A unified generalized thermoelasticity; solution for cylinders and spheres

A new unified formulation for the generalized theories of the coupled thermoelasticity based on the Lord–Shulman, Green–Lindsay, and Green–Naghdi models is proposed in this paper. The unified form of the governing equations is presented by introducing the unifier parameters. The formulations are derived and given for the anisotropic heterogeneous materials. The unified equations are reduced for the isotropic and homogeneous materials. Transforming the governing equations into the Laplace domain, they are analytically solved in the space domain for a hollow sphere and cylinder, where a parameter is introduced to consolidate the solution for the sphere and cylinder in a unified form. A thermal shock load is applied to the inner surface of the sphere and cylinder and the results are presented using a numerical inversion technique of the Laplace transform. The results are validated with the known data in the literature.     

Thermoelastic waves in coated homogeneous anisotropic materials

In this article the effect of anisotropy and temperature on the dispersive wave propagation in composite substrate has been investigated. The propagation of guided waves in coated homogeneous anisotropic thermoelastic media is of interest in electronics and related areas. In recent years, cladded fiber-reinforced composites are being developed for use as aerospace structures. This paper deals with the guided wave propagation in a cladded (or coated) thermoelastic homogeneous anisotropic medium in the context of linear generalized thermoelasticity. The cladding (coating) is assumed to be thin homogeneous isotropic layer, which is bonded to a transversely isotropic substrate with the axis of symmetry parallel to the layer. It is shown that the anisotropy of the substrate affects the dispersion behaviour in a manner that is substantially different than that in case of isotropic substrate. In addition, the effect of variation of temperature on the dispersion curves and attenuation coefficient of thermoelastic waves is also studied. The results in case of classical coupled thermoelasticity (CT) and uncoupled thermoelasticity (UCT) can be obtained as special cases from the present analysis by omitting thermal relaxation time and thermo mechanical coupling effects, respectively. Finally, the numerical solution of the model is obtained by computer simulations for a magnesium material half-space in different situations and the computed dispersion curves and attenuation coefficient profiles have been presented graphically in order to illustrate different phenomenon involved.     

Axial effects investigation in fixed-end circular bars under torsion with a finite deformation model based on logarithmic strain

In this paper the torsion problem of a circular bar with fixed ends is solved using a finite deformation constitutive model based on the corotational rates of the logarithmic strain. The logarithmic, Green–Naghdi and Eulerian corotational rates of the logarithmic strain are used in the model. The solution is based on a von Mises type yield function that incorporates isotropic and kinematic hardenings. For the kinematic hardening, a modified Armstrong–Fredrick hardening model with the corotational rate of the logarithmic strain is used. Assuming incompressible behavior, the fixed-end torsion problem is simplified to the simple shear problem. Solving the problem, the stress components are integrated to calculate the torque and axial force. It is qualitatively shown that the results based on the logarithmic corotational rate are in good agreement with the experimental results.     

On applications of generalized functions to the analysis of Euler–Bernoulli beam–columns with jump discontinuities

In this article some applications of the distribution theory of Schwarz to the analysis of beam–columns with various jump discontinuities are offered. The governing differential equation of an Euler–Bernoulli beam–column with jump discontinuities in flexural stiffness, displacement, and rotation, and under an axial force at the point of discontinuities, is obtained in the space of generalized functions. The auxiliary beam–column method is introduced. Using this method, instead of solving the differential equation of the beam–column in the space of generalized functions, another differential equation can be solved in the space of classical functions. Some examples of beam–columns and columns with various jump discontinuities are solved. Deflections of beam–columns and buckling loads for columns with jump discontinuities are calculated using the Laplace transform method in the space of generalized functions.     

