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.

Dynamical response of hyper-elastic cylindrical shells under periodic load

Dynamical responses, such as motion and destruction of hyper-elastic cylindrical shells subject to periodic or suddenly applied constant load on the inner surface, are studied within a framework of finite elasto-dynamics. By numerical computation and dynamic qualitative analysis of the nonlinear differential equation, it is shown that there exists a certain critical value for the internal load describing motion of the inner surface of the shell. Motion of the shell is nonlinear periodic or quasi-periodic oscillation when the average load of the periodic load or the constant load is less than its critical value. However, the shell will be destroyed when the load exceeds the critical value. Solution to the static equilibrium problem is a fixed point for the dynamical response of the corresponding system under a suddenly applied constant load. The property of fixed point is related to the property of the dynamical solution and motion of the shell. The effects of thickness and load parameters on the critical value and oscillation of the shell are discussed.

THE GLOBAL DEFORMATION AND LOCAL DAMAGE ANALYSIS OF FILLED METALLIC CYLINDRICAL SHELLS IMPACTED BY MISSILES

A group of theoretical models has been developed for analyzingtransient dynamic re- sponse to filled metallic cylindrical shellsimpacted by flat-nosed missiles at normal obliquity on the ba- sis ofthe analogy modeling method of beam-on-foundation. It can be used forsolving the global defor- mation and the local failure of cylindricalshells in the impact process. the ballistic limit speed and im- pactresponse history have been calculated by this group of theoreticalmodels, and the inner pressure effect on the ballistic limit speedand some parameters are discussed at length.

A state space solution for the bending problem of thick laminated piezoelectric open cylindrical shells

Based on the theories of three-dimensional elasticity and piezoelectricity, and by assuming appropriate boundary functions, we established a state equation of piezoelectric cylindrical shells. By using the transfer matrix method, we presented an analytical solution that satisfies all the arbitrary boundary conditions at boundary edges, as well as on upper and bottom surfaces. Our solution takes into account all the independent elastic and piezoelectric constants for a piezoelectric orthotropy, and satisfies continuity conditions between plies of the laminates. The principle of the present method and corresponding results can be widely used in many engineering fields and be applied to assess the effectiveness of various approximate and numerical models.

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.

DYNAMIC BUCKLING OF STATICALLY PRELOADED RING-STIFFENED CYLINDRICAL SHELLS UNDER AXIAL FLUID-SOLID IMPACT LOADING

The Initial Imperfection Amplified Criterion is applied toinvestigate the geometric nonlinear dynamic buckling of staticallypreloaded ring-stiffened cylindrical shells under axial fluid-solidimpact. Tak- ing account of the effects of large deformation andinitial geometric imperfection, the governing equations are obtainedby the Galerkin method and solved by the Runge-Kutta method. Theeffects of static preloading (uniform external radial pressure) onthe buckling features and the load-carrying ability of ring-stiffenedcy- lindrical shells against axial impact are discussed.

The Influence of Residual Stress on Plastic Buckling of Cylindrical Shells

-This paper adopts approximate formulas for residual stresses caused by cold bending for plates with stress-strain curve form a = K n. A typical distribution of the longitudinal residual stress due to welding is also assumed. The effects of residual stress due to cold bending and welding on plastic buckling of axially compressed cylindrical shells are studied by the finite element method.

KOITER-BOUNDARY LAYER SINGULAR PERTURBATION METHOD FOR AXIAL COMPRESSED STIFFENED CYLINDRICAL SHELLS

The double singularities induced by bifurcation point and boundary layer in non-dimensionalized nonlinear boundary-layer Karman-Donnell equations for axially compressed stiffened cylindrical shells can be treated by Koiter-boundary layer singular perturbation method in this paper. It is demonstrated that the method has high computing efficiency and accuracy based on the analysis of AS-2 shell, and some new conclusions can be directly obtained from the perturbation formulas which are very well in agreement with experimental phenomenon of axially compressed stiffened cylindrical shells.

AXISYMMETRIC PROBLEMS OF CYLINDRICAL SHELLS WITH VARIABLE WALL THICKNESS

The purpose of this paper is to give the general solutions for axisymmetric eylindrical shells with paraholically varying wall thickness.

AN EXACT ANALYTIC METHOD APPLIED TO NONHOMOGENEOUS RING-AND STRINGER-STIFFENED CYLINDRICAL SHELLS

In this paper, the nonlinear axial symmetric deformation problem of nonhomogeneous ring- and stringer-stiffened shells is first solved by the exact analytic method. An analytic expression of displacements and stress resultants is obtained and its convergence is proved. Displacements and stress resultants converge to exact solution uniformly. Finally, it is only necessary to solve a system of linear algebraic equations with two unknowns. Four numerical examples are given at the end of the paper which indicate that satisfactory results can be obtained by the exact analytic method.

THE GENERAL SOLUTION ON NONLINEAR AXIAL SYMMETRICAL DEFORMATION OF NONHOMOGENEOUS CYLINDRICAL SHELLS

In this paper, the general solution on nonlinear axial symmetrical deformation of nonhomogeneous cylindrical shells is obtained by step reduction method[1]. The general formula of displacements and stress resultants, which is used to solve the bending problems of nonhomogeneous cylindrical shells under arbitrary axial symmetric loads, is derived. Its uniform convergence is proved. Finally, it is only necessary to solve one set of binary linear algebraic equations. A numerical example is given at the end of the paper which indicates satisfactory results of displacement and stress resultants can be obtained and converge to the exact solution.

