Evaluation of stress intensity factor under pure shear stress in orthotropic material

Various types of composite materials are currently being developed and used for automobiles, airplanes, ships and other structures in response to required service conditions which are getting increasingly more severe. Of growing importance under such circumstances is the study of stress analysis and fracture mechanics for these composite material structures. Particularly, the primary concern in design of structures and machines should be the initiation of cracks due to excessive deformation, delamination in material or other material defects. In evaluating safety, it is indispensable from the structural design point of view that K value should be known by an analysis conducted in advance. In this study, stress intensity factor (mode II) under a pure shear stress was obtained using the photoelastic method and caustic method and applying an isotropic material and orthotropic material (copper fibre epoxy composite (CFEC) developed by the authors), each containing the crack. Results were compared with theoretical values. As a result, this method was found useful and the effect of the direction of the primary axis of this material on the stress intensity factor was clarified.     

正交各向异性材料结构热变形和热应力分析的无网格法计算模型及应用正交各向异性材料结构热变形和热应力分析的无网格法计算模型及应用

利用无网格伽辽金法（Element-free Galerkin,EFG）建立了正交各向异性材料结构热变形和热应力分析的计算模型,并推导了正交各向异性材料结构热弹性问题的EFG法离散控制方程。选择复合材料冷却栅管算例验证了计算模型和程序的正确性,利用该计算模型分析了具有不同材料方向角及热导率因子、热膨胀系数因子和主次泊松比因子的汽轮机叶轮,得到了其热变形总位移和Mises应力,讨论了材料方向角和上述正交各向异性材料因子对其热变形总位移和Mises应力的影响规律,给出了这些参数的合理取值范围,并选取一组参数与各向同性材料结构进行了热变形和热应力对比分析。结果表明,基于EFG法的热变形总位移和Mises应力的计算精度比有限元法高,材料方向角同时影响热变形总位移和Mises应力的大小和方向,而正交各向异性材料因子只影响热变形总位移和Mises应力的大小,不影响其方向。在复合材料结构设计过程中,合理选取材料方向角和正交各向异性材料因子可有效减小结构热变形和热应力。      

Symmetric loading of a Griffith crack by transient concentrated forces in an orthotropic material

Body forces are used to model the effect of fasteners and stiffeners. This paper contains results of a study that was undertaken to examine the effect of symmetric impact loading by concentrated body forces on a Griffith crack located in an orthotropic material. The integral transform method along with certain potential functions was used to obtain expressions for the stress intensity factor (SIF). Four different loading cases were considered. Numerical calculations show the typical overshoot in the dynamic SIF reaching values as much as 22% of the corresponding static SIF. The magnitude of the overshoot is affected by the material properties as well as the relative position between the crack and the body forces. In fact as the distance between the application of the body force and the crack increases, the magnitude of the peak value decreases. In addition, as the relative distance increases, the time at which the peak value of the overshoot occurs increases. Furthermore, the time interval over which the overshoot is maintained increases as the relative position increases. The results of the study imply that for stiffened or fastened orthotropic materials, the location of the fasteners or stiffeners may significantly affect the stress intensity factors.     

Rayleigh surface wave propagation in an orthotropic rotating magneto-thermoelastic medium subjected to gravity and initial stress

Abstract

The prime objective of the present article is to analyze the effects of rotation and initial stress on the propagation of Rayleigh surface waves in a homogeneous, orthotropic magneto-thermoelastic half space subjected to gravity field. The frequency equations in closed form are derived and the amplitude ratios of surface displacements, temperature change during the Rayleigh wave propagation on the surface of half space have been computed analytically. The highlights of this study are the effects of different parameters (rotation, magnetic field, initial stress, and gravity) on the velocity of Rayleigh waves. Variation in phase velocity of Rayleigh waves against a wave number is shown graphically. Some particular cases have been deduced. Also, the classical Rayleigh wave equation is obtained as a special case of the present study. Numerical example has been carried out and represented by the means of graphs. Impacts of various involved parameters appearing in the solutions are carefully analyzed. In fact, in the absence of various parameters, these equations are in agreement with the results for isotropic medium.     

