Relation of fragment with air shock wave intensity for explosion in a shell

A new analytical method is suggested for the computation of primary fragment velocity for an explosion in a shell (or case). The influence of the shell on the intensity of explosion-generated air shock waves is discussed, which shows that it is determined by the wall thickness (or the mass) of the location at which the fragment occurs, not by the total mass of the shell. By experimentation the air shock wave overpressures and the damage effects of simulative targets that are caused by the explosions of explosive charges in a shell and without a shell are examined under the same charge mass and shape, to verify the validity of the presented result in this work. By using the suggested theoretical method, the upper bound of fragment velocity and the lower bound, respectively, are calculated. The fragment velocity depends on the thickness of a shell, and the thicker or the heavier the shell, the more serious the influence of the shell on blast shock wave intensity.     

弹性圆柱壳结构振动有源控制理论分析

以两端为简支边界条件的弹性圆柱壳为研究对象,基于Donnell—Mushtari的壳理论分析了圆柱壳自由振动固有频率和结构模态,应用模态叠加方法得出圆柱壳在简谐点力激励下的响应。采用不同控制策略,对圆柱壳结构振动进行有源控制,并结合二次最优理论建立圆柱壳振动有源控制理论模型,得出不同控制策略下的最优次级力。基于所建模型进行计算机仿真,对两种控制策略下圆柱壳结构振动有源控制进行比较分析,所得结论对圆柱壳结构有源控制相关研究具有参考意义。     

Magneto-thermo-elasticity of an electroconductive circular cylindrical shell featuring nonlinear deformations

The magneto-thermo-elastic interactions of a circular cylindrical shell immersed in applied magnetic and thermal fields are modeled and the shell’ nonlinear response and stability are investigated. The shell is made of a transversely isotropic, perfectly electroconductive non-ferromagnetic material. The shell’s deformation is characterized by small strains and moderately small rotations. A geometrically nonlinear, first-order transverse shear deformation shell model is developed and Galerkin’s method is used for spatial semi-discretization. The close connection between the static nonlinear response and the temperature-frequency interaction is explored to interpret the multi-solutions of the nonlinear response. Influence of prebuckling deformations on the buckling results is addressed and the significance of the applied magnetic fields on the response and stability is evaluated.     

A new asymptotic model of flexible composite shells of a regular structure

A new model of a flexible composite shell of a regular structure is obtained within the framework of the nonlinear membrane theory. The fundamental relations which describe the geometry and deformation of a thin shell on the basis of the geometrically nonlinear theory are used. It is assumed that the shell is made of an inhomogeneous composite material of a periodic structure, i.e. the midsurface consists of a large number of piecewise-homogeneous unit cells, whose dimensions are small in comparison with the characteristic tangential dimensions of the shell. Using the two-scale asymptotic homogenization technique, a system of nonlinear constitutive equations is obtained and a formulation is given of local problems on a unit cell, from whose solution the effective stiffnesses of the shell are determined. The general theory is applied to the derivation of the constitutive relations of the high-modulus reinforced flexible shells.     

Transverse impact of a ball on a sphere with allowance for waves in the target

The transverse impact of a solid projectile on an elastic spherical shell with a pivoting contour support has been studied. Inside the contact zone, the projectile-target interaction is described by a solution of the standard system of equations. Outside the contact zone, the points of the shell are displaced and the shell is deformed due to propagation of a nonstationary wave front. A solution in this region is constructed using ray series with variable coefficients representing jumps of the time derivatives of the unknown functions on the wave surface of strong discontinuity. These coefficients are determined to within arbitrary constants using momentless equations of motion of the shell points. The constants are determined by matching two solutions at the contact zone boundary. Using the obtained analytical expressions and plotted dependences for the contact force and dynamic inflection, it is possible to judge on the influence of the shell structure design on the dynamic characteristics of impact interaction.     

Shell elements with drilling degree of freedoms based on micropolar elasticity theory

Based on the theory of micropolar elasticity, new degenerated shell elements with drilling degree of freedoms are presented. The proper stiffness on the drilling degree of freedom is derived and no spurious modes are encountered in these elements. The implementation of these new shell elements on general structural finite element programs has many advantages, especially for the analysis of a folded shell or the treatment of the twist moment normal to the shell. Several numerical examples are carried out to demonstrate the accuracy and applicability of the present elements. The effects of the coupling factor and the body moment induced in magneto-solid mechanics are also studied.     

