Transient thermal stresses in two-dimensional functionally graded thick hollow cylinder with finite length

In this paper transient thermal stresses in a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) based on classical theory of thermoelasticity are considered. The volume fraction distribution of materials, geometry and thermal load are assumed to be axisymmetric but not uniform along the axial direction. The finite element method with graded material properties within each element is used to model the structure. Temperature, displacements and stress distributions through the cylinder at different times are investigated. Also the effects of variation of material distribution in two radial and axial directions on the thermal stress distribution and time responses are studied. The achieved results show that using 2D-FGM leads to a more flexible design so that time responses of structure, maximum amplitude of stresses and uniformity of stress distributions can be modified to a required manner by selecting suitable material distribution profiles in two directions.     

Stress field of orthotropic cylinder subjected to axial compression

Based on the constancy hypothesis of material volume, the circumferential and radial stresses of a cylinder specimen are analyzed when the cylinder is subject to a loading along the axial direction. The circumferential and radial stress distribution is a power function of radius parameter when the constitutive relation of specimen material is orthotropic. The stress distribution is a quadratic function of radius parameter for transversely isotropic material. Along the cylinder axial line, the circumferential and radial stresses are maximum and equal to each other. In the circumference boundary surface, the radial stress is zero and the circumferential stress value is minimal. The failure theory of maximum tensile circumferential strain is applied to calculate the critical axial loading. The circumference-boundary-layer failure criterion of orthotropic cylinders is described with the Hill-Tsai strength theory. The obtained strength theory is related to axial stress and mechanical properties of specimen material and to the specimen axialdeformation strain rate and the change rate of strain rate.     

Acoustoelastic determination of stress in slightly orthotropic materials

A method is proposed to determine stresses in acoustoelasticity by making use of orthotropic stress-acoustic relations and the equations of equilibrium. It is derived theoretically that shear stress is determined ny ultrasonic data ofB and ?, which denote a magnitude of acoustic birefringence and its principal direction, respectively. Other stress components are obtained by numerical integration of the equilibrium equation with the shear stress thus determined. Experiments were carried out to show the validity and usefulment of the method. This method was applied to the measurement of stress field on a plate with a circular hole subjected to axial tension. Ultrasonic measurements were made by a Y-cut quartz transducer with 5-MHz fundamental frequency. The specimen was cut out from 1100 aluminum plate of 4-mm thickness, which shows a slight orthotropy due to roll working. The values ofB and ? were measured in both stressed and unstressed state. Then, stress distributions were determined by the method proposed here, and are compared with the known theoretical distributions.     

初应力对单向复合材料圆柱板周向波的影响

基于“增量变形力学”理论,研究了径向和轴向均匀初应力作用下单向复合材料圆柱板中周向波的传播特性,应用Legendre多项式方法求解了耦合波动方程。讨论了单向复合材料纤维方向分别为周向和轴向时,初应力对圆柱板中的周向类Lamb波和SH波的影响。数值分析结果表明初应力对周向类Lamb波和周向SH波的影响是非常不同的;轴向初应力对频散曲线、位移和应力分布的影响与径向初应力的影响也不相同。     

Transient heat conduction in two-dimensional functionally graded hollow cylinder with finite length

In this paper a thick hollow cylinder with finite length made of two dimensional functionally graded material (2D-FGM) subjected to transient thermal boundary conditions is considered. The volume fraction distribution of materials, geometry and thermal boundary conditions are assumed to be axisymmetric but not uniform along the axial direction. The finite element method with graded material properties within each element is used to model the structure and the Crank–Nicolson finite difference method is implemented to solve time dependent equations of the heat transfer problem. Two-dimensional heat conduction in the cylinder is considered and variation of temperature with time as well as temperature distribution through the cylinder are investigated. Effects of variation of material distribution in two radial and axial directions on the temperature distribution and time response are studied. The achieved results show that using two-dimensional FGM leads to a more flexible design so that transient temperature, maximum amplitude and uniformity of temperature distributions can be modified to achieve required specifications by selecting a suitable material distribution profile in two directions.     

Measurement of residual internal stresses in optical fiber preforms

A non-destructive experimental procedure is presented which enables the determination of residual thermal stresses in optical fiber preforms. The procedure is based on integrated photoelasticity. We carry out the measurement of the optical retardation using the traditional Sénarmont compensation method combined with a fringe shifting technique. The radial distribution of the axial stress is reconstructed using Abel transform. We have investigated two different refractive-index profiles, adopted in the realization of monomode and multimode optical fibers. It was shown that in both cases the results obtained experimentally and those analytically predicted by the Timoshenko elastic model were in good agreement. To obtain accurate experimental results, it was necessary to apply a correction procedure to take into account the fact that the trafectories of the light rays inside the preforms are not straight lines.     

