Fractional heat conduction equation for an infinitely generalized,thermoelastic, long solid cylinder

In this work, we consider the one-dimensional problem for an infinitely long solid cylinder in the context of the theory of generalized thermoelasticity with one relaxation time. The heat conduction equation with the Caputo fractional derivative of order α is used. The curved surface of the cylinder is assumed to be in contact with a rigid surface and is subjected to constant heat flux. By means of the Laplace transform and numerical Laplace inversion the problem is solved. Numerical computations for the temperature, displacement and stress distributions are carried out and displayed graphically as well as the results are discussed comprehensively.     

Interaction of torsional waves with an annular crack in an infinitely long cylinder

The Hankel transform is used to obtain a complete solution for the dynamic stresses and displacements around a flat annular surface of a crack embedded in an infinite elastic cylinder, which is excited by normal torsional waves. The curved surface of the cylinder is assumed to be stress free. Solution of the problem is reduced to three simultaneous Fredholm integral equations. By finding the numerical solution of the simultaneous Fredholm integral equations the variations of the dynamic stress-intensity factors are obtained which are displayed graphically.     

两点沿曲面最短路径的遗传算法研究

求两点沿曲面最小距离的关键是正确选择两点间沿曲面的最短路径。遗传算法是一种全局性概率搜索算法。它在整个问题空间实施搜索,可得到问题的全局最优解,本文应用了遗传算法的理论与方法。首先,将整个曲面作为搜索空间,路径长度作为目标函数,设定了路径优化问题。其次,建立了椭圆坐标系,满足了遗传编码完备性的要求,实现了二维实数编码。运用排序选择方法,单一交叉和最小变异操作,完成了遗传算法,同时获得了最短路径。该方法适用于各种形式的曲面。     

谈谈圆柱体锻件端面的模锻斜度设计

主要介绍了圆柱体锻件端面模锻斜度设计的平面模锻斜度和球面模锻斜度的详细制图步骤,指出了制图要点,正确绘制出平面、球面与圆柱面相截时的相贯线,并且利用Pro/E作出了圆柱体锻件端面的平面模锻斜度和球面模锻斜度的三维图.     

面向多种类型和复杂边界的曲面近似展开系统

通过对曲面近似展开系统的研究，主要解决两方面关键性的技术问题，一是如何从界面中识别公式表达式并转换成系统所能识别的变量和函数；二是如何解决复杂边界的展开问题，随着这些问题的解决，研制成功了面向多种类型和复杂边界的曲面近似展开系统。     

The motion of the free-surface separation point during the initial stage of horizontal impulsive displacement of a floating circular cylinder

The initial stage of unsteady two-dimensional flow caused by the impulsive horizontal motion of a floating circular cylinder is investigated by using methods of asymptotic analysis. Initially the cylinder is half-submerged and the liquid free surface is flat and horizontal. The liquid is of infinite depth. Then the cylinder suddenly starts to move horizontally with a speed given as a function of time. The liquid is assumed ideal and incompressible and its flow potential. The initial flow is provided by pressure-impulse theory, with an account of a possible separation of the liquid free surface from the trailing face of the rigid surface of the cylinder. The initial position of the separation point on the surface of the moving body is determined by using the condition that the fluid velocity is finite at the separation point (Kutta condition). The motion of the separation point along the surface of the cylinder is numerically determined with the help of the second-order outer solution of the problem and the Kutta condition at the moving separation point. It is shown that the length of the wetted part of the cylinder surface increases at a rate proportional to the speed of the cylinder. The speed of the separation point depends on the Froude number. The pressure on the wetted part of the cylinder can be below the atmospheric pressure for relatively high speed.     

Electromagnetic modelling of curved lossy dielectric surface and cylinder

A new electromagnetic model for curved dielectric surfaces and cylinder has been introduced. The model considers scatterers as a lossy dielectric body. The theoretical and simulation results have been compared with the literature and the model agrees with the published results of the hollow cylinder for which an exact solution exists. Figures of relative error versus ka and kT of hollow cylinder (a) single- (b) three-layered cylinder are used for the parameters. The curved dielectric scatterer is discretised to N small element, and then the contributions of each element are sum up coherently to find the total response. Finally, the simulations for curved cylinder and convex surfaces of arbitrary shape are presented.     

Dissipative heating of a hollow viscoelastic cylinder subjected to the action of normal loads moving along its surface with constant angular velocity

We consider a two-dimensional quasistatic problem of the stress-strain state and dissipative heating of a hollow circular viscoelastic cylinder subjected to the action of two, normal diametrically opposite loads moving along the surface of the cylinder with constant angular velocity. It is assumed that the physicomechanical properties of the material are independent of temperature. In this case, the combined problem of thermoviscoelasticity splits into two linear problems: the problem of the stress-strain state of the cylinder without axial symmetry and the axisymmetric problem of heat conduction with temperature averaged over a cycle and a known heat source. The exact solutions of these problems are obtained. The influence of both the coefficient of heat transfer on the inner boundary of the cylinder and the sizes of the cylinder on the temperature of dissipative heating are investigated. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 67–73, March–April, 1999.     