热冲击下的复合材料壳刚柔耦合动力学研究

研究了在热冲击下任意形状(仅一个方向有曲率)复合材料壳的非线性刚柔耦合动力学响应。根据Mindlin理论,建立了任意形状的复合材料壳的非线性应变-位移关系。借助于数学理论以及几何关系,描述了壳上任意点的变曲率。用虚功原理建立了动力学变分方程,并采用等参单元对壳的连续动力学方程进行离散,建立了中心刚体-复合材料壳的刚-柔耦合动力学方程。用高斯积分计算常值阵,为了提高计算效率,采用广义-α法结合Newton-Raph-son迭代法对动力学方程进行积分。将采用该方法计算得到的频率与ANSYS软件计算得到的作对比,验证了模型的正确性。通过算例分析了在热冲击作用下复合材料壳的线性、非线性的动力学特性,以及曲率、材料特性对动力学响应的影响。     

Generalized coupled thermoelasticity of functionally graded cylindrical shells

In this paper, the response of a circular cylindrical thin shell made of the functionally graded material based on the generalized theory of thermoelasticity is obtained. The governing equations of the generalized theory of thermoelasticity and the energy equations are simultaneously solved for a functionally graded axisymmetric cylindrical shell subjected to thermal shock load. Thermoelasticity with second sound effect in cylindrical shells based on the Lord–Shulman model is compared with the Green–Lindsay model. A second‐order shear deformation shell theory, that accounts for the transverse shear strains and rotations, is considered. Including the thermo‐mechanical coupling and rotary inertia, a Galerkin finite element formulation in space domain and the Laplace transform in time domain is used to formulate the problem. The inverse Laplace transform is obtained using a numerical algorithm. The shell is graded through the thickness assuming a volume fraction of metal and ceramic, using a power law distribution. The effects of temperature field for linear and non‐linear distributions across the shell thickness are examined. The results are validated with the known data in the literature. Copyright © 2006 John Wiley & Sons, Ltd.     

A mesh-free method for analysis of the thermal and mechanical buckling of functionally graded cylindrical shell panels

The buckling response of functionally graded ceramic-metal cylindrical shell panels under axial compression and thermal load is presented here. The formulation is based on the first-order shear deformation shell theory and element-free kp-Ritz method. The material properties of shell panels are assumed to vary through their thickness direction according to a power-law distribution of the volume fraction of constituents. Approximations of the displacement field are expressed in terms of a set of mesh-free kernel particle functions. A stabilized conforming nodal integration approach is employed to estimate the bending stiffness, and the shear and membrane terms are evaluated using a direct nodal integration technique to eliminate membrane and shear locking for very thin shells. The mechanical and thermal buckling responses of functionally graded shell panels are investigated, and the influences of the volume fraction exponent, boundary conditions, and temperature distribution on their buckling strengths are also examined.     

Buckling behavior under radial loading of orthotropic oval cylindrical shells with parabolically varying thickness

In this article, the framework of the Flügge's shell theory, the transfer matrix approach, and the Romberg integration method have been employed to investigate the buckling analysis of a radial loaded oval cylindrical shell with parabolically varying thickness along its circumference. Trigonometric functions are used to form the modal displacements of the shell and Fourier's approach is used to separate the variables. The mathematical analysis is formulated to overcome the difficulties related to mode coupling of variable curvature and thickness of the shell. Using the transfer matrix of the shell, the buckling equations of the shell are reduced to eight first-order differential equations in the circumferential coordinate and rewritten in a matrix form and solved numerically. The proposed model is adopted to get the critical buckling loads and the corresponding buckling deformations for the symmetrical and antisymmetrical modes of buckling. The influences of the shell geometry, orthotropic parameters, ovality parameter, and thickness ratio on the buckling parameters and the bending deformations are presented for different type-modes of buckling.     