桥面铺装对钢桥面板疲劳应力幅的影响

钢桥面板厚度小,铺装层的相对刚度较大,钢桥面板疲劳设计时,应该考虑铺装层与钢桥面板的共同作用。假设桥面铺装与顶板没有相对滑移,采用有限元方法探讨了桥面铺装弹性模量和厚度对正交异性钢桥面板疲劳应力幅的影响。     

Analytical and numerical analysis of 3D grid-reinforced orthotropic composite structures

A comprehensive micromechanical investigation of 3D periodic composite structures reinforced with a grid of orthotropic reinforcements is undertaken. Two different modeling techniques are presented; one is based on the asymptotic homogenization method and the other is a numerical model based on the finite element technique. The asymptotic homogenization model transforms the original boundary value problem into a simpler one characterized by effective coefficients which are shown to depend only on the geometric and material parameters of a periodicity cell. The model is applied to various 3D grid-reinforced structures with generally orthotropic constituent materials. Analytical formula for the effective elastic coefficients are derived, and it is shown that they converge to earlier published results in much simpler case of 2D grid reinforced structures with isotropic constituent materials. A finite element model is subsequently developed and used to examine the aforementioned periodic grid-reinforced orthotropic structures. The deformations from the finite element simulations are used to extract the elastic and shear moduli of the structures. The results of the asymptotic homogenization analysis are compared to those pertaining to their finite element counterparts and a very good agreement is shown between these two approaches. A comparison of the two modeling techniques readily reveals that the asymptotic homogenization model is appreciably faster in its implementation (without a significant loss of accuracy) and thus is readily amenable to preliminary design of a given 3D grid-reinforced composite structure. The finite element model however, is more accurate and predicts all of the effective elastic coefficients. Thus, the engineer facing a particular design application, could perform a preliminary design (selection of type, number and spatial orientation of the reinforcements) and then fine tune the final structure by using the finite element model.     

Elastic stress transmission in cellular systems—Analysis of wave propagation

A closely packed array of thin-walled rings constitutes an idealisation of a cellular structure. Elastic waves propagating through such structures must do so via the ring (cell) walls. A theoretical investigation into the propagation of elastic stresses in thin-walled circular rings is undertaken to examine the nature of wave transmission. Three modes of motion, corresponding to shear, extensional and flexural waves, are established and their respective velocities defined by a cubic characteristic equation. The results show that all three waves are dispersive. By neglecting extension of the centroidal axis and rotary inertia, explicit approximate solutions can be obtained for flexural waves. Employment of Love's approach for extensional waves [Love AEH. A treatise on the mathematical theory of elasticity, 4th ed. New York: Dover Publications; 1944. p. 452–3] enables approximate solutions for shear waves to be derived. The three resulting approximate solutions exhibit good agreement with the exact solutions of the characteristic equation over a wide range of wavelengths. The effects of material property, ring wall thickness and ring diameter on the three wave modes are discussed, and the results point to flexural waves as the dominant means of elastic energy transmission in such cellular structures. Wave velocities corresponding to different frequency components determined from experimental results are compared with theoretical predictions of group velocity for flexural waves and good correlation between experimental data and theory affirms this conclusion.     

基于一种新修正偶应力理论的平面正交各向异性功能梯度梁静弯曲模型及尺度效应

基于一种新修正偶应力理论建立了微尺度平面正交各向异性功能梯度梁模型。模型中包含两个材料尺度参数,因此能够分别描述在两个正交方向上由尺度效应带来的不同大小弯曲刚度增强。基于最小势能原理推导了平衡方程和边界条件,并以自由端受集中载荷作用的悬臂梁为例给出了弯曲问题的解析解。该梁模型的控制方程以及解的形式和经典梁模型是一致的,只是在刚度项中增加了一项和尺度效应有关的项。算例结果表明:采用本文模型所预测的梁挠度总是小于经典理论的结果,即捕捉到了尺度效应。尺度效应会随着梁几何尺寸的减小而增大,并在梁的几何尺寸远大于尺度参数时逐渐消失。     

The discrete method of separation of variables for composite material problems

In this paper, we propose the discrete method of separation of variables for the numerical solutions of the composite material problems on a polygon. After a suitable transformation of coordinates, the original boundary value problem is reduced to a discontinuous coefficients problem on a semi-infinite strip. Then we get the semi-discrete approximation of the discontinuous coefficients problem which is equivalent to a boundary value problem of a system of ordinary differential equations (O.D.E's) with constant coefficients. After solving the boundary value problem of the system by a direct method, then the semi-discrete approximation of the original problem is obtained. Especially we can see that the semi-discrete approximation in form of separable variables naturally possesses the singularity of the original problem. Finally, the numerical examples show that our method is feasible and very effective for solving composite material problems numerically.     

