditions cannot be neglected for FGCSs being rich in thermal sensitive compositions.

By considering the effect of stress waves in a Hamiltonian system, this paper treats dynamic buckling of an elastic cylindrical shell which is subjected to an impact torsional load. A symplectic analytical approach is employed to convert the fundamental equations to the Hamiltonian canonical equations in dual variables. In a symplectic space, the critical torsion and buckling mode are reduced to solving the symplectic eigenvalue and eigensolution, respectively. The primary influence factors, such as the impact time, boundary conditions and thickness, are discussed in detail through some numerical examples. It is found that boundary conditions have limited influence except free boundary condition in the context of the scope in this paper. The localization of dynamic buckling patterns can be observed at the free end of the shell. The new analytical and numerical results serve as guidelines for safer designs of shell structures.

This study concerns a theoretical analysis on the buckling of cylindrical shells under axial compression in a new energy conservative symplectic system. By introducing four pairs of dual variables and employing the Legendre transformation, the governing equations that are expressed in stress function and radial displacement are re-arranged into Hamiltonian’s canonical equations. The critical loads and buckling modes are reduced to solving for symplectic eigenvalues and eigensolutions, respectively. The obtained results conclude that buckling solutions are mainly grouped into two types according to their nature of different buckling modes: non-uniform buckling with deflection localized at the vicinity of the ends and uniform buckling with deformation waves distributed uniformly along the axial direction, and the complete solving space only consists of the basic eigensolutions. The influence of geometric parameters and boundary conditions on the critical loads and buckling modes is discussed in detail, and some insights into this problem are analyzed.

A symplectic approach is developed within the perspective of stress wave propagation to study theoretically the localization of dynamic buckling of a cylindrical shell subjected to an axial impact. In this analysis, a set of lower-order fundamental equations, the Hamiltonian canonical equations, is presented in dual variables. Subsequently, the critical load and buckling mode are reduced to solving the symplectic eigenvalue and eigensolution, respectively. The result shows that the localization of dynamic buckling patterns in the elastic shell is mainly caused by the relaxation of boundary conditions. With stress wave propagation and no reflection, the corresponding buckling mode deformation should exist near the impact end. This behavior has significant influence on the reduction of dynamic buckling loads. In conclusion, this paper provides some new analytical and numerical rules for dynamic buckling and the new results are useful in the critical design of shell structures against 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.

Buckling behavior of cylindrical shells subjected to combined pressure, torsion and axial compression is presented by employing a symplectic method. Both symmetric and non-symmetric boundary conditions are considered. Hamiltonian canonical equations are established by introducing four pairs of dual variables. Then, solution of fundamental equations is converted into a symplectic eigenvalue problem. It is concluded that the influence of pressure on buckling solutions is more significant than that due to compressive load, in particular for a longer external pressured cylindrical shell. Besides, buckling loads and circumferential wavenumbers can be reduced greatly by relaxed in-plane axial constraints.

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.