湍流池湍流特征研究

在用于激光束传输和控制模拟实验的湍流池中温度脉动测量结果表明,原始温度变化曲线上有明显的斜坡（ｒａｍｐ）结构,温度三阶及五阶结构函数和理论预计一致和大气对流边界层的测量相似,斜坡结构的出现对二阶结构函数的影响较小,加热面和冷却附近有明显的猝发现象出现,温度脉动的峰度系数大于３,表现了较大的间歇性。     

Transient dynamic fracture analysis by an extended meshfree method with different crack-tip enrichments

Investigation of transient dynamic stress intensity factors (DSIFs) of two-dimensional fracture problems of isotropic solids and orthotropic composites by an extended meshfree method is described. We adopt the recently developed extended meshfree radial point interpolation method (X-RPIM), which combines either the standard branch functions or the new linear ramp function associated with Heaviside functions to capture crack-tip behaviors. It is the first time the linear ramp function integrating into meshfree X-RPIM has been presented in a dynamical fracture context. We are particularly interested in exploring insight into the behaviors of DSIFs under dynamic impact loadings (e.g., step, blast and sine loading types) using our meshfree method. For some of these problems numerical examples have been performed using the new ramp functions, and the obtained results of DSIFs have also been compared with those using the standard enrichment functions under which the two schemes have the same setting. In each case it is found that the numerical solutions delivered using the X-RPIM associated with the ramp enrichments are in good agreement with those with the standard functions. The paper first describes formulations and then provides verification of our developed approach through a series of numerical examples in transient dynamic fracture for both solids and orthotropic composites. Illustration of scattered elastic stress waves propagating in the cracked body is depicted to take an insight look at the behavior of dynamic response.     

Finite ramp time correction method for non-linear viscoelastic material model

In this paper, a simple formula for the prediction of stress (strain) in the relaxation (creep) period is derived for a non-linear viscoelastic material model which takes into account the finite ramp time. Usually, it is assumed that the ramp time is small and, therefore, loading can be described via Heaviside step function. This assumption, when applied to the material parameters identification process, can lead to a large errors in the values of the approximated material parameters. Especially, for the materials which undergo significant stress decay in the beginning of relaxation the assumption of infinite small ramp time can induce severe errors. With the help of the derived formula more reliable material parameter identification can be accomplished. The proposed method is tested with numerical simulations and compared with analytical results, Heaviside step loading case and method described by Nordin and Varna. Simulations show good agreement with analytical results.     

Using the logarithmic strain measure for solving torsion problems

The problems of free and constrained torsion of a rod of solid circular cross-section are solved numerically using a tensor linear constitutive relation written in terms of the energy compatible Cauchy stress and Hencky logarithmic strain tensors. The only function used to determine the properties of the isotropic incompressible material of the rod is a power-law function that approximates the shear diagram and corresponds to an elastoplastic material with power-law hardening. The solution obtained shows that, despite the tensorial linearity of the state law, the use of the logarithmic strain measure allows one to describe qualitatively the effect of significant elongation of the rod in free torsion (the Poynting effect) as well as the arising normal longitudinal, radial, and circumferential stresses, whose values are commensurable, at large deformations, with the maximum tangential stresses in the cross-section. Computational dependences of the torsional moment on the angle of twist in free and constrained torsion are obtained. These dependences are found to be significantly different from each other; the limitmoment and the correspondingmaximum angle of twist for free torsion are found to be considerably lower than those for constrained torsion. It follows that the shear strength, which is traditionally calculated from the maximum torsional moment, becomes indeterminate. For constrained torsion, the dependence of the longitudinal compressive force on the angle of twist is obtained.     