不同参数下的单、双层圆柱壳体速度场研究

研究圆柱壳体表面速度场的重构：疗法对潜艇水下辐射噪声的预报具有重要的意义。采用了分区段重构轻外壳速度场的思想，在此基础上建立无限流体中的有限长单、双层加肋圆柱壳模型，分析了壳体表面速度场随不同结构参数的变化规律，并对单、双层圆柱壳体，以及双层圆柱壳体内、外壳的振动响应性能作了一定的比较。得到了单区段壳体长度的选取、模型刚度特性以及不同频段内壳体间耦合作用等对壳体速度场的影响，为研究潜艇轻外壳速度场重构方法提供了理论依据。     

Buckling of moderately thick laminated cylindrical shells: a review

The present paper is a review article on the problem of buckling of moderately thick, laminated, composite shells subjected to destabilizing loads. The loads consist of uniform axial compression, uniform lateral pressure and torsion applied individually or in combination. In all the works reported in the literature, the analysis is based on higher-order shear deformation (HOSD) shell theory and/or first-order shear deformation (FOSD) shell theory with or without a shear correction factor. Results obtained by these two shell theories and by employing classical thin shell theory are compared to determine the range of applicability of each in predicting critical conditions. The effect of stacking sequence, radius-to-thickness ratio and length-to-radius ratio is assessed. Typical numerical results are presented in tabular form. Moreover, some limited results, which are based on limit point analysis are also presented (imperfection sensitivity studies).     

Vibration analysis of functionally graded carbon nanotube-reinforced composite shell structures

This article deals with the vibration analysis of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shell structures. The material properties of an FG-CNTRC shell are graded smoothly through the thickness direction of the shell according to uniform distribution and some other functionally graded (FG) distributions (such as FG-X, FG-V, FG-O and FG-\({\Lambda}\)) of the volume fraction of the carbon nanotube (CNT), and the effective material properties are estimated by employing the extended rule of mixture. An eight-noded shell element considering transverse shear effect according to Mindlin’s hypothesis has been employed for the finite element modelling and analysis of the composite shell structures. The formulation of the shell midsurface in an arbitrary curvilinear coordinate system based on the tensorial notation is also presented. The Rayleigh damping model has been implemented in order to study the effects of carbon nanotubes (CNTs) on the damping capacity of such shell structures. Different types of shell panels have been analyzed in order to study the impulse and frequency responses. The influences of CNT volume fraction, CNT distribution, geometry of the shell and material distributions on the dynamic behavior of FG-CNTRC shell structures have also been presented and discussed. Various types of FG-CNTRC shell structures (such as spherical, ellipsoidal, doubly curved and cylindrical) have been analyzed and discussed in order to compare studies in terms of settling time, first resonant frequency and absolute amplitude corresponding to first resonant frequency based on the impulse and frequency responses, and the effects of CNTs on vibration responses of such shell structures are also presented. The results show that the CNT distribution and volume fraction of CNT have a significant effect on vibration and damping characteristics of the structure.     

A simple and efficient finite element for general shell analysis

A simple, efficient and versatile finite element is introduced for shell applications. The element is developed based on a degeneration concept, in which the displacements and rotations of the shell mid-surface are independent variables. Bilinear functions are employed in conjunction with a reduced integration for the transverse shear energy. Several examples are tested to demonstrate the effectiveness and versatility of the element. The numerical results indicate that the shell element performs accurately for both thick and thin shell situations.     

芯材增强对夹层圆柱壳动力学性能影响的有限元分析

将表层、增强材料与芯材分开,应用有限元分析软件ANSYS,采用8节点SOLID45实体单元,对增强型夹层圆柱壳建立物理模型,进行自由振动及瞬态动力学过程分析。考虑树脂材性、尺寸以及分布等参数的变化,分析了点阵增强和齿槽增强对夹层圆柱壳动力学性能的影响,将两种增强方式进行了对比。结果显示,树脂柱及树脂齿槽均可改变圆柱壳的振动特性,对降低瞬态荷载下的动力响应有积极作用。其中树脂材性的影响较小,而点阵和齿槽的尺寸与分布对圆柱壳动力学性能的影响较为明显,分析显示,点阵增强对于提高结构固有频率比齿槽增强更好一些,而齿槽增强对于降低端部受冲击荷载时的动力位移比点阵增强更好一些。     

