Nonlinear deformation analysis of a U-shaped bellows with varying thickness

Summary The nonlinear integral equations for a U-shaped bellows with compressed angle and varying wall-thickness are derived according to the simplified Reissner theory of large deflection for revolution shells and integral-equation method. The iteration procedure for nonlinear analysis is developed by means of the integral equation iteration in conjunction with the gradient method. Numerical solutions for a U-shaped bellows under the action of axial compression force and internal pressure are obtained, which are compared with previous theories and experiments. The present results are shown to have a good accuracy, and may be applied directly to the design of bellows. Received 13 November 1997; accepted for publication 6 July 1999     

PROBLEMS OF U-SHAPED BELLOWS WITH NONLINEAR DEFORM TION OF LARGE AXISYMMETRICAL DEFLECTION(Ⅰ)—COUNTING NONLINEAR DEFORMATIONS OF RING SHELLS AND COMPRESSED ANGLE OF BELLOWS

This paper follows the work of[1,2].There are some progress in dealing withmoderately small rotations(the squares of rotation angles are the order of magnitudeof strains)of middle surface normals of inside and outside ring shells and compressedangle of bellows.Calculation results agree with experiments well.To bellow design,the method given in this paper is of practical value and the discussion of the influenceof compressed angle on characteristic relation is helpful.     

裂纹尖端张开角准则的稳态裂纹扩展实验研究

ASTM和ISO已发布获得低约束条件下断裂性能和裂纹稳态扩展阻力曲线的标准,标准中采用多种试验方法确定临界裂纹张开角度来表征板材的裂纹稳态扩展。本文采用准静态裂纹扩展试验方法,通过摄像技术测定裂纹尖端张开角(CTOA),验证标准对1mm厚度2024-T3铝合金板稳态裂纹扩展行为的有效性。研究了试样构型、裂纹尺寸和是否疲劳预制裂纹对裂纹稳态扩展过程中CTOA的影响。试验结果表明:裂纹扩展2mm后,距离裂纹尖端1mm处的CTOA趋于一个恒定值6°,这个值与试样构型和裂纹长度无关;同时,不预制疲劳裂纹对CTOA值和试样的最大剩余强度影响较小。     

Generalized Strongly Nonlinear Quasi-Complementarity Problems

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Effects of the stress state on plasticity and ductile failure of an aluminum 5083 alloy

The experimental and numerical work presented in this paper reveals that stress state has strong effects on both the plastic response and the ductile fracture behavior of an aluminum 5083 alloy. As a result, the hydrostatic stress and the third invariant of the stress deviator (which is related to the Lode angle) need to be incorporated in the material modeling. These findings challenge the classical J₂ plasticity theory and provide a blueprint for the establishment of the stress state dependent plasticity and ductile fracture models for aluminum structural reliability assessments. Further investigations are planned to advance, calibrate and validate the new plasticity and ductile fracture models.     

GENERALIZED THEORY OF NONLINEAR AND UNSTEADY MECHANICS AND APPLICATIONS TO PARTICLE PHYSICS

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Mechanics of fluid-activated,clustered satellite bellows

A bellows, or a closed thin-walled elastic tube with corrugated walls, undergoes longitudinal extension when subjected to internal fluid pressure. Investigated herein is the mechanical behavior of several pressurized bellows in clusters, which are designed to bend and twist as well as to extend and compress longitudinally. Bellows in clusters can be employed as robotic limbs, such as manipulator arms and legs for walking machines. For limb bending, analysis shows that there is an optimal geometry for satellite bellows, or a set of identical bellows clustered longitudinally about a central core. For limb torsion, the bellows are clustered in a cylindrical helix whose angle is chosen to produce the desired load–displacement relationships, for instance the highest rotation for a given torque. For both bending and torsional limbs, experimental results are included that exhibit the predicted mechanical behavior.     

Iterative construction of solutions to nonlinear equations of lipschitzian and local strongly accretive operators

In this paper, we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X. Let T: X→X be a Lipschitzian and local strongly accretive operator and the set sol(T) of solutions of the equation Tx=f be nonempty. We show that sol(T) is a singleton and the Ishikawa sequence converges strongly to the unique solution of the equation Tx=f. In addition, whenever T is a Lipschitzian and local pseudocontractive mapping from a nonempty convex subset K of X and the set F(T) of fixed points of T is nonempty, we prove that F(T) is a singleton and the Ishikawa sequence converges strongly to the unique fixed point of T. Our results are the improvements and extension of the results of Deng and Ding⁽⁴⁾ and Tan and Xu⁽⁵⁾.     

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications （II）

This paper is a continuum of the preceding paper of author. Some new systems of generalized vector quasi-equilibrium problems involving condensing mappings are introduced and studied in locally FC-uniform spaces. By applying the existence theorem of maximal elements of condensing set-valued mappings in locally FC-uniform spaces obtained by author in the preceding paper, some new existence theorems of solutions for the systems of generalized vector quasi-equilibrium problems are proved in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Project supported by the Natural Science Foundation of Sichuan Education Department of China (No. 2003A081 and SZD0406)     

Subharmonic and ultra-subharmonic response of nonlinear elastic beams subjected to harmonic excitation

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THE NONLINEAR CHARACTERISTICS OF U-SHAPED BELLOWS——CALCULATIONS BY THE METHOD OF PERTURBATION

In this paper,the linear exact solution and nonlinear solutionfor U-shaped bellows have been obtained by using the general so-lution of circular ring shell and the method of perturbation.     

