Transient impact responses of laminated composite cylindrical shells

The generalized ray method(GRM) has been successfully used to study the transient elastic wave transmitting in the beams,planar trusses,space frames and infinite layered media.In this letter,the GRM is extended to investigate the early short time transient responses of laminated composite cylindrical shells under impact load.By using the Laplace transformation and referring to the boundary conditions,the ray groups transmitting in the finite laminated cylindrical shells under the shock load are obtained and the transient response related to each ray group can be derived via FFT algorithm.From the numerical results,it is shown that the early short time transient accelerations of the laminated composite cylindrical shell under impact loads are very large.But the short time transient shear strain and displacement are very small.

Analysis of energy release rate for composite delaminated cylindrical shells subjected to axial compression

In this paper, the postbuckling governing equations and the analytical expression of the energy release rates associated with delamination growth in a compression-loaded cylindrical shell are derived by using the variational principle of moving boundary and the Griffith fracture criterion. The finite difference method is used to generate the postbuckling solutions of the delaminated cylindrical shells, and with these solutions, the values of the energy release rates are determined. In simulational examples, the effects of a wide range of parameters, such as delamination sizes and depths, boundary conditions, geometrical parameters, material properties and laminate stacking sequences on the energy release rates of axisymmetrical laminated cylindrical shells are intensively discussed.

Delamination growth for composite laminated cylindrical shells under external pressure

The delamination growth may occur in delaminated cylindrical shells＇under external pressure. This will lead to failure of structure. By using the variational principle of moving boundary and considering the contact effect between delamination regions, in this work, the delamination growth was investigated for cylindrical shells under the action of external pressure. At the same time, according to the Griffith criterion, the formulas of energy release rate along the delamination front were obtained. In the numerical calculation, the delamination growth of axisymmetrical laminated cylindrical shells was analyzed, and the effects of delamination sizes and depths, the geometrical parameters, the material properties, and the laminate stacking sequences on delamination growth were discussed.

Dynamic Structure-Fluid Interaction Response of a Composite Cylindrical Shell Submerged in Water

This paper analyzes the dynamic structure-fluid interaction response of a submerged composite cylindrical shell. Dynamic equations based on the first-order shear deformation theory include the initial stresses and structure-fluid interaction forces due to fluid. The field equation is solved by expanding the velocity potential into series similar to transverse deflection of the cylindrical shell and the structure-fluid interaction force is obtained. The dynamic response is investigated by means of series expansion method. The effects of structure-fluid interaction on dynamic response are discussed.

Wave transmission through laminated composite double-walled cylindrical shell lined with porous materials

A study on free harmonic wave propagation in a double-walled cylindrical shell, whose walls sandwich a layer of porous materials, is presented within the framework of the classic theory for laminated composite shells. One of the most effective components of the wave propagation through the porous core is estimated with the aid of a flat panel with the same geometrical properties. By considering the effective wave component, the porous layer is modeled as a fluid with equivalent properties. Thus, the model is simplified as a double-walled cylindrical shell trapping the fluid media. Finally, the transmission loss （TL） of the structure is estimated in a broadband frequency, and then the results are compared.

Buckling of composite cylindrical shells with ovality and thickness variation subjected to hydrostatic pressure

The initial geometric imperfection is one of the primary factors affecting the buckling behaviors of composite cylindrical shells under hydrostatic pressure.In this study,ovality and thickness variations as two representative types of the geometric imperfections are considered.After measuring the geometric imperfections,a typical carbon fiber reinforced polymers(CFRP)cylindrical shell is tested to obtain the buckling pressure.The buckling behaviors of the shell sample are analyzed in combination with the strain responses.By using the nonlinear numerical analysis,the buckling shapes of the CFRP cylinder shells with different combinations of ovality and thickness variation are firstly discussed.The rules of influence of such imperfections on the buckling pressure are then obtained by nonlinear regression method.Finally,an empirical formula is proposed to predict the buckling pressure of the composite cylinder shells,and the calculated results from the formula are in good agreement with the numerical results.