Effects of radially varying moduli on stress distribution of nonhomogeneous anisotropic cylindrical bodies

In this study, the stress distribution in a nonhomogeneous anisotropic cylindrical body is investigated. Using equilibrium equations, Hooke’s law and strain–displacement relations, a system of equations is obtained in cylindrical coordinates in terms of stress potentials where elastic properties change in radial direction. Young’s and shear moduli are expressed as power functions of r and Poisson’s ratios are kept constant. Closed-form solutions for stress potentials and stress distribution are obtained for an axisymmetric, orthotropic cylinder. Results are checked with FE results. A pressurized thick walled cylinder example is studied in details. Stresses in radial, tangential and axial directions and Von Mises stresses are plotted for different powers of r.     

Mode I crack tip field with strain gradient effects

A plane strain mode I crack tip field with strain gradient effects is investigated. A new strain gradient theory is used. An elastic-power law hardening strain gradient material is considered and two hardening laws, i. e. a separation law and an integration law are used respectively. As for the material with the separation law hardening, the angular distributions of stresses are consistent with the HRR field, which differs from the stress results^[19]; the angular distributions of couple stresses are the same as the couple stress results^[19]. For the material with the integration law hardening, the stress field and the couple stress field can not exist simultaneously, which is the same as the conclusion^[19], but for the stress dominated field, the angular distributions of stresses are consistent with the HRR field; for the couple stress dominated field, the angular distributions of couple stresses are consistent with those in Ref. [19]. However, the increase in stresses is not observed in strain gradient plasticity because the present theory is based on the rotation gradient of the deformation only, while the crack tip field of mode I is dominated by the tension gradient, which will be shown in another paper. Supported by the National Science Foundation of China (No. 19704100), Science Foundation of Chinese Academy of Sciences (Project KJ951-1-20), CAS K. C. Wong Post-doctoral Research Award Fund and the Post Doctoral Science Fund of China.     

Boundary Effects in the Eigenstrain Method

We present a comprehensive study of the effects of internal boundaries on the accuracy of residual stress values obtained from the eigenstrain method. In the experimental part of this effort, a composite specimen, consisting of an aluminum cylinder sandwiched between steel cylinders of the same diameter, was uniformly heated under axial displacement constraint. During the experiment, the sample temperature and the reaction stresses in the load frame in response to changes in sample temperature were monitored. In addition, the local (elastic) lattice strain distribution within the specimen was measured using neutron diffraction. The eigenstrain method, utilizing finite element modeling, was then used to predict the stress field existing within the sample in response to the constraint imposed by the load frame against axial thermal expansion. Our comparison of the computed and measured stress distributions showed that, while the eigenstrain method predicted acceptable stress values away from the cylinder interfaces, its predictions did not match experimentally measured values near them. These observations indicate that the eigenstrain method is not valid for sample geometries with this type of internal boundaries.     

Stress Separation of Interferometrically Measured Isopachics in a Perforated Plate

A method for the stress separation of interferometrically measured isopachics using an Airy stress function is proposed in this study. A Poisson equation that represents the relationship between the sum of principal stresses and an Airy stress function is solved using a finite element method. The Dirichlet boundary condition for solving the Poisson equation is determined by the approximation of an assumed Airy stress function along the boundary of the model. Therefore, the distribution of the Airy stress function is obtained from the measured isopachic contours. Then, the stresses are obtained from the computed Airy stress function. The effectiveness of the proposed method is validated by applying the proposed method to the isopachic contours in a perforated plate obtained by Mach-Zehnder interferometry. Results indicate that stress components around a hole in a plate can be obtained from isopachics by the proposed method.     

Pull-in voltage analysis of electrostatically actuated MEMS with piezoelectric layers: A size-dependent model

A size-dependent model for electrostatically actuated microbeam-based MEMS (micro-electro-mechanical systems) with piezoelectric layers attached is developed based on a modified couple stress theory. By using Hamilton's principle, the nonlinear differential governing equation and boundary conditions of the MEM structure are derived. In the newly developed model, the residual stresses, fringing-field and axial stress effects are considered for the fixed–fixed microbeam with piezoelectric layers. The results of the present model are compared with those from the classical model. The results show the size effect becomes prominent if the beam dimension is comparable to the material length scale parameter (MLSP). The effects of MLSP, the residual stresses and axial stress on the pull-in voltage are also studied. The study may be helpful to characterize the mechanical and electrostatic properties of small size MEMS, or guide the design of microbeam-based devices for a wide range of potential applications.     