Saint-Venant torsion of a circular bar with radial cracks incorporating arbitrarily varied surface elasticity

We analytically investigate the contribution of arbitrarily varied surface elasticity to the Saint-Venant torsion problem of a circular cylinder containing a radial crack. The varied surface elasticity is incorporated by using a modified version of the continuum-based surface/interface model of Gurtin and Murdoch. In our discussion, the surface shear modulus is assumed to be arbitrarily varied along the crack surfaces. Both internal and edge cracks are studied. By using Green's function method, the boundary value problem is reduced to the Cauchy singular integro-differential equation of first order, which can be numerically solved by using the Gauss–Chebyshev integration formula, the Chebyshev polynomials, and the collocation method. The torsion problem of a cylinder containing two symmetric collinear radial cracks of equal length with symmetrically varied surface elasticity is also solved by using a similar method. Our numerical results indicate that the variation of the surface elasticity exerts a significant influence on the strengths of the logarithmic stress singularity at the crack tips, the torsional rigidity, and the jump in warping function.     

Finite element analysis of quasi-prismatic bodies using Chebyshev polynomials

A new kind of finite element is presented in this paper which is designed to work efficiently for bodies that are either prismatic or ‘quasi-prismatic’ in shape. Quasi-prismatic shapes are those which can be obtained from prismatic shapes by mere distortion. The element which is formulated in this paper may be coupled with other types of three-dimensional elements to allow the modelling of structures which are only partially prismatic or which have prismatic shapes within them. The element allows for a variety of boundary conditions, yet yields meshes which are easy to generate. The performance of this element is evaluated by numerical experiments that compare its results with analytical solutions for a thick cylinder problem and a curved beam problem. The element has also been demonstrated on a turbine blade model.     

Thermoelastic contact of a retaining ring with a cylinder under the conditions of frictional heat generation

We give the mathematical statement and construct the solution of the static thermoelastic problem of contact interaction of an elastic retaining ring with a circular hollow cylinder inserted in it. The bodies are compressed by a load varying along the axis of the system under the conditions of load-free contact on the surface of the ring or along an arc of the circle. In the case where radial displacements of the contact surface of the retaining ring are approximated by displacements of the surface of a long circular hollow cylinder and the process of stationary frictional heat generation is taken into account, we reduce the posed problem to systems of integral equations whose structure is determined by the type of conditions of thermal contact. We propose a numerical algorithm for the solution of these systems and study the influence of the input parameters of the problem on the distributions of contact pressure and temperature. On the basis of these results, we make a conclusion that the influence of the character of variation of the compressive load along the axis on the distribution of contact pressure is significant in the case where the kinematic conditions of interaction of the bodies are described by the Hertz theory. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 36. No. 3. pp. 42–52, May-June, 2000.     

Torsional impact of a layer or a cylinder bonded to an elastic half-space

In this paper two torsional impact problems are considered. The first problem deals with the solution of a layer bonded to an elastic half-space when the layer is driven by the torsional impact over a bonded rigid circular disc. In the second problem sudden torsion by a rigid disc attached over the plane face of a circular cylinder is considered and the rest of the plane surface of the cylinder is stress free. The cylinder is bonded to the half-space, making use of Laplace and Hankel transforms the solution of each problem is reduced into Fredholm integral equations of the second kind. A numerical Laplace inversion technique is then used to recover the time depencence of the solution. The numerical values for the applied torque at the surface of rigid disc are calculated for each problem and then are displayed graphically.     

Ductility of thin copper films on rough polymer substrates

Electronic components in modern flexible electronics are connected by interconnects, which typically have the form of metal films resting on polymer substrates. This paper firstly studies experimentally the ductility of Cu films deposited on polyimide substrate with roughened surface (due to sandblasting) and finds that, upon tensile loading along the direction of film surface, the density of surface cracks in the film decreases with increasing surface roughness. The method of finite elements is subsequently employed to study the distribution of tensile stresses in the film and their influence on film cracking (initiation and propagation). It is demonstrated that a rough (curved) interface can reduce the tensile stresses along the film surface so as to restrain channel cracking of the film. Finally, the cohesive zone model is used to study the initiation and spreading of damage in the film and interfacial debonding of the curved interface. Both the interfacial damage and interface crack length are reduced as a result of interface roughening.     