Characterizing Torsional Properties of Microwires Using an Automated Torsion Balance

In order to characterize the torsional behavior of microwires, an automated torsion tester is established based on the principle of torsion balance. The main challenges in developing a torsion tester at small scales are addressed. An in-situ torsional vibration method for precisely calibrating the torque meter is developed. The torsion tester permits the measurement of torque to nN m, as a function of surface shear strain to a sensitivity of sub-microstrain. Using this technique, we performed (monotonic and/or cyclic) torsion tests on polycrystalline copper and gold wires. It is found that (i) a size effect appears in both the initial yielding and the plastic flow of torsional response; (ii) a reverse plasticity occurs upon unloading in cyclic torsion response; and (iii) the Hall-Petch effect and the strain gradient effect are synergistic. We also performed cyclic torsion tests on human hairs and spider silk which are natural protein fibers with a different morphological structure to metallic wires. It is shown that the single hair exhibits torsional recovery, and that the spider silk displays torsionally superelastic behavior whereby it is able to withstand great shear strain.     

A novel semi-inverse solution method for elastoplastic torsion of heat treated rods

Torsion rods are a primary component of many power transmission and other mechanical systems. The behavior of these rods under elastoplastic torsion is of major concern for designers. Different methods have so far been proposed which deal with the elastoplastic torsion of rods, most of which assume constant yield stress. This assumption produces rough and inaccurate results when the rods are heat treated, since in the process of heat treatment the form of yield stress distribution across the rod cross section changes. We propose a new method for calculating elastoplastic torsion of rods of simply connected cross section which is based on heat treatment observations. In our method the full plastic stress function is obtained by using the semi-inverse method. Elastoplastic stress function is obtained by generalizing the idea of the membrane analogy and using a piecewise continuous stress function. Since the proposed form of yield stress distribution can not be handled by the current Finite Element packages, we produce a computer package with a 3D graphical interface capable of calculating and displaying the 3D elastoplastic stress function, shear stress contours, and torque-angle of rotation per unit length. We show that our method produces excellent agreement for several known cross sections in comparison to methods which assume constant yield stress.     

A duality theorem for plastic torsion

Limit analysis of prismatic torsion bars was the earliest attempt to apply plasticity theory to a continuum. The simplicity of the problem made it feasible to use the two-dimensional Prandtl stress function, defined for the elastic torsion problems, for the plastic stress distributions as well. The gradient of the stress functions for plastic torsion has a constant magnitude, and hence a function of this type assumes the profile of a sand hill. This sand hill analogy of Nadai (1950, The Theory of Flow and Fracture of Solids. McGraw-Hill, U.K.) gave a visual sense of possible nonsmoothness of such stress functions and thus discontinuous stress fields. Many stress functions of plastic torsion for relatively simple cross-sections have been constructed graphically. However, collapse modes in terms of warping functions were much less reported. In this paper, we shall establish a duality theorem which relates the correct stress function to the correct warping function, thus providing the means to obtain complete static and kinematic solutions. This dual variational principle leads naturally to a general numerical algorithm which guarantees convergence and accuracy. In this paper, we shall only present three exact solutions to verify the theorem, to demonstrate the possible non-smooth feature of the solutions and to reiterate this effective dual variational approach to limit analysis in general.     

Optimization of straight-sided spline design

Spline connection of shaft and hub is commonly applied when large torque capacity is needed together with the possibility of disassembly. The designs of these splines are generally controlled by different standards. In view of the common use of splines, it seems that few papers deal with splines and the subject of improving the design. The present paper concentrates on the optimization of splines and the predictions of stress concentrations, which are determined by finite element analysis (FEA). Using different design modifications, that do not change the spline load carrying capacity, it is shown that large reductions in the maximum stress are possible. Fatigue life of a spline can be greatly improved with up to a 25% reduction in the maximum stress level. Design modifications are given as simple analytical functions (modified super elliptical shape) with only two active design parameters and the designs are practical realizable. Some generality is found in the design parameters.     

Effective properties of a nonuniform beam under torsion

Effective characteristics are considered in the pure torsion problem for a nonuniform beam. The Saint-Venant semi-inverse method is used. A torsion stress function is introduced; this function can be found by solving a cross-sectional boundary value problem for a partial differential equation with variable coefficients. Two special boundary value problems are formulated for such an equation; after solving these problems, some effective characteristics are calculated in the case of torsion. It is shown that these effective characteristics satisfy the conditions of symmetry and positive definiteness. The case of an infinite in-plane layer of nonuniform thickness is discussed.     