Nonlinear stability of advanced sandwich cylindrical shells comprising porous functionally graded material and carbon nanotube reinforced composite layers under elevated temperature

The nonlinear stability of sandwich cylindrical shells comprising porous functionally graded material(FGM) and carbon nanotube reinforced composite(CNTRC)layers subjected to uniform temperature rise is investigated. Two sandwich models corresponding to CNTRC and FGM face sheets are proposed. Carbon nanotubes(CNTs) in the CNTRC layer are embedded into a matrix according to functionally graded distributions. The effects of porosity in the FGM and the temperature dependence of properties of all constituent materials are considered. The effective properties of the porous FGM and CNTRC are determined by using the modified and extended versions of a linear mixture rule, respectively. The basic equations governing the stability problem of thin sandwich cylindrical shells are established within the framework of the Donnell shell theory including the von K’arm’an-Donnell nonlinearity. These equations are solved by using the multi-term analytical solutions and the Galerkin method for simply supported shells.The critical buckling temperatures and postbuckling paths are determined through an iteration procedure. The study reveals that the sandwich shell model with a CNTRC core layer and relatively thin porous FGM face sheets can have the best capacity of thermal load carrying. In addition, unlike the cases of mechanical loads, porosities have beneficial effects on the nonlinear stability of sandwich shells under the thermal load. It is suggested that an appropriate combination of advantages of FGM and CNTRC can result in optimal efficiency for advanced sandwich structures.

NONLINEAR THEORY OF DYNAMIC STABILITY FOR LAMINATED COMPOSITE CYLINDRICAL SHELLS

Hamilton principle war used to derive the general governing equations of nonlinear dynamic stability far laminated cylindrical shell in which, factors of nonlinear large deflection, transverse shear and longitudinal inertia force were concluded. Equations were salved by variational method. Analysis reveals that under the action of dynamic load, laminated cylindrical shells will fall into a store of parametric resonance and enter into the dynamic unstable region that causes dynamic instability of shells. Laminated shells of three typical composites were computed : i.e. T300/5 208 graphite epoxy E-glass epoxy, and ARALL shells. Results show that all factors will induce important influence for dynamic stability of laminated shell. So, in research of dynamic stability for laminated shells, to consider these factors is important.

Axial impact response of composite cylindrical shell

Following Love's shell theory and classical lamination theory, governing equation of composite cylindrical shell in the axisymmetric deformation was established with radial displacements expressed in terms of Fourier series, and numerical results given for axial impact response of laminated shell with simple support will be used to further study of dynamic stability of composite shell.

Stress analysis of clamped-free grid composite cylindrical shell under various end loadings

Stress analysis of cylindrical grid-stiffened composite shells was conducted under transverse loading,pure bending,torsion and axial compression under clamped-free boundary condition.Electrical strain gauges were employed to measure the strains in transverse loading case to validate the finite element analysis which was conducted using ANSYS software.Good agreement was obtained between the two methods.It was observed that stiffening the composite shell with helical ribs decreased the average equivalent Von Mises stress on the shell.The reduction of the stress seemed to be higher in the intersection of two ribs.It was also seen that the stress reduction ratio was higher when the structure was under bending compared to torsion and axial compression.The reduction ratio was approximately 75% in pure bending in the intersection point of the ribs,while it was approximately 25% in torsion.Therefore,it is concluded that the presence of the ribs is more effective under bending.Failure analysis was done using Tsai-Wu criterion.The ribs were observed to result in maximum and minimum increase in the failure load of the structure under transverse bending and torsional loading,respectively.

Nonlinear Dynamic Buckling of Damaged Composite Cylindrical Shells

Based on the first order shear deformation theory(FSDT), the nonlinear dynamic equations involving transverse shear deformation and initial geometric imperfections were obtained by Hamilton's philosophy. Geometric deformation of the composite cylindrical shell was treated as the initial geometric imperfection in the dynamic equations, which were solved by the semi-analytical method in this paper. Stiffness reduction was employed for the damaged sub-layer, and the equivalent stiffness matrix was obtained for the delaminated area. By circumferential Fourier series expansions for shell displacements and loads and by using Galerkin technique, the nonlinear partial differential equations were transformed to ordinary differential equations which were finally solved by the finite difference method. The buckling was judged from shell responses by B-R criteria, and critical loads were then determined. The effect of the initial geometric deformation on the dynamic response and buckling of composite cylindrical shell was also discussed, as well as the effects of concomitant delamination and sub-layer matrix damages.

Predicting buckling of carbon fiber composite cylindrical shells based on backpropagation neural network improved by sparrow search algorithm

The buckling load of carbon fiber composite cylindrical shells(CF-CCSs)was predicted using a backpropagation neural network improved by the sparrow search algorithm(SSA-BPNN).Firstly,two CF-CCSs,each with an inner diameter of 100 mm,were manufactured and tested.The buckling behavior of CF-CCSs was analyzed by finite element and experiment.Subsequently,the effects of ply angle and length–diameter ratio on buckling load of CF-CCSs were analyzed,and the dataset of the neural network was generated using the finite element method.On this basis,the SSA-BPNN model for predicting buckling load of CF-CCS was established.The results show that the maximum and average errors of the SSA-BPNN to the test data are 6.88%and 2.24%,respectively.The buckling load prediction for CF-CCSs based on SSA-BPNN has satisfactory generalizability and can be used to analyze buckling loads on cylindrical shells of carbon fiber composites.