Dynamic Buckling of Elasto-Plastic Cylindrical Shells Under Axial Fluid-Solid Impact Load

The dynamic buckling of elasto-plastic cylindrical shells under axial fluid-solid impact is investigated theoretically. A simplified liquid- gas- structure model is given to approximately imitate the problem. The basic equation of the structure is derived from a minimum principle in dynamics of elasto-plastic continua at finite deformation, and the flow theory of plasticity is employed. The liquid is incompressible and the gas is compressed adiabatically. A number of numerical results are presented and the characteristics of the buckling behavior under fluid-solid impact are illustrated.

Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer

An analytical method for the three-dimensional vibration analysis of a functionally graded cylindrical shell integrated by two thin functionally graded piezoelectric （FGP） layers is presented. The first-order shear deformation theory is used to model the electromechanical system. Nonlinear equations of motion are derived by considering the von Karman nonlinear strain-displacement relations using Hamilton＇s principle. The piezoelectric layers on the inner and outer surfaces of the core can be considered as a sensor and an actuator for controlling characteristic vibration of the system. The equations of motion are derived as partial differential equations and then discretized by the Navier method. Numerical simulation is performed to investigate the effect of different para- meters of material and geometry on characteristic vibration of the cylinder. The results of this study show that the natural frequency of the system decreases by increasing the non-homogeneous index of FGP layers and decreases by increasing the non-homogeneous index of the functionally graded core. Furthermore, it is concluded that by increasing the ratio of core thickness to cylinder length, the natural frequencies of the cylinder increase considerably.

Vibration and Acoustic Radiation from Orthogonally Stiffened Infinite Circular Cylindrical Shells in Water

Based on the motion differential equations of vibration and acoustic coupling system for thin elastic shells with ribs, by means of the Fourier integral transformation and the Fourier inverse transformation, as well as the stationary phase method, an analytic solution, which has satisfying computational effectiveness and precision, is derived for the solution to the vibration and acoustic radiation from a submerged stiffened infinite circular cylinder with both ring and axial ribs. It is easy to analyze the effect of stiffening supports in the acoustic radiation field by use of the formulas obtained by the presented method and corresponding numerical computation. It is shown that the axial-stiffeners can improve the mechanical and acoustical characteristics. Moreover, the present method can be used to study the acoustic radiation mechanism of the type of structure.

Dynamic behavior of single-layer latticed cylindrical shells subjected to seismic loading

The single-layer latticed cylindrical shell is one of the most widely adopted space-fl'amed structures.In this paper,free vibration properties and dynamic response to horizontal and vertical seismic waves of single-layer latticed cylindrical shells are analyzed by the finite element method using ANSYS software.In the numerical study,where hundreds of cases were analyzed,the parameters considered included rise-span ratio,length-span ratio,surface load and member section size.Moreover,to better define the actual behavior of single-layer latticed shells,the study is focused on the dynamic stress response to both axial forces and bending moments.Based on the numerical results,the effects of the parameters considered on the stresses are discussed and a modified seismic force coefficient method is suggested.In addition,some advice based on these research results is presented to help in the future design of such structures.

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.

Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities

The free thermal vibration of functionally graded material(FGM) cylindrical shells containing porosities is investigated. Both even distribution and uneven distribution are taken into account. In addition, three thermal load types, i.e., uniform temperature rise(UTR), nonlinear temperature rise(NLTR), and linear temperature rise(LTR), are researched to explore their effects on the vibration characteristics of porous FGM cylindrical shells. A modified power-law formulation is used to describe the material properties of FGM shells in the thickness direction. Love’s shell theory is used to formulate the straindisplacement equations, and the Rayleigh-Ritz method is utilized to calculate the natural frequencies of the system. The results show that the natural frequencies are affected by the porosity volume fraction, constituent volume fraction, and thermal load. Moreover,the natural frequencies obtained from the LTR have insignificant differences compared with those from the NLTR. Due to the calculation complexity of the NLTR, we propose that it is reasonable to replace it by its linear counterpart for the analysis of thin porous FGM cylindrical shells. The present results are verified in comparison with the published ones in the literature.

FREE VIBRATION OF PIEZOELECTRIC CYLINDRICAL SHELLS

Three displacement functions are introduced to represent each mechanical displacement according to the 3-D theory in this paper. By expanding the displacement functions and the electric potential in orthogonal series, the free vibration equation of piezoelectric cylindrical shells satisfying SS3 boundary conditions can be obtained. The equation was solved by utilizing Bessel functions with complex arguments. Results are presented graphically as well as in table, and compared with those of other references. Some frequencies that were missing in Ref. [9] are discovered.

A NOVEL SEMI-ANALYTICAL METHOD FOR SOLVING ACOUSTIC RADIATION FROM LONGITUDINALLY STIFFENED INFINITE NON-CIRCULAR CYLINDRICAL SHELLS IN WATER

Based on the extended homogeneous capacity high precision integration method and the spectrum method of virtual boundary with a complex radius vector, a novel semi-analytical method, which has satisfactory computation efectiveness and precision, is presented for solving the acoustic radiation from a submerged infnite non-circular cylindrical shell stifened by longitudinal ribs by means of the Fourier integral transformation and stationary phase method. In this work, besides the normal interacting force, which is commonly adopted by some researchers, the other interacting forces and moments between the longitudinal ribs and the non-circular cylindrical shell are considered at the same time. The efects of the number and the size of the cross-section of longitudinal ribs on the characteristics of acoustic radiation are investigated. Numerical results show that the method proposed is more efcient than the existing mixed FE-BE method.

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.