斜波压缩实验数据的正向Lagrange处理方法研究

提出了一种联合使用Lagrange方法和转换函数方法来处理斜波压缩实验数据的新途径，和传统的数据处理方法相比，该方法更适合处理材料的复杂力学响应并具有较好的精度，同时该方法使用过程中对样品材料参数的初猜值精度要求更低。分析了转换函数方法的可靠性和健壮性，讨论了转换函数和Lagrange方法联合在斜波压缩强度实验数据处理中的应用，获得了可靠的结果。     

The warping functions of regular prismatic bars under torsion evaluated by caustics

Reflection of a bundle of coherent light on the warped cross section of a prismatic bar submitted to torsion forms a caustic on a receiver plane. From the mathematical expression of this curve and the theory of reflected caustics, it is possible to evaluate accurately the warping function of the cross section. Using this idea, it was possible to study the torsion problem in prismatic bars with sections which were equilateral triangles and squares. It was observed that the shape of the caustic is an hypocycloid curve with three or four cusps respectively. By evaluating the warping function by using elements from the respective caustics it was possible to find out that, for the triangular cross section, the expression for the warping function coincided exactly with the expression given by the exact solution of the problem. For the square cross section, a closed-form solution for its warping function was readily derived, to which the series approximation solution differed only by a few percent at maximum for the shear stresses. Since the method can be readily extended to any canonical polygonic cross section, it constitutes a general solution for the torsion of prismatic bars, which approximates their exact deformations better than the solutions based on the Saint-Vénant assumptions.     

Phase transition and dynamics of iron under ramp wave compression

The ramp wave compression experiments of iron with different thicknesses were performed on the magnetically driven ramp loading device CQ-4. Numerical simulations of this process were done with Hayes multi-phase equation of state (H-MEOS) and dynamic equations of phase transition. The calculated results of H-MEOS are in good agreement with those of shock phase transition, but are different from those under ramp wave compression. The reason for this is that the bulk modulus of the material in the Hayes model and the wave velocity are considered constant. Shock compression is a jump from the initial state to the final state, and the sound speed is related to the slope of the Rayleigh line. However, ramp compression is a continuous process, and the bulk modulus is no longer a constant but a function of pressure and temperature. Based on Murnaghan equation of state, the first-order correction of the bulk modulus on pressure in the Hayes model was carried out. The numerical results of the corrected H-MEOS agree well with those of pure iron in both ramp and shock compression phase transition experiments. The calculated results show that the relaxation time of iron is about 30 ns and the phase transition pressure is about 13 GPa. There are obvious differences between the isentropic and adiabatic process in terms of pressure–specific volume and temperature–pressure. The fluctuation of the sound speed after 13 GPa is caused by the phase transition.     

Torsion in nonlinearly elastic incompressible circular cylinders

We consider a variable torsion deformation for incompressible right-circular cylinders and investigate the possibility of equilibrium states other than simple torsion in isotropic hyperelasticity. Our problem formulation also provides generalized versions of Rivlin's universal relations in torsion. In this more general setting, it is shown that simple torsion persists as the only solution for large classes of strain energies. When one allows for more general boundary conditions, variable torsion solutions are possible for special forms of the stored energy function. We derive such a form and develop general results.     

扇形截面杆扭转问题的差分线法

导出了扇形截面杆扭转问题偏微分方程的差分线法常微分方程组, 并解析求解了该方程组, 得到了扭转应力函数的半解析解, 计算了扭转应力及扭转刚度. 计算过程中, 用追赶法计算 常微分方程组的特解, 用公式计算三对角矩阵的特征值与特征向量, 利用实对阵矩阵的特征 向量相互正交的特性避免矩阵求逆计算, 利用复化梯形公式计算扭转刚度. 整个求解过程在 角度方向离散微分方程和用复化梯形公式进行面积积分时引入了误差, 其他求解过程是精确 的. 计算结果与已有结果进行了对比, 显示了算法的正确性. 该算法对工程中扇形截面扭 转杆的设计有一定的实用价值.     