Numerical study on the dynamic fracture of explosively driven cylindrical shells

Research on the expansion and fracture of explosively driven metal shells has been a key issue in weapon development and structural protection.It is important to study and predict the failure mode,fracture mechanism,and fragment distribution characteristics of explosively driven metal shells.In this study,we used the finite element-smoothed particle hydrodynamics(FE-SPH)adaptive method and the fluid-structure interaction method to perform a three-dimensional numerical simulation of the expansion and fracture of a metal cylindrical shell.Our method combined the advantages of the FEM and SPH,avoiding system mass loss,energy loss,and element distortion;in addition,the proposed method had a good simulation effect on the interaction between detonation waves and the cylindrical shell.The simulated detonation wave propagation,shell damage morphology,and fragment velocity distribution were in good agreement with theoretical and experimental results.We divided the fragments into three regions based on their shape characteristics.We analyzed the failure mode and formation process of fragments in different regions.The numerical results reproduced the phenomenon in which cracks initiated from the inner surface and extended to the outer surface of the cylindrical shell along the 45°or 135°shear direction.In addition,fragments composed of elements are identified,and the mass and characteristic lengths of typical fragments at a stable time are provided.Furthermore,the mass and size distribution characteristics of the fragments were explored,and the variation in the fitting results of the classical distribution function under different explosion pressures was examined.Finally,based on mathematical derivation,the distribution formula of fragment velocity was improved.The improved formula provided higher accuracy and could be used to analyze any metal cylindrical shells with different length-to-diameter ratios.

Strength Reliability Analysis of Stiffened Cylindrical Shells Considering Failure Correlation

The stiffened cylindrical shell is commonly used for the pressure hull of submersibles and the legs of offshore platforms. There are various failure modes because of uncertainty with the structural size and material properties, uncertainty of the calculation model and machining errors. Correlations among failure modes must be considered with the structural reliability of stiffened cylindrical shells. However, the traditional method cannot consider the correlations effectively. The aim of this study is to present a method of reliability analysis for stiffened cylindrical shells which considers the correlations among failure modes. Firstly, the joint failure probability calculation formula of two related failure modes is derived through use of the 2D joint probability density function. Secondly, the full probability formula of the tandem structural system is given with consideration to the correlations among failure modes. At last, the accuracy of the system reliability calculation is verified through use of the Monte Carlo simulation. Result of the analysis shows the failure probability of stiffened cylindrical shells can be gained through adding the failure probability of each mode.

BUCKLING AND POSTBUCKLING OF LAMINATED THIN CYLINDRICAL SHELLS UNDER HYGROTHERMAL ENVIRONMENTS

The influence of hygrothermal effects on the buckling and postbuckling of composite laminated cylindrical shells subjected to axial compression is investigated using a micro-to-macro-mechanical analytical model. The material properties of the composite are affected hy the variation of temperature and moisture, and are hosed on a micromechanical model of a laminate. The governing equations are based on the classical laminated shell theory, and including hygrothermal effects. The nonlinear prebuckling deformations and initial geometric imperfections of the shell were both taken into account. A boundary layer theory of shell buckling was extended to the case of laminated cylindrical shells under hygrothermal environments, and a singular peturbation technique was employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical shells under different sets of environmental conditions. The influences played by temperature rise, the degree of moisture concentration, fiber volume fraction, shell geometric parameter, total number of plies, stacking sequences and initial geometric imperfections are studied.

The deformation and failure mechanism of cylindrical shell and square plate with pre-formed holes under blast loading