Torsion problems for a cylinder with a rectangular hole and a rectangular cylinder with a crack

Using the method of singular integral equation and the crack-cutting technique, the rigorous solutions are obtained for a cylinder with a rectangular hole and a rectangular cylinder with a crack, which exactly satisfy the boundary conditions and the conditions at the corner points. After that the torsional rigidities and the stress intensity factors at the crack tip are determined. Next, for the doubly connected circular cylinder with a rectangular hole the expressions for the singular stresses around the concave corner points are derived and the generalized stress intensity factors are then defined. Since the crack-cutting technique is used in this paper, the solution of the matching rectangular cylinder is also obtained and its numerical results coincide with those in references. Thus the method proposed here is verified. The project supported by National Natural Science Foundation of China     

Analysis of dynamic stress intensity factors of thick-walled cylinder under internal impulsive pressure

Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary condi- tions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier-Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack sub- jected to internal impulsive pressure are given by dynamic weight function method. The finite element method is utilized to verify the results of numerical examples, showing the validity and feasibility of the proposed method.     

A General Formulation of Stress Distribution in Cylinders Subjected to Non-Uniform External Pressure

This work presents a two-dimensional stress analysis for elastic solid cylinders subjected to combined loading. The loading is generally formed with a number of concentrated and partially distributed forces all applied radially on the outer surface. The distributed forces cause pressures with non-uniform intensity along the circumferential direction. The cylinder is assumed to be long so that a state of plane-strain is valid. To obtain the stress distribution for the problem of partially distributed forces a new approach is followed first introduced in this paper. It is based on the expressions formed after using the theory of simple radial stress distribution when point-forces are applied on the cylinder and leads to the solution after direct integration. The total stresses due to both concentrated and distributed forces are obtained using the method of superposition. Apart from its simplified formulation, this general solution is always preferable since it proved to have a great advantage. As a result of not containing Fourier series, it eliminates some problems of convergence of the series at the boundaries that appear due to the Gibbs phenomena when the boundary conditions are a discontinuous function. Numerical results are presented for some interesting cases of loading conditions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Phase Shifting Full-Field Interferometric Methods for Determination of In-Plane Tensorial Stress

A new method that combines phase shifting photoelasticity and transmission Coherent Gradient Sensing (CGS) is developed to determine the tensorial stress field in thin plates of photoelastic materials. A six step phase shifting photoelasticity method determines principal stress directions and the difference of principal stresses. The transmission CGS method utilizes a standard four step phase shifting method to measure the x and y first derivatives of the sum of principal stresses. These stress derivatives are numerically integrated using a weighted preconditioned conjugate gradient (PCG) algorithm, which is also used for the phase unwrapping of the photoelastic and CGS phases. With full-field measurement of the sum and difference of principal stresses, the principal stresses may be separated, followed by the Cartesian and polar coordinate stresses using the principal stress directions. The method is demonstrated for a compressed polycarbonate plate with a side V-shaped notch. The experimental stress fields compare well with theoretical stress fields derived from Williams solution for a thin plate with an angular corner.     

Thermal stress analysis of a silicon carbide/aluminum composite

Thermal deformations and stresses were studied in a silicon-carbide/aluminum filamentary composite at temperatures up to 370°C (700°F). Longitudinal and transverse thermal strains were measured with strain gages and a dilatometer. An elastoplastic micromechanical analysis based on a one-dimensional rule-of-mixtures model and an axisymmetric two-material composite cylinder model was performed. It was established that beyond a critical temperature thermal strains become nonlinear with decreasing longitudinal and increasing transverse thermal-expansion coefficients. This behavior was attributed to the plastic stresses in the aluminum matrix above the critical temperature. An elastoplastic analysis of both micromechanical models was performed to determine the stress distributions and thermal deformation in the fiber and matrix of the composite. While only axial stresses can be determined by the rule-of-mixtures model, the complete triaxial state of stress is established by the composite cylinder model. Theoretical predictions for the two thermal-expansion coefficients were in satisfactory agreement with experimental results.     

