Nonlinear finite element analysis of a laminated cylindrical shell with transverse matrix cracks

A clamped laminated cylindrical shell is presented to investigate nonlinear structural behavior involving geometrically nonlinear deformation. In the investigation, transverse matrix cracks are considered in the stiffness of the laminated cylindrical shell. Stiffness degradation is examined for several laminated angles and transverse crack density. Micro-mechanics theory on the composite material was used to derive the degraded stiffness of the laminated cylindrical shell due to the crack density. Iterative numerical scheme was developed to calculate the degraded composite stiffness which is a complicated relation with the crack density. A nonlinear finite element program was developed using 3-D degenerated shell element and the fist order shear deformation theory to consider the large deformation of the clamped laminated cylindrical shell. The updated Lagrangian method is used for nonlinear finite element analysis. Nonlinear structural responses of the laminated cylindrical shell were examined for various stacking sequences and crack density under transversely loaded pressure. Also, the effect of crack opening/closed was considered in the examination. Through this study, it is realized that the transverse matrix crack causes moderate stiffness reduction and affects the responses of the composite shell.     

Buckling of shallow spherical shells including the effects of transverse shear deformation

The large deflection equation of a shallow spherical shell under uniformly distributed transverse loads is established in this paper with consideration of effects of transverse shear deformation on flexural deformation. Using an updated iteration method, an analytical solution for nonlinear stability of a shallow spherical shell is obtained. Formulae for estimating the critical buckling loads are presented for two types of boundary conditions. Discussions on the influences of the geometric and physical parameters on the critical buckling loads are given.     

Nonlinear finite element analysis of composite shell under impact

Large deflection dynamic responses of laminated composite cylindrical shells under impact are analyzed by the geometrically nonlinear finite element method based on a generalized Sander’s shell theory with the first order transverse shear deformation and the von-Karman large deflection assumption. A modified indentation law with inelastic indentation is employed for the contact force. The nonlinear finite element equations of motion of shell and an impactor along with the contact laws are solved numerically using Newmark’s time marching integration scheme in conjunction with Akay type successive iteration in each step. The ply failure region of the laminated shell is estimated using the Tsai-Wu quadratic interaction criteria. Numerical results, including the contact force histories, deflections and strains are presented and compared with the ones by linear analysis. The effect of the radius of curvature on the composite shell behaviors is investigated and discussed.     

Postbuckling of cross-ply laminated cylindrical shells with piezoelectric actuators under complex loading conditions

A postbuckling analysis is presented for a cross-ply laminated cylindrical shell with piezoelectric actuators subjected to the combined action of mechanical, electric and thermal loads. The temperature field considered is assumed to be a uniform distribution over the shell surface and through the shell thickness and the electric field is assumed to be the transverse component E_z only. The material properties are assumed to be independent of the temperature and the electric field. The governing equations are based on the classical shell theory with a von Kármán–Donnell-type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of hybrid laminated cylindrical shells. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical thin shells with fully covered or embedded piezoelectric actuators subjected to combined mechanical loading of external pressure and axial compression, and under different sets of thermal and electric loading conditions. The effects played by temperature rise, applied voltage, shell geometric parameter, stacking sequence, as well as initial geometric imperfections are studied.     

Nonlinear bending response of laminated composite spherical shell panel with system randomness subjected to hygro-thermo-mechanical loading

In the present paper, the effect of random system properties on transverse nonlinear central deflection of laminated composite spherical shell panel subjected to hygro-thermo-mechanical loading is investigated. System properties such as material properties, thermal expansion coefficients, hygro-contraction coefficients, load intensity and lamina plate thickness are taken as independent random variables. The higher order shear deformation theory and von-Karman nonlinear kinematics are used for basic mathematical formulation. The elastic and hygrothermal properties of the composite material, which are considered to be dependent on temperature and moisture concentration, have been obtained based on micromechanical modeling. A direct iterative based C⁰ nonlinear finite element method combined with mean centered first-order perturbation technique (FOPT) proposed by present authors for the plate is extended for the spherical shell panel subjected to hygro-thermo-mechanical loading. The influences of random system properties with plate geometry, stacking sequences, support conditions, fiber volume fraction and temperature, and moisture distributions on the response of laminated spherical shell panel are examined in detail. The performance of the proposed approach is validated through comparison with those available in the literature and independent Monte Carlo simulation (MCS).     