Effects of voids and rotation on plane waves in generalized thermoelasticity

In the present paper, we study the influence of rotation, thermal and voids parameters on the reflection phenomenon of plane waves in generalized thermoelastic solid with one relaxation time. The governing field equations for isotropic and homogeneous thermoelastic half-space with voids and rotation are formulated in the context of Lord and Shulman theory of generalized thermoelasticity. The solutions of these governing equations indicate the existence of four coupled plane waves, namely; P₁; P; P₃ and P₄ waves in the thermoelastic medium. The boundary conditions at stress-free thermally insulated surface are satisfied to obtain the system of four nonhomogenous equations in the reflection coefficients of various reflected waves for the incidence of P₁ wave. A particular material is modeled as the thermoelastic solid half-space to compute the complex absolute values of speeds and reflection coefficients. The speeds and reflection coefficients are shown graphically to observe the influences of rotation, thermal relaxation time and voids parameters.     

Mechanical and microstructural analysis on the superplastic deformation behavior of Ti–6Al–4V Alloy

The present investigation has been made to study the superplastic deformation behavior of Ti–6Al–4V alloy based on the theory of inelastic deformation, and to analyze the boundary sliding characteristics using transmission electron microscopy. Flow characteristics for the microstructures of 2.5–16 μm grain sizes were analyzed by the load relaxation tests at various temperatures ranging from 600 to 927°C. The results showed that at relatively low temperatures such as 600°C the grain matrix deformation was dominant and found to be consistent with the state equation based on the dislocation dynamics. On the contrary, above the temperature of 800°C, the grain boundary sliding became dominant resulting in the change of curvature in the stress–strain rate curves, which was more pronounced in the finer microstructures. However, the deformation mode changes from grain boundary sliding to grain matrix deformation with the increase in grain size as evidenced by transmission electron microscopy.     

Numerical and experimental investigations of contact in thin and thick rings

The objective of this study is to obtain the appropriate variational inequalities formulation corresponding to shell contact. Specifically, the work is concerned with the prediction of the nonlinear deformation behaviour as well as the stress and strain states resulting from contact in thin rings. The new formulations account for large deformations and rotations in a total Lagrangian framework by adopting the second Piola–Kirchhoff stress and the Green–Lagrange strain measures. In order to validate the newly proposed numerical approach, detailed photoelastic and strain gauge measurements were conducted using different rings. Two aspects of the work were accordingly examined. The first is concerned with the validation of the developed algorithms, while the second is concerned with the variation of the contact pressure with the thickness of the ring. The results reveal close agreement between the numerical predictions and the experimentally measured values.     

Numerical simulation of the localization behavior of hydrostatic-stress-sensitive metals

The present paper deals with the numerical simulation of the elastic–plastic deformation and localization behavior of solids which are plastically dilatant and sensitive to hydrostatic stresses. The model is based on a generalized macroscopic theory taking into account macroscopic as well as microscopic experimental data obtained from tests with iron-based metals. It shows that hydrostatic components may have a significant effect on the onset of localization and the associated deformation modes, and that they generally lead to a notable decrease in ductility. The continuum formulation relies on a generalized I₁–J₂–J₃ yield criterion to describe the effect of the hydrostatic stress on the plastic flow properties of metals. In contrast to classical theories of metal plasticity, the evolution of the plastic part of the strain rate tensor is determined by a non-associated flow rule based on a plastic potential function which is expressed in terms of stress invariants and kinematic parameters. Numerical simulations of the elastic–plastic deformation behavior of hydrostatic-stress-sensitive metals show the physical effects of the model parameters and also demonstrate the efficiency of the formulation. Their results are in excellent agreement with available experimental data. A variety of large-strain elastic–plastic problems involving pronounced localizations is presented, and the influence of various model parameters on the deformation and localization behavior of hydrostatic-stress-sensitive metals is discussed.     

Generalized thermodiffusion for an unbounded body with a spherical cavity subjected to periodic loading

In this paper, a general solution to the field equations of generalized thermodiffusion in an infinite thermoelastic body with a spherical cavity has been obtained in the context of the theory of generalized thermoelastic diffusion. The bounding surface of the sphere is subjected to periodic loading and the temperature and chemical potential are assumed to be zero on the curved surface. The generalized theory of thermoelasticity is applied to account for finite velocity of heat propagation. The closed form solutions for distributions of displacement, temperature and stresses are obtained. The solutions valid in the case of small frequency are deduced and the results are compared with the corresponding results obtained in other generalized thermoelasticity theories. Numerical results applicable to a copper-like material are also presented graphically and the nature of variations of the physical quantities with radial coordinate and with frequency of vibration is analyzed.     