COMBINATION OF ADAPTIVITY AND MESH SMOOTHING FOR THE FINITE ELEMENT ANALYSIS OF SHELLS WITH INTERSECTIONS

A compatible hierarchical adaptive scheme is proposed which allows to control both density and geometrical properties of meshes with four-node linear finite shell elements. The algorithm produces a sequence of meshes with two aims, nearly equal distribution of the local error in each element and a mesh with regular elements, thus internal element angles near 90° and length ratios of adjacent element sides near unity. This goal is achieved in an efficient manner imposing a combination of a local smoothing algorithm with the adaptive mesh generation. New created nodes are positioned on the real shell surface and shell boundaries which may be given e.g. by CAD data. Also the shell directors are determined from the normals on the real geometry. Shell intersections are detected automatically as common curves of two adjacent shell parts. As a shell continuum cannot be assumed for these intersections and thus simple standard adaptive schemes fail, shell intersections have to be treated in a way similar to shell boundaries. For some numerical examples the developed algorithms are demonstrated and the resulting meshes are shown. © 1997 by John Wiley & Sons, Ltd.     

Review of shell models for contrast agent microbubbles

Micrometer-scale encapsulated gas bubbles, known as ultrasound contrast agents, are used in ultrasound medical diagnostics for enhancing blood-tissue contrast during an ultrasonic examination. They are also employed in therapy as an activator of drug incorporation or extravasation. Adequate modeling of the effect of encapsulation is of primary importance because it is the encapsulating shell that determines many of the functional properties of contrast agents. In this review, existing approaches to the modeling of the radial motion of an encapsulated bubble are discussed and comparative analysis of available shell models is conducted. The capabilities of the shell models are evaluated in the context of recent experimental observations, such as compression-only behavior and the dependence of shell material properties on initial bubble radius. It is shown that for early shell models, the main problem is that the behavior of encapsulation is described by linear elastic and viscous laws, whereas recent experimental data attest to complicated rheological properties inherent in shell materials. Currently, a trend toward models involving nonlinear laws for shell elasticity and viscosity is observed. In particular, nonlinear models have been proposed that allow one to reproduce compression-only behavior. However, the problem of the radius dependence of shell material parameters remains unsolved.     

Coupled axisymmetric vibration of nonlocal fluid-filled closed spherical membrane shell

In this paper, the axisymmetric vibration of a fluid-filled spherical membrane shell is studied based on nonlocal elasticity theory. The membrane shell is considered elastic, homogeneous and isotropic. The shell model is reformulated using the nonlocal differential constitutive relations of Eringen. The membrane shell is completely filled with an inviscid fluid. The motion of the fluid is governed by the wave equation. Nonlocal governing equations of motion for the fluid-filled spherical membrane shell are derived. Along the contact surface between the membrane and the fluid, the compatibility requirement is applied and Legendre polynomials, associated Legendre polynomials and spherical Bessel functions are used to obtain the natural frequencies of the fluid-filled spherical membrane shells. The frequencies for both empty and fluid-filled spherical membrane shell are evaluated, and their comparisons are performed to confirm the validity and accuracy of the proposed method. An excellent agreement is found between the present and previous ones available in the literature. The variations of the natural frequencies with the small-scale parameter, density ratio, wave speed ratio and Poisson’s ratio are also examined. It is observed that the frequencies are affected when the size effect is taken into consideration.     

Elasticity Solution of a Laminated Clamped Cylindrical Shell with Piezoelectric Layer under Dynamic Load

Dynamic elasticity solution for a clamped, laminated cylindrical shell with two orthotropic layers bounded with a piezoelectric layer and subjected to impulse load distributed on inner surface is presented. The piezoelectric layer serves as sensor/actuator. The governing elasticity PDE equations are reduced to ordinary differential equations by means of Legendre polynomial expansion for displacement and electric potential in the axial direction. The resulting equations are transferred into state space form and reduced to an eigenvalue problem by using Galerkin's finite element in radial direction. The static and dynamic results are presented for [0/90/Piezo] lamination. The radius to thickness ratio effect on dynamic behavior is studied. The results are compared for different thickness ratios and applied electric loads with simply-supported shell results. Time responses for sensor and actuated shell are presented and natural frequencies are compared with simply-supported shell results.