变截面悬臂层合板几何非线性分析

采用三维曲面退化等参板壳单元，考虑了横向剪切效应，对复合材料变截面悬臂层合板几何非线性进行了计算，分析了变截面对变形的影响，并与现有的试验结果进行了比较。     

Linear and nonlinear vibration analysis of sandwich cylindrical shell with constrained viscoelastic core layer

Damping characteristics of three-layered sandwich cylindrical shell for thin and thick core viscoelastic layers are studied using semi-analytical finite element method. The finite element method is developed based on the linear and nonlinear variations of the displacement distribution through the thickness of the core layer. Transient vibration has been conducted using the developed linear and nonlinear models and shown that the nonlinear formulation exhibits more damping property than the linear model. The effect of geometric nonlinearity due to the large deformation of the shell has also been considered assuming small strain and moderate rotation. Different assumptions based on the continuity and discontinuity in transverse shear stresses and slope of in-plane displacements are considered in the finite element formulation and their effects have been investigated. Considering nonlinearity of eigenvalue problem due to the frequency dependent property of viscoelastic material, an efficient algorithm has been developed to find the natural frequencies and loss factors of the viscoelastic cylindrical shell considering large deformation. The effect of imperfect bonding between the layers has also been investigated in the modeling and it is shown that slippage between layers at the interfaces leads to reduction in loss factor at the majority of modes.     

A high-order shear element for nonlinear vibration analysis of composite layered plates and shells

This paper introduces a family of high-order facetted shell elements for linear and nonlinear stress and vibration analysis of composite layered plate and shell structures. Engineering slope angles are employed in element equations, and transverse stresses are expanded over the thickness. The lateral deflection is modelled by conforming or non-conforming Hermitian shape functions, within rectangular or paralellogrammic and triangular elements. Nonlinear terms associated with geometrical nonlinearity are also derived using a practical approach based upon the actual components of strain. A finite element programming package was designed employing the newly developed elements. Several case studies have been investigated and package results were compared with existing theoretical and/or experimental results. It has been proved that the developed elements can lead to accurate estimations of natural frequencies. The effect of fibre angles on natural frequencies has also been investigated with some case studies, and the results proved that the package can be a useful tool for the design optimization of composite layered plate and shell structures.     

横向磁场中导电圆柱壳体的超谐波共振

研究磁场环境中受机械载荷作用圆柱薄壳的三阶超谐波共振问题.在给出横向磁场和机械动载共同作用下圆柱薄壳的振动方程基础上,应用伽辽金积分法,并进行无量纲化处理,进一步导出相应的非线性磁弹性振动微分方程.采用多尺度法对三阶超谐波共振问题进行求解,得到稳态运动下的幅频响应方程与解的稳定性判别式.通过算例,给出几种情况下反映振幅...     

Assessment of shell theories for hybrid piezoelectric cylindrical shell under electromechanical load

The assessment of classical lamination shell theory and first-order shear deformation theory is presented for simply supported finite circular cylindrical hybrid shell with cross-ply composite laminate as elastic substrate under electromechanical static load. Navier-type solutions are obtained and used in threedimensional equilibrium equations and transverse strain—displacement relation to obtain transverse stress components and improved value of deflection. These solutions are assessed by comparison with the threedimensional solution. The error in the two-dimensional shell theories increases as the shell becomes thicker and it is more for the patch loads in comparison to the uniformly distributed and sinusoidal loads.     