Comparison of different stress-state dependent cohesive zone models applied to thin-walled structures

Two different approaches that explicitly incorporate the stress triaxiality into cohesive zone models applicable to thin-walled structures are compared to identify the relative merits and limitation of these models. The number of model parameters involved, the ease of parameter determination and the predictive capabilities of the models over a wide range of thin-walled geometries are investigated. The first model, proposed recently by the authors, uses basic elastic–plastic constitutive equations combined with a model parameter depending on the average triaxiality in plane stress conditions. The second model incorporates stress-state through exponential dependence of cohesive strength on triaxiality, similar to plane strain studies earlier. The respective parameters for both models are identified and subsequently applied to several notched and precracked specimens. It is shown that in contrast to stress-state independent models, both constraint dependent models are able to predict well failure of a wide range of structures. While the model incorporating triaxiality dependent cohesive parameters has more parameters to be determined, it is not restricted to any specific stress condition and therefore can be extended to arbitrary three-dimensional stress-states.     

The effect of a bump on wave propagation in a fluid-filled elastic tube

In the present work, treating the arteries as a thin walled prestressed elastic tube with variable cross-section, and using the longwave approximation, we have studied the propagation of weakly nonlinear waves in such a fluid-filled elastic tube by employing the reductive perturbation method. By considering the blood as an incompressible viscous fluid the evolution equation is obtained as the perturbed Korteweg-de Vries equation with variable coefficients. It is shown that this type of equations admit a solitary wave type of solution with variable wave speed. It is observed that, the wave speed gets smaller and smaller as we go away from the center of the bump. The wave speed reaches to its maximum value at the center of the bump.     

梁与正交各向异性板弯曲波的传递特性研究

以正交各向异性板与各向同性梁耦合系统弹性波传递特性为研究对象,基于弯曲波传播的动力学分析,推导出子系统间的功率流传递系数(power flow transmission coefficient,PTC)和耦合边界处的耦合损耗因子(coupling loss factor,CLF)表达式.计算分析了内损耗因子、频率和方向...     

The elastic displacement and stress in a material to promote reflection and transmission of an incoming wave

The conditions on elastic displacement and stress in a material that will promote reflection and transmission of an incoming wave are calculated. It is found, for example, that to optimize reflection and transmission, scalar potentials of the displacement in the wave and in the material will be related to rotations in planes perpendicular and parallel to the direction of propagation to the wave. When a pulse is constructed and its path analyzed through short distances, it is shown that abrupt transitions in tension and compression in a material will maximize reflection of the pulse. When strain energy is minimized where reflection and refraction are to occur, differences in tension and compression become prominent again. Finally, an approximate volume of material is calculated for an electron to harness the restoring forces in a material to balance the energy lost in inelastic scattering.     

Patterned structures fabricated on chalcogenide phase-change thin films by laser direct writing

In laser direct writing technology, the pattern is usually written in a photoresist. In this work, we use the chalcogenide phase change thin films as the laser direct writing materials, and patterned structures with different shapes and sizes were directly written with different laser wavelengths. Compared with traditional photoresist materials, the patterned structures can be directly formed in the chalcogenide phase change thin films without developing and etching procedures, and also can be directly written with different laser wavelengths. By tuning the laser parameters precisely, patterned structures with different sizes and shapes could be obtained as well. The analysis indicates that the formation mechanism of the patterned structure is mainly due to the volume expansion caused by material vaporization and the interior of the patterned structure is hollow with some solid leavings, and the chalcogenide phase change thin films are very good candidate materials for patterned structure formation.     

