透平转子的可靠性设计

介绍透平转子的可靠性设计方法。该方法以传统的转子强度和振动的设计方法为基础,把透平转子的静应力、材料静强度、应力幅、尺寸系数、表面加工系数、应力集中系数、材料疲劳极限、热疲劳累积损伤程度、材料低周疲劳程度、蠕变寿命、固有频率、激振力频率、不平衡响应等处理为随机变量,使用机械概率设计法确定转子设计的可靠度。文中给出了透平转子静强度、疲劳强度、热疲劳、蠕变寿命、避开弯曲共振、避开扭转共振和限制不平稳响     

The Explicit Expression of Internal Forces in Prismatic Membered Structures*

ABSTRACT

Analytic expressions for member forces in linear elastic redundant trusses have recently been given by the author. It was shown that the internal forces in a truss are the ratios of two multilinear homogeneous polynomials in the longitudinal stiffnesses of the elements of the structure. The order of the polynomials is equal to the number of nodal degrees of freedom of the structure. The number of terms of each polynomial is equal to the number of statically determinate stable substructures that can be derived from the original structure. It was shown that coefficients of the polynomials can be computed through the equilibrium equations and by enforcing global compatibility of deformations. This paper generalizes these results to the case of linear elastic structures, composed of uniform prismatic elements that have extensional, flexural, and torsional stiffness. This is done by replacing each bi-modal bending element with a unimodal moment element and a unimodal shear element. This allows the representation of deformation of the elements by six uncoupled basic deformation patterns in the case of structures in space, thus paving the way for truss-type analysis for general structures that are composed of uniform prismatic elements. As a result, multilinear polynomials that appear in expressions for stress resultants are the products of axial, bending, and torsional stiffnesses of subsets of the original structure. The number of terms appearing in the polynomials renders the exact analytic expressions intractable for practical engineering structures. However, the construct of the analytic equations may constitute a basis for writing approximate expressions for member forces in frames, explicitly in terms of rigidities of components of the structure. This paper describes such an approximate expression, with a reduced number of terms in the polynomials. The theory is illustrated with numerical examples of analysis of planar structures     

Linear viscoelastic model for bending and torsional modes in fluid membranes

This paper develops and applies a linear viscoelastic model for bending and torsional modes of fluid membranes, based on the nonlinear Cosserat surface fluid model. The linearized fluid membrane model in spherical and cylindrical geometries is shown to decouple bending and torsional viscoelastic modes. It is found that solutions of the membrane viscoelastic model to small-amplitude oscillatory bending and torsion allows for the measurement of the bending and the torsion viscosity. The model and its potential in characterizing the bending and torsion viscoelasticity of membranes complements the on-going efforts to establish the role of curvature in dissipative process of biological membranes.     

Using continuous models in the analysis of vibrational spectra for carbon nanotubes

The rod models of longitudinal, torsional, and bending vibrations are used to find the natural vibration spectra of a carbon nanotube. The spectrum of natural radial vibrations is found using the membrane theory of cylindrical shells. The coefficients of these models are chosen by comparing the results obtained on the basis of the micromodel with the Keating interaction potential in the framework of the long-wave approximation and on the basis of a continuous model. It is shown that the spectra of longitudinal, radial, and torsional vibrations of the carbon nanotube are of the same order of magnitude (the minimum frequency is about 10¹¹ Hz), whereas the natural frequency spectrum for the bending vibrations is of two orders of magnitude less (the minimum frequency is about 10⁹ Hz). These spectra belong to the super-high frequency range.     

FINITE ELEMENT MODELING AND ROBUST VIBRATION CONTROL OF TWO-HINGED PLATE USING BONDED PIEZOELECTRIC SENSORS AND ACTUATORS

Active vibration control for a kind of two-hinged plate is developed in this paper. A finite element model for the hinged plate integrated with distributed piezoelectric sensors and actuators is derived, including bending and torsional modes of vibration. In this model, the hinges are simplified as regular plate elements to facilitate operation. The state space representations for bending and torsional vibrations are obtained. Based on two low-order models of the bending and torsional motion, two H ∞ robust controllers are designed for suppressing the vibrations of the bending and torsional modes, respectively. The simulation results indicate the effectiveness and feasibility of the designed H ∞ controllers. The vibration magnitudes of the low-order modes can be reduced without affecting the high frequency modes.     