Transient thermal contact problem for axial crack in a hollow circular cylinder

The transient behavior of an axial-cracked hollow circular cylinder subjected to a sudden heating is investigated. It is shown that surface heating may induce compressive thermal stress near the inner surface of the cylinder which in turn may force the cracked surfaces to close together. Assuming that the existence of the crack does not alter the temperature distribution, this problem can be divided into two parts and solved by the principle of superposition. First, the temperature and transient thermal stress distributions along the axisymmetric surface of the imaginary cylinder without a crack are obtained by finite element/implicit time integration method. The calculated temperature and thermal stress distributions are in good agreement with the values predicted by the analytical method. Secondly, the opposite senses of the stress distributions along the cracked surfaces, which are obtained previously, are treated as the traction boundary conditions, and the contact length and contact pressure of the real cracked cylinder are obtained by a modified elimination finite element scheme. In this scheme, the concepts of contact-node-pairs' penetration, contact-double-forces and compliance matrix are introduced. The calculated results indicate that the contact length ratio becomes smaller when the crack length ratio increases, and becomes larger as the radius ratio increases. Finally, the normalized stress intensity factor for the crack tip of the cylinder is obtained. It is shown that the larger the crack length ratio the higher the stress intensity factor.     

Coupled transient thermoelastic contact problems for axial cracks in hollow cylinders

A coupled transient thermoelastic behaviour of an axial-cracked hollow circular cylinder subjected to a sudden heating is investigated in this study. It is shown that surface heating may induce the compressive thermal stress near the inner surface of the cylinder which in turn may force the cracked surfaces to close together. Assuming that the existence of the crack does not alter the temperature distribution, we can divide this problem into two parts and solve it by the principle of superposition. First, the temperature and transient thermal stress distributions along the axisymmetric surface of the imaginary cylinder without crack are obtained by finite element implicit time integration method Secondly, the opposite sense of the stress distributions along the cracked surfaces, which is obtained previously, is treated as the traction boundary conditions; the contact length and contact pressure of the real cracked cylinder are obtained by modified elimination finite element scheme. Finally, we also obtained the normalized stress intensity factor for the crack tip of the cylinder. It is concluded that the effect due to thermoelastic coupling term on stress intensity factor becomes more important for higher coupling coefficient, and this coupling term also results in a small time lag in temperature, thermal stress and stress intensity factor.     

压电复合材料中幂函数型曲线裂纹的反平面问题

通过构造新保角映射, 利用Stroh公式研究了远场受反平面剪应力和面内电载荷共同作用下无限大压电复合材料中幂函数型曲线裂纹的断裂行为。给出了电不可渗透边界条件下裂纹尖端场强度因子和机械应变能释放率的解析解。该解析解在幂函数的幂次为零时, 可退化为已有文献中无限大压电复合材料含直线裂纹的结果, 证明了其合理性。由解析解可知, 裂纹几何形状一定时, 电场分布将不受机械载荷的影响。最后, 通过数值算例讨论了幂函数的幂次、 系数及其在 x₁轴上的投影长度对机械应变能释放率的影响。结果表明, 当压电体仅受 x₂方向载荷作用时, 对于给定幂次与开口的曲线裂纹, 在 x₁轴上的投影长度存在一临界值使其最容易开裂; 而对于给定投影长度与幂次的曲线裂纹, 开口越大裂纹越容易扩展。      

不可展曲面近似展开方法的合理性判断标准

对同一不可展曲面的展开可有多种近似展开方法,究竟哪种方法更为合理应建立相应的评判标准。以一直角等径管接头展开为例,使用圆柱、椭圆柱、三角形3种不同的展开方法对其进行近似展开,以面积、体积、拼缝为判据对3种近似展开方法的合理性进行分析,从而使使用者能够根据不同的使用要求选择合适的展开方法。     

Uniform version of the modified theory of physical optics based boundary diffraction wave theory

The potential function of the modified theory of physical optics based boundary diffraction wave theory is made uniform by using the principles of the uniform theory of diffraction. The line integration of this new function along the edge contour gives the uniform diffracted fields which are finite for the transition regions of the diffraction geometry. The method is applied to the diffraction problem by the edge of a curved surface.     

Free vibration analysis and shape optimization of prismatic folded plates and shells with circular curved planform

This paper deals with the elastic free vibration analysis and structural shape optimization of prismatic folded plate and shell structures with circular curved planform. The structures are supported on diaphragms at two opposite edges. The basic formulation of a family of curved variable thickness C(0) Mindlin–Reissner finite strips is presented. The accuracy and performance of these newly developed strips are explored through a series of examples including annular plate sectors, a box girder bridge and a cylinder with an interior longitudinal plate. Numerical results obtained are compared with results from other sources. The whole shape optimization process is carried out by integrating finite strip analysis, cubic spline shape and thickness definition, sensitivity analysis and mathematical programming. The objective is either the maximization of the fundamental frequency or the minimization of volume by changing the shape or thickness variation of the cross-section of the structure with constraints on the volume or natural frequencies. Several examples are included to illustrate and highlight various features of the optimization, including annular sector plates, a curved box girder bridge and a cylinder shell segment with curved pianform.