Numerical calculations of elastic wave propagation in anisotropic thin films deposited on substrates

In this work, we present a generalized numerical model to study the dispersion curves of elastic waves in anisotropic thin layer/substrate systems. Dispersion curves as a function of wave frequency for different propagation angles are calculated. The nature of the mode (Rayleigh or Love) is identified by analyzing the polarization of the three-dimensional displacement field. This numerical model has been applied to the system Au(0 0 1)/Ni(0 0 1).     

Preliminary study on cost optimisation of aircraft composite structures applicable to liquid moulding technologies

This paper details the initial development of a method for determining the associated recurring labour costs for the manufacture of a aircraft component that will form the basis for a computerised methodology for determining the optimum manufacturing method for a component design. The research focuses on the flow of process steps to manufacture an aircraft component for the vacuum-assisted resin transfer moulding and resin transfer moulding manufacturing process. The methodology developed is based on applying MIT cost equations to process steps from which cost variables and constants are established to represent an estimated costing of the aircraft structure. This research will assist in providing a swifter and more accurate conceptual design/manufacturing system that includes an analysis of cost and will assist the production of trade studies that consider the manufacture of aircraft components using cost-effective technologies, such as liquid moulding.     

Modeling of viscoelastic structures with random material properties using time-separated stochastic mechanics

Modeling and simulation of materials with stochastic properties is an emerging field in both mathematics and mechanics. The most important goal is to compute the stochastic characteristics of the random stress, such as the expectation value and the standard deviation. An accurate approach are Monte Carlo simulations; however, they consume drastic computational power due to the large number of stochastic realizations that have to be simulated before convergence is achieved. In this paper, we show that a recently published approach for accurate modeling of viscoelastic materials with stochastic material properties at the material point level in the work of Junker and Nagel is also valid for macroscopic bodies. The method is based on a separation of random but time-invariant variables and time-dependent but deterministic variables for the strain response at the material point (time-separated stochastic mechanics [TSM]). We recall the governing equations, derive a simplified form, and discuss the numerical implementation into a finite element routine. To validate our approach, we compare the TSM simulations with Monte Carlo simulations, which provide the “true” answer but at unaffordable computational costs. In contrast, the numerical effort of our approach is in the same range as for deterministic viscoelastic simulations.     

The transfer length in concrete structures repaired with composite materials: a survey of some analytical models and simplified approaches

This work focuses on the closed-form solutions for the shear distribution that takes place in the adhesive between composite and concrete in RC structures repaired with composite plates. Three different loading cases are studied. It is shown that the exact shear stress distributions, which are rather complicated, can be simplified to provide very similar expressions in the three studied cases. The main parameters that govern the shear distribution are then clearly highlighted. This leads to an easy understanding of the influence of some geometrical and material parameters on the shear distribution, as illustrated through a parametric study.     

On the static equilibrium of an elastic orthotropic medium with an arbitrarily oriented elliptical crack

We analyze the problem of the stress distribution in an elastic orthotropic medium with an arbitrarily oriented elliptical crack. To construct the problem solution, the Willis approach is used which is based on the triple Fourier transformation of spatial variables and Fourier-image of Green’s function for an infinite anisotropic space. The investigation results in special cases are compared with the data of other authors. The effect of the elliptical crack orientation in an orthotropic space on the distribution of the stress intensity factors along its contour is studied. __________ Translated from Problemy Prochnosti, No. 4, pp. 146–159, July–August, 2007.     

Clamping effects on the dynamic characteristics of composite machine tool structures

Substituting composite structures for conventional metallic structures has many advantages for structural dynamic characteristics because composite materials have the higher specific stiffness and damping characteristics than conventional materials. However, the dynamic characteristics such as the fundamental natural frequency and damping of composite structures are influenced much by their joints. In this work, the effects of clamping conditions on the dynamic characteristics of cantilever type composite machine tool structures with clamped joint were investigated to increase the natural frequency and damping of structures. In order to improve the shear property of the clamping part of composite machine tool bar, a new method for the clamping part was developed with metal core or sleeve inserted in the composite body at the clamping part. From the finite element and experimental results, suitable clamping conditions for the maximum dynamic stiffness were obtained for the composite structures with clamped joint.