Coupled torsional and longitudinal wave propagation in a neo-hookean bar

When a cylindrical hyperelastic bar is subjected to finite twist there is a second order effect, namely there is a change in length, or an axial force is required if this change in length is constrained. In this paper we consider the finite deformation elastodynamic problem of the coupling that results, because of this second order effect, between longitudinal and torsional waves. An approximate theory is presented and some similarity solutions are obtained.     

Application of the extended Kantorovich method to the bending of clamped cylindrical panels

Applicability and performance of the extended Kantorovich method (EKM) to obtain highly accurate approximate closed form solution for bending analysis of a cylindrical panel is studied. Fully clamped panel subjected to both uniform and non-uniform loadings is considered. Based on the Love–Kirchhoff first approximation for thin shallow cylindrical panels, the governing equations of the problem in terms of three displacement components include a system of two second order and one forth order partial differential equations. The governing PDE system is converted to a double set of ODE systems by assuming separable functions for displacements together with utilization of the extended Kantorovich method. The resulted ODE systems are solved iteratively. In each iteration, exact closed form solutions are presented for both ODE systems. Rapid convergence and high accuracy of the method is shown for various examples. Both displacement and stress predictions show close agreement with other analytical and finite element analysis.     

基于二阶双渐近法的双层圆柱壳在水下爆炸作用下的鞭状运动

针对潜艇在水下爆炸载荷下的鞭状运动,从波动方程出发,推导了二阶双渐近法后期近似,并结合声固耦合法初步解决了双层圆柱壳的内域问题,然后将其与显式有限元耦合形成了圆柱壳结构水下爆炸流固耦合分析方法。通过简单算例验证了本文分析方法的有效性和精度。最后,基于此方法分析了双层圆柱壳结构在水下爆炸载荷下的总体响应特性以及周期比和爆距比对其影响规律。     

热环境中功能梯度圆柱薄壳分岔屈曲的边界约束效应

基于前屈曲一致理论,研究了热环境中受轴压功能梯度圆柱薄壳分岔屈曲的边界约束效应问题.导出前屈曲变形的解析解,结合分离变量法与有限差分法求解分岔屈曲控制方程,由此导出确定临界轴压的非线性特征值问题.考虑材料热物性质与温度的相关性,分别就两端简支和两端固支边界条件,分析了温度梯度、初始几何缺陷、组分材料体积分数对分岔屈曲临...     

有限长圆柱壳受径向冲击的塑性动力屈曲分析

讨论两端固定的圆柱薄壳在均布外部冲击下的塑性动力屈曲。依据实验现象对位移场作出假设，用扰动法求得屈曲的扰动控制方程组，降阶后用标准的龙格库塔法进行数值求解。其中物理关系采用Ｌｅｖｙ－Ｍｉｓｅｓ流动理论，材料为刚线性强化模型。计算结果同Ｆｌｏｒｅｎｃｅ等的Ｂｅｓｓｅｌ函数解作了比较，对边界对屈曲的影响作了讨论。本文的结果对潜艇抗水下爆炸的研究有重要意义。     

Local solution of the stress and strain fields in the necking section of cylindrical bars under uniaxial tension

The problem of finding the stress and strain fields over the minimum cross section of necked cylindrical bars under uniaxial tensile load has been solved locally using a new fast numerical method. The scheme delivers both the accuracy of the finite element analysis and the applicability of simple closed-form analytical solutions. The required inputs are the distributions of curvature radii for both isostatic and material lines. It is numerically observed that the mathematical formulas available in the literature fail to adequately predict these distributions. Introducing the stress normalized strain-hardening rate as the most decisive parameter affecting the curvature radii, a database and interpolation technique have been developed in order to estimate the necessary information based on the results of the previously FE analyzed samples. Finally, a practical case has been solved and compared with the FE results.     

球面各向同性球体内的动态热应力集中

利用有限克尔变换得到了求面各向同笥球体的热冲击作用下的动态热应力解析表达式。从表达式中,可以看出球中向同性球体的动态热应力集中现象明显不同于各向同性球体。另外,所描述的动态热应力集中现象与文献「１,３」也有一定的区别。     

Transient analysis of viscoelastic helical rods subject to time-dependent loads

The transient analysis of viscoelastic helical rods subject to time-dependent loads are examined in the Laplace domain. The governing equations for naturally twisted and curved spatial rods obtained using the Timoshenko beam theory are rewritten for cylindrical helical rods. The curvature of the rod axis, effect of rotary inertia and, shear and axial deformations are considered in the formulation. The material of the rod is assumed to be homogeneous, isotropic and linear viscoelastic. The viscoelastic constitutive equations are written in the Boltzmann–Volterra form. Ordinary differential equations in canonical form obtained in the Laplace domain are solved numerically using the complementary functions method to calculate the dynamic stiffness matrix of the problem. The solutions obtained are transformed to the real space using an appropriate numerical inverse Laplace transform method. Numerical results for quasi-static and dynamic response of viscoelastic models are presented in the form of graphics.     