Nonlinear dynamics of three-dimensional belt drives using the finite-element method

In this paper, new nonlinear dynamic formulations for belt drives based on the three-dimensional absolute nodal coordinate formulation are developed. Two large deformation three-dimensional finite elements are used to develop two different belt-drive models that have different numbers of degrees of freedom and different modes of deformation. Both three-dimensional finite elements are based on a nonlinear elasticity theory that accounts for geometric nonlinearities due to large deformation and rotations. The first element is a thin-plate element that is based on the Kirchhoff plate assumptions and captures both membrane and bending stiffness effects. The other three-dimensional element used in this investigation is a cable element obtained from a more general three-dimensional beam element by eliminating degrees of freedom which are not significant in some cable and belt applications. Both finite elements used in this investigation allow for systematic inclusion or exclusion of the bending stiffness, thereby enabling systematic examination of the effect of bending on the nonlinear dynamics of belt drives. The finite-element formulations developed in this paper are implemented in a general purpose three-dimensional flexible multibody algorithm that allows for developing more detailed models of mechanical systems that include belt drives subject to general loading conditions, nonlinear algebraic constraints, and arbitrary large displacements. The use of the formulations developed in this investigation is demonstrated using two-roller belt-drive system. The results obtained using the two finite-element formulations are compared and the convergence of the two finite-element solutions is examined.     

开口厚壁截面短构件的约束扭转1）

为了分析开口厚壁截面短构件的约束扭转问题,采用统一分析梁模型与有限节线法,对T形和L形厚壁截面短构件约束扭转时横截面的翘曲和应力分布情况等问题进行了分析研究.算例计算结果表明：开口厚壁截面短构件存在与其横截面形心位置不一致的扭转（弯曲）中心,构件在不过扭转中心的外力作用下会产生弯扭耦合变形,其横截面将产生不均匀翘曲,横截面上的翘曲正应力和扭转剪应力均呈非线性分布.     

Torsin of Functionally Graded Isotropic Linearly Elastic Bars

The purpose of this research is to investigate the effects of material inhomogeneity on the torsional response of linearly elastic isotropic bars. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e. materials with spatially varying properties tailored to satisfy particular engineering applications. The classic approach to the torsion problem for a homogenous isotropic bar of arbitrary simply-connected cross-section in terms of the Prandtl stress function is generalized to the inhomogeneous case. The special case of a circular rod with shear modulus depending on the radial coordinate only is examined. It is shown that the maximum shear stress does not, in general, occur on the boundary of the rod, in contrast to the situation for the homogeneous problem. It is shown that the material inhomogeneity may increase or decrease the torsional rigidity compared to that for the homogeneous rod. Optimal upper and lower bounds for the torsional rigidity for nonhomogeneous bars of arbitrary cross-section are established. A new formulation of the basic boundary-value problem is given. The results are illustrated using specific material models used in the literature on functionally graded elastic materials. This revised version was published online in August 2006 with corrections to the Cover Date.     

轴向冲击载荷作用下锥壳中弹性应力波传播的计算和实验研究

本文利用有限元分析和模型实验研究了在轴向冲击载荷作用下,锥壳中弹性应力波的传播、计算和实验结果表明,结构中存在着弹性纵波和弹性弯曲波的传播,它们传播的速度各不相同,使壳面承受不同的应力状态;讨论了纵波和弯曲波随壳面的衰减;实验指出,由于边界的影响,即使纵波的反射也会产生新的反射弯曲波沿锥面传播。     

Zigzag carbon nanotubes—Molecular/structural mechanics and the finite element method

This paper discusses in details the relation between the bond bending stiffness used in molecular mechanics and the bending stiffness used in structural mechanics for zigzag carbon nanotubes (CNTs).Recent publications assumed the structural bending stiffness EI/a to be a constant and set it equal to the molecular bond bending stiffness C. By developing a closed form expression for the deformation of zigzag CNTs under simple tension, we suggest that the relation between EI/a and C is more complex. It actually depends on the bond bending stiffness C, the torsional angle φ and the lattice translational index n. In the limit of an infinite tube radius, which represents a graphene sheet, EI/a tends to C/2. Numerical simulations are also presented that validate the results.     