Frequencies and mode shapes for thick truncated hollow cones

The finite element method of analysis is employed to study the vibration of truncated thick hollow cones. The three-dimensional strain–displacement equations are used to formulate the finite element in the conical coordinate system. Axial symmetry is assumed and the formulation is reduced to two dimensions while maintaining the three-dimensional character of the analysis. The accuracy of the analysis is established by comparing results for free–free boundary conditions with existing solutions. The effects of different boundary conditions, including fixed–free and fixed–fixed, are studied to determine their effects on the frequency of vibration. Frequency results are given for an additional boundary condition corresponding to a layer attached to the exterior of a rigid cone. Nondimensional results for an isotropic material with Poisson's ratio of 0.3 are presented in terms of tables, plots of frequency versus cone apex angle and plots of selected mode shapes.     

The envelope order spectrum based on generalized demodulation time–frequency analysis and its application to gear fault diagnosis

The generalized demodulation time–frequency analysis is a novel signal processing method, which is particularly suitable for the processing of multi-component amplitude-modulated and frequency-modulated (AM–FM) signals as it can decompose a multi-component signal into a set of single-component signals whose instantaneous frequencies own physical meaning. While fault occurs in gear, the vibration signals measured from gearbox would exactly display AM–FM characteristics. Therefore, targeting the modulation feature of gear vibration signal in run-ups and run-downs, a fault diagnosis method in which generalized demodulation time–frequency analysis and envelope order spectrum technique are combined is put forward and applied to the transient analysis of gear vibration signal. Firstly the multi-component vibration signal of gear is decomposed into some mono-component signals using the generalized demodulation time–frequency analysis approach; secondly the envelope analysis is performed to each single-component signal; thirdly each envelope signal is re-sampled in angle domain; finally the spectrum analysis is applied to each re-sampled signal and the corresponding envelope order spectrum can be obtained. Furthermore, the gear working condition can be identified according to the envelope order spectrum. The analysis results from the simulation and experimental signals show that the proposed algorithm was effective in gear fault diagnosis.     

摩擦约束有限变形非线性弹性广义变分不等原理的半反推法

研究了有限变形非线性弹性接触问题变分不等方程的逆问题 ,用半反推法成功地导出了变分不等问题的势能型能量泛函 ,并巧妙地处理了由于变分不等式引起的困难。     

Local adaptive differential quadrature for free vibration analysis of cylindrical shells with various boundary conditions

This paper presents the formulation and numerical analysis of circular cylindrical shells by the local adaptive differential quadrature method (LaDQM), which employs both localized interpolating basis functions and exterior grid points for boundary treatments. The governing equations of motion are formulated using the Goldenveizer–Novozhilov shell theory. Appropriate management of exterior grid points is presented to couple the discretized boundary conditions with the governing differential equations instead of using the interior points. The use of compactly supported interpolating basis functions leads to banded and well-conditioned matrices, and thus, enables large-scale computations. The treatment of boundary conditions with exterior grid points avoids spurious eigenvalues. Detailed formulations are presented for the treatment of various shell boundary conditions. Convergence and comparison studies against existing solutions in the literature are carried out to examine the efficiency and reliability of the present approach. It is found that accurate natural frequencies can be obtained by using a small number of grid points with exterior points to accommodate the boundary conditions.     