多层横观各向同性圆柱壳的三维弹性理论解

本文从三维弹性理论出发,用特征函数法研究多层横观各向同性圆柱壳的轴对称问题.把位移和应力分量的齐次解表达成特征函数展开式,并把特解部分用Fourier级数表示.以多层圆柱壳的内、外柱面作为齐次边界,同时考虑层间的连续条件,推导出问题的特征方程并用Muller法求解.文中运用传递矩阵技术处理多层问题,并用边界型最小二乘配点法处理端部边界条件.作为实例,对双层圆柱壳作了数值计算.     

Slip, stick, and reverse slip characteristics during dynamic fibre pullout

Inertial effects in the mechanism of fibre pullout (or push-in) are examined, with emphasis on how the rate of propagation of stress waves along the fibre, and thence the pullout dynamics, are governed by friction and the propagation of companion waves excited in the matrix. With a simple shear lag model (assuming zero debond energy at the fibre/matrix interface), the effect of uniform frictional coupling between the fibre and the matrix is accounted for in a straightforward way. Analytical solutions are derived when the pullout load increases linearly in time. The process zone of activated material is generally divided into two or three domains along the axis of the fibre. Within these domains, slip in the sense implied by the load, slip in the opposite sense (reverse slip), and stick may be observed. The attainable combinations define three regimes of behavior, which are realized for different material parameter values. The elastodynamic problem is also solved more accurately using a plane stress finite element method, with friction represented by an interfacial cohesive zone. The predictions of the shear lag theory are broadly confirmed.     

Contact problems for a circular plate with sliding fixation at the end face

Two mixed elasticity problems of punch indentation into a circular plate placed without clearance in a rigid cylindrical holder with smooth walls are considered. In the first problem, the plate lies without friction on a rigid base, and in the second problem, the plate is rigidly fixed to the base. The problems are solved by a method that was developed for bodies of finite dimensions and is based on the properties of closed systems of orthogonal functions. Each of the problems is reduced to two integral equations, namely, a Volterra integral equation of the first kind for the contact pressure function and a Fredholm integral equation of the first kind for the derivatives of the displacement of the plate upper surface outside the punch. The displacement function is sought as the sum of a trigonometric series and a power function with a root singularity. After truncation, the obtained illposed system of linear algebraic equation has a stable solution. A method for solving Volterra integral equations is given. The contact pressure distribution function and the dimensionless indentation force are determined. Examples of calculation of the plate interaction with the plane punch are given. Contact problems were earlier studied for a rectangle and a circular plate with a stress-free end both without taking account of their fixation [1, 2] and with regard for their fixation [3, 4]. The solution method described here was used to study the interaction of elastic hollow cylinder of finite length with a rigid bandage and a rigid insert [5, 6]. Other papers dealing with contact problems for bodies of finite dimensions, in particular, for a circular plate, should also be mentioned. In these papers, the problems under study were solved by the method of homogeneous solutions [7, 8] and by the method of coupled series-equations [9].     

Coupled thermoelasticity of functionally graded cylindrical shells

The coupled thermoelastic response of a functionally graded circular cylindrical shell is studied. The coupled thermoelastic and the energy equations are simultaneously solved for a functionally graded axisymmetric cylindrical shell subjected to thermal shock load. 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 are 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 results are validated with the known data in the literature.     

Chaotic interaction dynamics of three structures: Two cylindrical shells nested into each other and their reinforcing local rib

This paper studies the chaotic dynamics of two cylindrical shells nested into each other with a gap and their reinforcing beam, also with a gap, which is subjected to a distributed alternating load. The problem is solved using methods of nonlinear dynamics and the qualitative theory of differential equations. The Novozhilov equations for geometrically nonlinear structures are used as the governing equations. Contact pressure is determined by Kantor’s method. Using finite elements in spatial variables, the partial differential equations for the beam and shells are reduced to the Cauchy problem, which is solved by explicit integration (Euler’s method). The chaotic synchronization of this system is studied.     

ELASTIC PULSE BUCKLING OF CYLINDRICAL SHELLS UNDER RADIAL IMPULSIVE LOADING

ＥＬＡＳＴＩＣＰＵＬＳＥＢＵＣＫＬＩＮＧＯＦＣＹＬＩＮＤＲＩＣＡＬＳＨＥＬＬＳＵＮＤＥＲＲＡＤＩＡＬＩＭＰＵＬＳＩＶＥＬＯＡＤＩＮＧＨｕａｎｇＣｈｅｎｇｙｉ（黄承义）ＬｉｕＴｕｇｕａｎｇ（刘土光）ＺｈｅｎｇＪｉｊｉａ（郑际嘉）（Ｄｅｐａｒｔｍｅｎｔｏ...     