Ultra High Speed DIC and Virtual Fields Method Analysis of a Three Point Bending Impact Test on an Aluminium Bar

This paper deals with the analysis of an aluminium beam impacted in a three point bending configuration using a Hopkinson bar device. Full-field deformation measurements were performed using Digital Image Correlation on images captured with an ultra high speed camera (16 frames at a time resolution of 10 μs). The performance of the deformation and strain measurements were evaluated and the data were then used quantitatively to analyse the very complex dynamic behaviour of the beam. It was shown that the deformation of the beam was controlled by the interaction between the striker and the flexural bending wave triggered by the initial impact. The principle of virtual work was used to reconstruct the impact force from the shear strains and to analyze how this impact force relates to the acceleration of the specimen (inertia forces) and the development of the bending stresses. The results are in good agreement with expectations. This opens up new perspectives in the quantitative use of full-field measurements to extract elasto-plastic constitutive parameters from such impact tests.     

Harmonic vibrations and waves in a cylindrical helically anisotropic shell

A Kirchhoff-Love type applied theory is used to study the specific characteristics of harmonic waves and vibrations of a helically anisotropic shell. Special attention is paid to axisymmetric and bending vibrations. In both cases, the dispersion equations are constructed and a qualitative and numerical analysis of their roots and the corresponding elementary solutions is performed. It is shown that the skew anisotropy in the axisymmetric case generates a relation between the longitudinal and torsional vibrations which is mathematically described by the amplitude coefficients of homogeneous waves. In the case of a shell with rigidly fixed end surfaces, the dependence of the first two natural frequencies on the shell length and the helical line slope α, i.e., the geometric parameter of helical anisotropy, is studied. A boundary value problem in which longitudinal vibrations are generated on one of the end surfaces and the other end is free of forces and moments is considered to analyze the degree of transformation of longitudinal vibrations into longitudinally torsional vibrations. In the case of bending vibrations, two problems for a half-infinite shell are studied as well. In the first problem, the waves are excited kinematically by generating harmonic vibrations of the shell end surface in the plane of the axial cross-section, and it is shown that the axis generally moves in some closed trajectories far from the end surface. In the second problem, the reflection of a homogeneous wave incident on the shell end is examined. It is shown that the “boundary resonance” phenomenon can arise in some cases.     

A new beam element for analyzing geometrical and physical nonlinearity

Based on Timoshenko＇s beam theory and Vlasov＇s thin-walled member theory, a new model of spatial thin-walled beam element is developed for analyzing geometrical and physical nonlinearity, which incorporates an interior node and independent interpolations of bending angles and warp and takes diversified factors into consideration, such as traverse shear deformation, torsional shear deformation and their coupling, coupling of flexure and torsion, and the second shear stress. The geometrical nonlinear strain is formulated in updated Lagarange （UL） and the corresponding stiffness matrix is derived. The perfectly plastic model is used to account for physical nonlinearity, and the yield rule of von Mises and incremental relationship of Prandtle-Reuss are adopted. Elastoplastic stiffness matrix is obtained by numerical integration based on the finite segment method, and a finite element program is compiled. Numerical examples manifest that the proposed model is accurate and feasible in the analysis of thin-walled structures.     