Finite element method for viscoelastic flows based on the discrete adaptive viscoelastic stress splitting and the discontinuous Galerkin method: DAVSS-G/DG

Accurate and robust finite element methods for computing flows with differential constitutive equations require approximation methods that numerically preserve the ellipticity of the saddle point problem formed by the momentum and continuity equations and give numerically stable and accurate solutions to the hyperbolic constitutive equation. We present a new finite element formulation based on the synthesis of three ideas: the discrete adaptive splitting method for preserving the ellipticity of the momentum/continuity pair (the DAVSS formulation), independent interpolation of the components of the velocity gradient tensor (DAVSS-G), and application of the discontinuous Galerkin (DG) method for solving the constitutive equation. We call the method DAVSS-G/DG. The DAVSS-G/DG method is compared with several other methods for flow past a cylinder in a channel with the Oldroyd-B and Giesekus constitutive models. Results using the Streamline Upwind Petrov–Galerkin method (SUPG) show that introducing the adaptive splitting increases considerably the range of Deborah number (De) for convergence of the calculations over the well established EVSS-G formulation. When both formulations converge, the DAVSS-G and DEVSS-G methods give comparable results. Introducing the DG method for solution of the constitutive equation extends further the region of convergence without sacrificing accuracy. Calculations with the Oldroyd-B model are only limited by approximation of the almost singular gradients of the axial normal stress that develop near the rear stagnation point on the cylinder. These gradients are reduced in calculations with the Giesekus model. Calculations using the Giesekus model with the DAVSS-G/DG method can be continued to extremely large De and converge with mesh refinement.     

磁电复合材料中拓扑磁结构的力学调控

磁性斯格明子是在一些铁磁材料中存在的一种重要拓扑磁结构,由于其具有独特的磁-电-力-热多场耦合特性,在未来新型自旋电子器件中有着广泛的应用前景。然而,磁性斯格明子一般需要在外加磁场下才能稳定存在,极大地限制了其在自旋电子器件中的实际应用。本文基于实空间下磁电材料的相场模拟,发现铁电和铁磁复合薄膜中铁电斯格明子可以通过界面变形来稳定铁磁斯格明子。由于力电耦合效应,铁电层中铁电斯格明子的非均匀分布极化在界面产生周期性的非均匀界面变形。界面变形通过力磁耦合效应,使铁磁层中的磁性斯格明子在没有外加磁场的条件下能够稳定存在。本文的研究结果表明,基于磁电复合材料中的力-电-磁耦合效应,通过优化设计复合材料中不同组元的结构,可以实现拓扑磁结构的力学调控,从而为设计基于拓扑磁结构的新型自旋电子器件提供了新思路。     

Thermoelastic transient response of an infinitely long annular multilayered cylinder

Thermoelastic transient response of multilayered annular cylinders of infinite lengths subjected to known temperature at traction-free inner and outer surfaces are considered. A method based on the Laplace transformation and finite difference method has been developed to analyze the thermoelasticity problem. Using the Laplace transform with respect to time, the general solutions of the governing equation are obtained in transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. Solutions for the temperature and thermal stress distributions in a transient state were obtained. It was found that the temperature distribution, the displacement and the thermal stresses change slightly as time increases. There is no limit of number of annular layers of the cylinder in the presented computational procedures.     

Measurement of the Distribution of Residual Stresses in Layered Thick-Walled GFRP Pipes

The objective of this study is to measure the axial, circumferential, shear and radial residual stress distributions in three thick-walled glass fibre reinforced plastic (GFRP) filament-wound pipes, two of which are layered. The measurement of residual stresses was carried out using a recently published layer removal method which overcomes the limitations of previous techniques and can be applied to layered anisotropic pipes of any wall thickness. Layers of approximately 0.3 mm thickness were incrementally ground from the outer surface of the pipes. The resulting strains were measured on the inner surfaces. A least-squares polynomial was fitted to each measured data set, and used to calculate the corresponding stress distributions. All of the resulting axial, hoop and shear stress distributions adhere to the requirement of self-equilibrium and the radial stress distributions all vanish to zero at the inner and outer surfaces. The radial stresses of the layered pipes showed a tendency to have two peaks, one for each layer, a consequence of the two-stage manufacturing process of these pipes. The measured axial and hoop stresses of all three pipes were similar at the inner surfaces despite significant differences in the stiffnesses in the principal directions arising from different wind angles.