U型波纹管大挠度变形的积分方程描述及其迭代算法

采用格林函数法,导出了U型波纹管圆环壳部分和截头扁锥壳部分的非线性的积分方程,其中的四个未知参数由圆环壳和截头扁锥壳的连接条件确定,联合应用梯度法和积分方程迭代法建立了U型波纹管大挠度分析的迭代算法,开发了相应的程序系统,数值结果表明,本文方法具有较高的精度,压缩角对峰值应力和刚度影响十分显著,应用作为波纹管设计的重要参数。     

Curvature sensitive nonlinear turbulence model

By modifying the Rodi assumption to take account of the influence of flow curvature, a new curvature modified algebraic stress model (CMASM) is developed from the second moment closure in the generalized curvilinear coordinate system. And the explicit form of the ASM, a new curvature modified nonlineark-ε model (CMNKE), is derived in the orthogonal curvilinear coordinate system. This new nonlineark-ε model is further validated by a numerical simulation of a two-dimensional U-type turnaround duct flow. The results show that the CMNKE can effectively capture the main characteristic of this curvature flow and simulate the damping effect of the shear stress by a convex curvature and the enhancing effect by a concave curvature. So, this model is a rational and effective simplification to the second moment closure. The project supported by the National Natural Science Foundation of China (19725208) and the National Climbing project of China     

高超声速自适应激波针数值研究

针对传统的与钝体轴线共线安装的固定式激波针方法在有攻角状态所存在的问题, 在前人工作基础上得到一种新型高超声速飞行器减阻/降热方法------自适应激波针方法. 将该方法应用于三维高超声速轴对称钝锥外形以及扁平楔外形, 并采用数值模拟的方法对其进行了概念验证. 在0○~120○攻角范围内, 对不同L/D参数的激波针外形流场以及前缘壁面的压力、热流分布等进行了对比分析. 结果表明, 这种新型自适应激波针方法无论在无攻角还是有攻角状态, 均可有效降低高超声速飞行器头部壁面的压力和热流, 可以有效解决传统激波针方法在较大攻角情况状态下失效的问题.      

ON PROBLEMS OF U-SHAPED BELLOWS WITH NONLINEAR DEFORMATION OF LARGE AXISYMMETRICAL DEFLECTION (Ⅱ)——COUNTING VARIATION OF THICKNESS DISTRIBUTION

On the basis of paper [1], assuming the logarithm of thickness at arbitrary point on a U-shaped bellows meridian is linear with the logarithm of distance between that point and axis of symmetry, perturbation solutions of the corresponding problems of large axisymmetrical deflection are given. The effects of thickness distribution variation, which result from technology factors, on stiffness of bellows are discussed.     

Kink band instability in layered structures

A recent two-dimensional prototype model for the initiation of kink banding in compressed layered structures is extended to embrace the two propagation mechanisms of band broadening and band progression. As well as interlayer friction, overburden pressure and layer bending energy, the characteristics of transverse layer compressibility and foundation stiffness are now included. Experiments on constrained layers of paper show good agreement with the predictions of angle of orientation, kink band width and post-kink load-deflection response obtained from the model.     

Propagation of nonlinear waves along a viscoelastic bar

Various types of nonlinear waves propagating along a viscoelastic bar are considered. The rheological equation of state has strong physical and geometric nonlinearities, and nonisothermal effects are included. Both weak (isentropic) and shock waves of loading and unloading are investigated. It is shown that, for certain rubber-like materials, stable shock waves of extension can exist along with the shock waves of compression at very large strains. We then consider the strike of a viscoelastic bar of finite length against a rigid obstacle. Numerical solutions to this problem illustrate the influence of stress relaxation on nonlinear wave processes. A model for sticking and bouncing off is formulated and the mass-averaged velocity of the bar at the moment when it bounces off the obstacle is calculated.     

A parametric type of KKM theorem in <Emphasis Type="Italic">FC</Emphasis>-spaces with applications

The paper first proves a characteristic property in FC-spaces. By the use of the connectedness of sets, a parametric type of KKM theorem is then established in noncompact FC-spaces by introducing a linear ordered space. As a consequence, some recent results, such as noncompact minimax inequalities, saddle point theorem, and section theorem, are improved. The results generalize the corresponding results in the literatures.     

Stability of nonlinear local axisymmetrical strains of shells of revolution

A brief review of the results of investigation of the stability of the axisymmetrical strains of elastic shells of revolution is contained in [1, 2]. In [3] the problem was formulated and solved for a round shell, uniformly loaded along its hinged edge by a radial compressive force. Below, this problem is formulated for an arbitrary shell of revolution with a uniformly compressed hinged edge. Results of its solution are given for conical and spherical shells.     

Effect of axial load on the propagation of elastic waves in helical beams

Helical structures are designed to support heavy loads, which can significantly affect the dynamic behaviour. This paper proposes a physical analysis of the effect of axial load on the propagation of elastic waves in helical beams. The model is based on the equations of motion of loaded helical Timoshenko beams. An eigensystem is obtained through a Fourier transform along the axis. The equations are made dimensionless for beams of circular cross-section and the number of parameters governing the problem is reduced to four (helix angle, helix index, Poisson coefficient, and axial strain). A parametric study is conducted. The effect of loading is quantified in high, medium and low-frequency ranges. Noting that the effect is significant in low frequencies, dispersion curves of stretched and compressed helical beams are presented for different helix angles and radii. This effect is greater as the helix angle increases. Both the effects of stress and geometry deformation are shown to be non-negligible on elastic wave propagation.