The deformation and failure mechanism of cylindrical shells and square plate with pre-formed holes under blast loading were investigated numerically by employing the Ansys 17.0 and Ls-Dyna 971.To calibrate the numerical model,the experiments of square plates with pre-formed circle holes were modeled and the numerical results have a good agreement with the experiment data.The calibrated numerical model was used to study the deformation and failure mechanism of cylindrical shells with pre-formed circle holes subjected to blast loading.The structure response and stress field changing process has been divided into four specific stages and the deformation mechanism has been discussed systematically.The local and global deformation curves,degree of damage,change of stress status and failure modes of cylindrical shell and square plate with pre-formed circular holes are obtained,compared and analyzed,it can be concluded as:(1)The transition of tensile stress fields is due to the geometrical characteristic of pre-formed holes and cylindrical shell with arch configuration;(2)The existence of preformed holes not only lead to the increasing of stress concentration around the holes,but also release the stress concentration during whole response process;(3)There are three and two kinds of failure modes for square plate and cylindrical shell with pre-formed holes,respectively.and the standoff distance has a key influence on the forming location of the crack initiating point and the locus of crack propagation;(4)The square plate with pre-formed holes has a better performance than cylindrical shell on blast-resistant capability at a smaller standoff distance,while the influence of pre-formed holes on the reduction of blast-resistant capability of square plate is bigger than that of cylindrical shell.

STACKING SEQUENCE OPTIMIZA-TION OF LAMINATED COMPOSITE CYLINDER SHELL FOR MAXIMAL BUCKLING LOAD

A new optimization method for the optimization of stacking of composite glass fiber laminates is developed. The fiber orientation and angle of the layers of the cylindrical shells are sought considering the buckling load. The proposed optimization algorithm applies both finite element analysis and the mode-pursuing sampling （MPS）method. The algorithms suggest the optimal stacking sequence for achieving the maximal buckling load. The procedure is implemented by integrating ANSYS and MATLAB. The stacking sequence designing for the symmetric angle-ply three-layered and five-layered composite cylinder shells is presented to illustrate the optimization process, respectively. Compared with the genetic algorithms, the proposed optimization method is much faster and efficient for composite staking sequence plan.

Multi-objective design optimization of composite submerged cylindrical pressure hull for minimum buoyancy and maximum buckling load capacity

This paper presents the design optimization of composite submersible cylindrical pressure hull subjected to 3 MPa hydrostatic pressure.The design optimization study is conducted for cross-ply layups[0_(s)/90_(t)/0_(u)],[0_(s)/90_(t)/0_(u)]s,[0_(s)/90_(t)]s and[90_(s)/0_(t)]s considering three uni-directional composites,i.e.Carbon/Epoxy,Glass/Epoxy,and Boron/Epoxy.The optimization study is performed by coupling a Multi-Objective Genetic Algorithm(MOGA)and Analytical Analysis.Minimizing the buoyancy factor and maximizing the buckling load factor are considered as the objectives of the optimization study.The objectives of the optimization are achieved under constraints on the Tsai-Wu,Tsai-Hill and Maximum Stress composite failure criteria and on buckling load factor.To verify the optimization approach,optimization of one particular layup configuration is also conducted in ANSYS with the same objectives and constraints.

An Analytical Approach for Nonlinear Buckling Analysis of Torsionally Loaded Sandwich Carbon Nanotube Reinforced Cylindrical Shells with Auxetic Core

The main aim of this paper is to present an analytical approach on the postbuckling for torsionally loaded sandwich carbon nanotube(CNT)reinforced cylindrical shells with the auxetic core.The considered shells consist of three layers,external and internal CNT reinforced layers,and the auxetic lattice core made by isotropic material.The homogenization model for honeycomb auxetic lattice core is utilized,and the equilibrium equations are formulated based on the nonlinear Donnell’s thin shell theory with von Karman geometrical nonlinearities.The three terms of deflection are considered,the Airy’s stress function and Galerkin’s method are utilized,the explicit expression of critical buckling of torsionally loaded shells and load-deflection expression of postbuckling states are achieved.The effects of two carbon nanotube reinforced layers,the auxetic core layer,the volume fraction of carbon nanotube on the torsional buckling behavior are examined and remarked.

Buckling Optimization of Composite Cylinders for Underwater Vehicle Applications Under Tsai-Wu Failure Criterion Constraint

An optimization framework is developed to maximize design pressure of composite cylindrical shell subjected to hydrostatic pressure. Genetic algorithm(GA) integrated with numerical analysis is used in the framework to find optimal winding pattern of the composite cylinders. As a novelty, unlike other studies only considering buckling, in this study, material failure is taken as design constraint in the optimization problem.Sensitivity analyses are performed to study the effects of design variables on the buckling pressure, material failure pressure and design pressure. Comparative study is carried out to analyze the buoyancy factors of the cylindrical shell made of metal alloys and composites. Results reveal that as the shell thickness of the cylinder increases, the material failure pressure instead of the buckling pressure determines the design pressure. It can be concluded that reliable winding pattern designs can be achieved for composite cylinders under hydrostatic pressure when the Tsai-Wu failure criterion is considered.