Simultaneous radiative and convective heat transfer in a variable porosity medium

 The flow of an incompressible grey fluid through a horizontal channel filled with a saturated medium of variable viscosity has been considered in this paper. Such flows in porous media have several applications in industrial processes. For the radiative effects a two flux model has been used in order to simplify the governing integro-differential equations for which closed-form solutions are not obtainable. The problem has been solved by employing a highly successful tri-diagonal, implicit, iterative, finite difference method. The effects of the pertinent parameters on the velocity and temperature distributions have been shown in several figures. Received on 6 December 1999     

无穷域势流问题的有限元／差分线法混合求解

提出了一种将有限元和差分线法相结合求解无穷域势流问题的算法。用两同心圆将求解域划分为存在重叠的有限和无限两个区域,在有限和无限域上分别用有限元和差分线法求解Laplace方程边值问题。用差分线法推导出的关系式修正有限元方程,求解该方程组从而得到原问题的解。本算法将求解无穷域问题转化为代数特征值问题和有限域内线性方程组的...     

Analysis of the stress state due to impulsive loading in cylindrical rods

Summary This study contains an analysis of the state of stress of two coaxial cylindrical rods of different length, subjected to longitudinal impulsive loads. Two different methods of general validity are used, the first based on the one-dimensional theory of longitudinal impact, and the second on finite element procedures which, though well known, have been specifically adapted for the present purpose in a manner which we believe provides a much more complete picture of the state of stress. One of the many problems of current technical interest which can be solved by means of the suggested procedures, i.e., the problem of impact stresses on rotary — percussive hydraulic drills, is dealt with by way of example.

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Sommario Nel lavoro si riferisce sull'analisi degli stati di tensione di due elementi cilindrici coassiali astiformi di diversa lunghezza, soggetti a forze longitudinali di carattere impulsivo. Vengono utilizzate due diverse metodologie di validità generale, l'una basata sulla teoria monodimensionale dell'urto longitudinale e l'altra su noti procedimenti di discretizzazione agli elementi finiti, ma con specifiche procedure all'uopo studiate, pervenendo alla conclusione che questo secondo metodo fornisce un quadro molto più esauriente dello stato di tensione. In via esemplificativa generale, viene affrontato uno dei numerosi problemi tecnicamente attuali, risolubili con l'impiego delle procedure proposte e, specificamente, quello relativo alle sollecitazioni d'urto nelle perforatrici idrauliche a rotopercussione.

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The torsion problem of a multilayered finite cylinder with the multiple interface cylindrical cracks

The torsion axisymmetric problem for a finite cylinder consisting of an arbitrary quantity of cylindrical coaxial layers is solved. Multiple cylindrical cracks with free of loading branches are situated on adjoining surfaces of the layers. The boundary problem is reduced to the system of integro-differential equations, its solution is found with the help of the orthogonal polynomials method. The novelty of the paper is in the construction of a solution for an arbitrary number of cylinder layers which allows the approximation of the initial problem for functionally graded materials by the problem for coaxial cylinders with jumplike changing elastic constants of the materials. Since the solution is built regardless of the number of layers (the elastic parameters of all layers are included in the constructed solution), one can refine an initial problem’s statement by increasing the number of layers. The stress intensity factors are found for an arbitrary number of cylindrical interface cracks in the multilayered cylinder of a finite length.     

Transient response of piezoelectric composites caused by the sudden formation of localized defects

A continuum model is presented which is capable of generating the transient electroelastic field in piezoelectric composites of periodic microstructure, caused by the sudden appearance of localized defects. These defects are simulated by associating to every one of the ten piezoelectric parameters of the constituents a distinct damage variable. This procedure enables the modeling of localized cracks, soft and stiff inclusions and cavities. As a result, the constitutive equations of the piezoelectric phases appear in a specific form that includes eigen-electromechanical field variables which represent these defects. The method of solution is based on the combination of two distinct approach. In the first one, the representative cell method is employed according to which the periodic composite, which is discretized into several cells, is reduced to a problem of a single cell in the discrete Fourier transform domain. The resulting coupled elastodynamic and electric equations, initial, boundary and interfacial conditions in the transform domain are solved by employing a wave propagation in piezoelectric composite analysis which forms the second approach. The method of solution is verified by comparison with an analytical solution for the transient response of a piezoelectric material with a semi-infinite mode III-crack. Several applications are presented for the sudden formation of cracks in homogeneous and layered piezoelectric materials which are subjected to various types of electromechanical loading, and for the sudden appearance of a cavity. The effect of electromechanical coupling on the dynamic response is discussed.     

Dynamic buckling of thin-walled composite plates with varying widthwise material properties

The paper deals with dynamic response of a thin-walled rectangular plate subjected to in-plane pulse loading. The plate is made of orthotropic (fibre composite) material in which the principal directions of orthotropy are parallel to the plate edges. The plate is characterised by a widthwise varying fibre volume fraction. The structures are assumed to be simply supported at the loaded ends and at non-loaded ends with five different boundary conditions (both simply supported, both fixed, simply supported fixed, simply supported free edge, fixed free edge). In order to obtain the equations of motion the non-linear theory of orthotropic thin-walled plates has been modified in such a way that it additionally accounts for all components of inertial forces. The differential equations of motion have been obtained from Hamilton’s Principle. The problem of nonlinear static stability was solved with the second order of the Koiter’s asymptotic stability theory of conservative systems. The results obtained from analytical–numerical method were compared with the results from finite element method (FEM).