Ultimate strength of a square plate with a longitudinal/transverse dent under axial compression

Thin shell structures are efficient structures because of their high load-carrying capacity and small weight. Thin plates are one of the common structural elements. Their load-carrying capacity mainly depends on their buckling behavior, which is in turn affected by the imperfections present in them. Dent is one of the common geometrical imperfections in thin shell structures, which may be formed in the plate as an impact of sharp objects, among other reasons. Using ANSYS nonlinear FEA, the present work conducts a numerical study of the effect of various dent parameters on the ultimate strength of a thin plate, with a longitudinal or a transverse dent located centrally on the plate, under uniaxial compressive loading with simply supported boundary conditions.     

Rigid-plastic collapse of compression-bent shallow shells

Limit analysis solutions are given for simply supported shallow spherical shells under combined external loading. The effect of transverse shear on collapse loads is examined in the paper. Lower bound and exact load interaction curves at collapse are given for several shell configurations. The shell material is assumed rigid-plastic and yields according to the von Mises criterion. The results indicate that the lower bound approach gives acceptable results when extremely shallow shells are considered. It is also shown that the reduction of collapse loads due to transverse shear is of the same order as found for circular plates.     

压力容器简体与补强圈间接触特性的研究

在应用薄壳理论对压力容器开孔补强结构进行分析时，常常假设补强圈与壳体间没有接触，对于该假设的合理性并没有相应的依据。文中采用ANSYS软件提供的非线性有限元技术，分别模拟内压、接管横向、纵向弯矩作用下补强圈与圆柱壳体间的接触行为。分析与试验数据表明，有限元接触分析能很好预测补强圈的应力场，同时对补强圈与简体之间的间隙量及开孔率对接触的影响也作了初步探讨。     

Dynamic response and damage of composite shell under impact

The dynamic response and damage of laminated composite cylindrical shell subjected to impact load is numerically investigated using the finite element method. A nine-node isoparametric quadrilateral element based on Sander's shell theory is developed, in which the transverse shear deformation is considered. A semi-empirical contact law that accounts for the permanent indentation is incorporated into the finite element program to evaluate the contact force. The Newmark time ingegration algorithm is used for solving the time dependent equations of the shell and the impactor. The Tsai-Wu failure criterion is used to estimate the failure of the laminated shell. Numerical results, including the contact force history, interlaminate damage zone, and failure indices in the shell are presented. Effects of curvature, impact velocity and mass of impactor on the composite shell behaviors are discussed.     

Postbuckling analysis of imperfect stiffened laminated cylindrical shells under combined external pressure and thermal loading

A postbuckling analysis is presented for a stiffened laminated cylindrical shell of finite length subjected to combined loading of external pressure and a uniform temperature rise. The formulation is based on a boundary layer theory of shell buckling which includes the effects of nonlinear prebuckling deformations, nonlinear large deflections in the postbuckling range and initial geometrical imperfections of the shell. The “smeared stiffener” approach is adopted for the stiffeners. The analysis uses a singular perturbation technique to determine the interactive buckling loads and the postbuckling equilibrium paths. Numerical examples are presented that relate to the performance of perfect and imperfect, stiffened and unstiffened cross-ply laminated cylindrical shells. Typical results are presented in dimensionless graphical form for different parameters and loading conditions.     

Postbuckling of shear deformable cross-ply laminated cylindrical shells under combined external pressure and axial compression

A postbuckling analysis is presented for a shear deformable cross-ply laminated cylindrical shell of finite length subjected to combined loading of external pressure and axial compression. The governing equations are based on Reddy's higher order shear deformation shell theory with von Kármán–Donnell type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of shear deformable laminated cylindrical shells under combined loading cases. A singular perturbation technique is employed to determine interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, unstiffened or stiffened, moderately thick, antisymmetric and symmetric cross-ply laminated cylindrical shells for different values of load-proportional parameters.     