The torsion of composite tubes and cylinders

Exact solutions are presented for the Saint-Venant torsion of circular tubes and solid cylinders which are reinforced by cylindrical inclusions of different material equally spaced around a concentric circle. The problems simulate those encountered in matrix rods reinforced by longitudinal fibers, and also in corresponding problems of reinforced concrete. Formulae are obtained for the boundary stress distributions and the torsional rigidities.Stress function formulations are made for the torsion of cylinders having multiply connected composite sections. Two systems of polar coordinates are employed, and use is made both of periodicity and symmetry. Three degenerate cases—the respective torsion of a homogeneous tube, ring of circular rods and tube with eccentric circular holes—are deduced for checking purposes. Several numerical examples are worked out and the results presented in tabular and graphical forms.     

涡轮冷却叶片气动与传热设计优化

提出了航空发动机涡轮冷却叶片叶栅气动与传热自动优化方法,利用函数解析成型方法实现了冷却叶片几何模型的参数化与自动生成,可以建立任意冷却内腔数量的叶片模型;基于N-S方程实现叶片流体域与固体域的流-热耦合分析;采用KS函数方法将多目标优化问题转化为单目标函数进行优化,以总压损失、叶片最高温度和平均温度最小为优化目标进行了自动优化,改善了叶片性能。     

Some analytical solutions for Saint-Venant torsion of non-homogeneous anisotropic cylindrical bars

The Saint-Venant torsion of linearly elastic anisotropic cylindrical bars with solid and hollow cross-section is treated. The shear flexibility moduli of the non-homogeneous bar are given functions of the Prandtl's stress function of considered cylindrical bar when its material is homogeneous. The solution of the torsion problem of non-homogeneous anisotropic bar is expressed in terms of the torsion and Prandtl's stress functions of the corresponding homogeneous anisotropic bar having the same cross-section as the non-homogeneous bar.     

Inverse laminar boundary-layer problems with assigned shear. The mechul function revisited

An inverse method is presented which accurately determines the pressure distribution for assigned wall shear in a two-dimensional, laminar, incompressible boundary layer. The method reformulates the mechul function scheme of Cebeci and Keller to produce a stable solution in the marching direction and to increase accuracy in the normal direction. In the reformulation a modified pressure gradient parameter variation in the normal direction is used in conjunction with three-point backward differences for streamwise derivatives and fourth-order accurate splines for normal derivatives. The resulting spline-finite difference equations are solved by Newton-Raphson iteration together with partial pivoting. Numerical solutions are presented for self-similar and non self-similar flows and compared with published results.     

扇形截面杆扭转的应力分析

柱体扭转的基本方程为非齐次偏微分方程,在极坐标系下,利用分离变量法及傅立叶级数展开法,求出了扭转应力函数,进一步即可计算出扇形截面杆在外力偶作用下,扭转角和横截面上剪应力的精确解答。这种方法为精确解法,在各种机械及其他工程设备中,对受扭转作用的扇形截面杆设计,有一定实用价值。     

Three-dimensional limit analysis of rigid blocks assemblages. Part I: Torsion failure on frictional interfaces and limit analysis formulation

The governing equations of plastic torsion of, arbitrarily shaped, frictional interfaces are established and a general solution is proposed. The case of rectangular interfaces is used to study the interactions of torsion strength with bending moments and shear forces. In order to solve limit analysis problems, a piecewise linear approximation of the yield function for rectangular interfaces is proposed. A model for the limit analysis of three-dimensional block assemblages interacting through no-tension frictional interfaces is presented including the proposal for the torsion failure mode. This model takes into account non-associated flow rules and limited compressive stresses at the interfaces.