Free vibration of elastic helicoidal shells

An elastic helicoidal structure modelled as a plate twisted around its axis is studied in this paper. Accurate strain–displacement relationships for the shell are derived by the Green strain tensor in general shell theory and first-order shear deformation theory. An energy equilibrium equation of free vibration is introduced by the principle of virtual work. Applying the Rayleigh–Ritz method, an analytical eigenvalue equation is formulated and solved via an efficient computational approach for vibration characteristics of the helicoidal structure. A set of normalized orthogonal polynomials generated by the Gram–Schmidt procedure is presented to approximate the admissible functions. The first polynomial is taken as a kinematically compliant geometric equation of boundary conditions of the shell. The convergence and the accuracy of the present method, and the effects of geometric parameters and boundary conditions on vibration of the helicoidal structure are investigated.     

Numerical study of the flange earring of deep-drawing sheets with stronger anisotropy

A Barlat–Lian anisotropy yield function is introduced into a quasi-flow corner theory of elastic–plastic finite deformation and the elastic–plastic large deformation finite element formulation based on the principle of virtual velocity and the discrete Kirchhoff triangle plate shell element model. The focus of the present researches is on the numerical simulation of the flange earring of deep-drawing process of circular sheets with stronger anisotropy, based on which, the schemes for controlling the flange earring are proposed.     

Safety and collapse of elastic–plastic beams against dynamic loads

The dynamic load-bearing capacity of elastic–plastic beam structures is analysed by the apparatus of shakedown theory. The reduced kinematic formulation for bending beams, which is equivalently deduced from Koiter’s kinematic theorem, combined with the plastic collapse’s method of hinge mechanisms appears effective in solving practical problems. The safety limits on the quasiperiodic dynamic loads as well as respective collapse mechanisms for a number of practical beams are determined.     

Stability analysis of a rotor bearing system due to surface waviness and number of balls

In the paper, the stability analysis of a rigid rotor supported by ball bearings has been studied. In the analytical formulation, the contacts between balls and races are considered as nonlinear springs, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The implicit type numerical integration technique Newmark-β with Newton–Raphson method is used to solve the nonlinear differential equations iteratively. The effects of surface waviness and the varying number of balls on stability of rotor bearing system are observed. All results presented in form of fast fourier transformations show that the vibration characteristics of the rotor and its bearings change, when the bearings operate in different regions of their nonlinear load deflection characteristics. From the analysis, it is implied that the number of balls and number of waves in the ball bearing are two important governing parameters affecting its dynamic behavior.     

广义模块化设计原理及方法

针对传统模块化设计的局限性,将参数化设计和变量化分析技术引入模块化设计,提出广义模块化设计方法,从而拓展模块化设计的应用领域,使其既可适用于系列分级特性比较明显的产品及其产品族的开发,又可满足工况复杂、大载荷,需要进行结构强度、刚度设计,系列分级特性不明显的机械产品的开发设计.对广义模块化设计原理、广义产品平台、基于广义模块组合和基于广义产品平台的产品族规划方法进行系统阐述.最后以液压机广义模块化设计和产品族规划为例,详细说明广义模块化设计的基本原理和方法.     

Free vibration of a laminated composite shell of revolution: Effects of shear non-linearity

Effects of shear non-linearity on free vibration of a laminated composite shell of revolution are investigated using a semi-analytical method based on the Reissner–Mindlin shell theory. The coupling between symmetric and anti-symmetric vibration modes of the shell is considered in the shear deformable shell element employed in this study. The Hahn–Tsai non-linearly elastic shear stress–shear strain relation is adopted. Numerical examples are given for laminated composite circular cylindrical and conical shells with various boundary conditions. The numerical results indicate that shear non-linearity may reduce significantly the fundamental frequencies of cross-ply composite shells of revolution.     

Analytical method for solving three-dimensional thermoelasticity problems for composite shells

A new method for solving thermoelasticity problems for thick and thin shells in the three-dimensional formulation is considered. According this method, a shell body is divided into N sampling surfaces parallel to the middle surface and located at Chebyshev polynomial nodes to choose temperatures and vectors of displacements of these surfaces as unknown functions. Such a choice of unknown functions makes it possible to represent governing equations of the proposed theory for composite shells in sufficiently compact form and to use deformation relationships describing correctly the shell displacement as a rigid body.