Analysis of nonlinear vibration response of a functionally graded truncated conical shell with piezoelectric layers

The nonlinear vibration response of a functionally graded materials (FGMs) truncated conical shell with piezoelectric layers is analyzed. The vibration amplitude is suppressed by the positive and inverse piezoelectric effects. And the bifurcation phenomenon is described to reveal the motion state of the conical shell. Firstly, a truncated conical shell composed of three layers is described. And the effective material properties of the FG layer are defined by the Voigt model and the power law distribution. Next, the electric potentials of piezoelectric layers are defined as cosine distribution along the thickness direction. Meanwhile, the constant gain negative velocity feedback algorithm is used to suppress the vibration amplitude by the electric potential produced by the sensor layer. Thereafter, considering the first-order shear deformation theory and the von Karman nonlinearity, the relationship between the strain and displacement is defined. And the corresponding energy of the conical shell is calculated. After that, the motion equations of the conical shell are derived based on the Hamilton principle. Again, the nonlinear single degree of freedom equation is derived by the Galerkin method and the static condensation method. In the end, the nonlinear vibration response of FGMs truncated conical shell with piezoelectric layers under the external excitation is analyzed via using the harmonic balance method and the Runge-Kutta method. The effects of various parameters, such as ceramic volume fraction exponent, external excitation’s amplitude, control gain and geometric parameters on the nonlinear vibration response of the system are evaluated by case studies. Results indicate that the control gain plays an important role on the suppression of the vibration amplitude. The ceramic volume fraction exponents are not sensitive to the nonlinear vibration response compared with other parameters. The bifurcation behavior is observed under different parameters. The FGMs truncated conical shell with piezoelectric layers has three types of motion state, such as periodic motion, multi-periodic motion, and chaos motion.

     

Geometrically nonlinear analysis of functionally graded shells

The nonlinear response of functionally graded ceramic-metal shell panels under mechanical and thermal loading is studied. The nonlinear formulation is based on a modified version of Sander's nonlinear shell theory, in which the geometric nonlinearity takes the form of von Kármán strains. It is assumed that the material properties vary through the thickness according to a power-law distribution of the volume fraction of the constituents. The displacement field is expressed in terms of a set of mesh-free kernel particle functions. The bending stiffness is evaluated using a stabilized conforming nodal integration technique, and the shear and membrane terms are computed using a direct nodal integration to eliminate shear and membrane locking. The arc-length method, combined with the modified Newton-Raphson approach, is employed to trace the full load-displacement path. The characteristic of the displacement and the axial stress in panels under thermal and mechanical loading is investigated, and the effects of the volume fraction exponent, boundary conditions, and material properties on the nonlinear response of shell panels are also examined.     

Effect of methods for fixing and loading of cylindrical shells on their stability and supercritical behavior

The effect of the methods of fixing and external-pressure loading of an elastic isotropic cylindrical shell on its sub- and supercritical deformation is investigated. A geometrically nonlinear statement of the edge problem in the form of the technical theory of finite deflection hollow shells is applied. The edge problem is digitized with the Rayleigh-Ritz method. The solution to the set of nonlinear algebraic equations is sought using the methods of continuation by the parameter close to the optimal one. The versions of shell sealing and supporting as well as uniform lateral pressure and uniform compression are considered. The trajectories of shell loading are plotted and the shapes of their supercritical equilibrium states are found. The axial compressing load is found to exert a larger effect on the upper and lower critical pressure as compared to the conditions of shell end fixing. Moreover, axial loading of short shells yields an increase in the critical pressure rather than its decrease, as is customary in the theory of shell stability.     

含裂纹的齿轮耦合转子系统非线性动力学特性分析

在考虑滑动轴承的非线性轴承油膜力以及齿轮齿侧间隙影响的情况下,综合了转轴裂纹以及齿轮质量偏心等常见故障,建立了齿轮耦合转子系统的振动模型并推导了系统的无量纲运动方程.利用数值积分对方程进行了求解,并分析了齿侧间隙以及转轴横向裂纹对齿轮耦合转子系统非线性动力学特性的影响.