Load-Deformation Behavior of Nitinol Stents

The rate of fracture of Nitinol stents in the superficial femoral artery (SFA) is higher than desirable. Development of more fracture-resistant stents requires a better understanding of in-vivo loads, how stents deform under these loads, and the influence of the artery on stent deformation. In the work reported here, testing devices were designed and constructed to measure loads in stents undergoing tensile, bending, and torsional deformations. Tests to measure mechanical stiffnesses were performed on stents, mock arteries, and stents emplaced in mock arteries. Significant stent/artery interaction was observed under tension and bending; little interaction occurred under torsion loads. The results are explained by changes in stent geometry under load. The deformation, load, and stent/artery interaction information will be useful in validating finite element codes for designing and analyzing stents.     

Torsion of circular cylinders containing η circular holes

In the present paper by using complex variable methods in linear elasticity and by means of analytic continuation, the author obtains for this problem a complex torsional function, shear stress components, displacement components,the torsional rigidity and shear stresses on boundaries expressed in terms of series.     

Finite Bending of a Rectangular Block of an Elastic Hencky Material

Hencky's elasticity model is an isotropic, finite hyperelastic equation obtained by simply replacing the Cauchy stress tensor and the infinitesimal strain tensor in the classical Hooke's law for isotropic infinitesimal elasticity with the Kirchhoff stress tensor and Hencky's logarithmic strain tensor. A study by Anand in 1979 and 1986 indicates that it is a realistic finite elasticity model that is in good accord with experimental data for a variety of engineering materials for moderate deformations. Most recently, by virtue of well-founded physical grounds and rigorous mathematical procedures it has been demonstrated by these authors that this model may be essential to achieving self-consistent Eulerian rate type theories of finite inelasticity, e.g., the J ₂-flow theory for metal plasticity, etc. Its predictions have been studied for some typical deformation modes, including extension, simple shear and torsion, etc. Here we are concerned with finite bending of a rectangular block. We show that a closed-form solution may be obtained. We present explicit expressions for the bending angle and the bending moment in terms of the maximum or minimum circumferential stretch in a general case of compressible deformations for any assigned stretch normal to the bending plane. In particular, simplified results are derived for the plane strain case and for the case of incompressibility. This revised version was published online in June 2006 with corrections to the Cover Date.     

Bending and vibration of composite laminated plates

Hybrid-stress finite element method is applied for analysis of bending and vibration of composite laminated plates in this paper. Firstly, based on the modified complementary principle, a rectangular hybrid-stress plate bending element is presented which applies to analysis of laminates. Inside the element, different stress parameters are assumed according to different layers. The boundary displacements are determined by means of the assumption of YNS theory on the boundary of elements. The element formed in this way not only can take effects of transverse shear deformation and local warping into account, but also has less degrees of freedom. Then, problems of bending and vibration of laminates are solved by using this element, and the numerical results are compared with the exact solutions. This shows that the results obtained in the paper are very close to the exact results.     

Stability of some shear flows for concentrated suspensions

In this paper we investigate the stability of some viscometric flows for a concentrated suspension model which allows for the effects of shear-induced migration, including plane and circular Couette and Poiseulle flows, and unbounded and bounded torsional flows. In the bounded torsional flow, where its radial outer boundary is assumed frictionless, an exact closeform solution is given. With the exception of torsional flows, we find that a limit point for all the steady-state solutions can exist for certain range in the parameter values. In all cases, disturbances can persist for a long time, O (H ²/a ²), where H is a dimension of the flow field, and a is the particles' radius.     

Criterion of aerodynamic performance of large-scale offshore horizontal axis wind turbines

With the background of offshore wind energy projects, this paper studies aerodynamic performance and geometric characteristics of large capacity wind turbine rotors （1 to 10 MW）, and the main characteristic parameters such as the rated wind speed, blade tip speed, and rotor solidity. We show that the essential criterion of a high- performance wind turbine is a highest possible annual usable energy pattern factor and a smallest possible dimension, capturing the maximum wind energy and producing the maximum annual power. The influence of the above-mentioned three parameters on the pattern factor and rotor geometry of wind turbine operated in China＇s offshore meteoro- logical environment is investigated. The variation patterns of aerodynamic and geometric parameters are obtained, analyzed, and compared with each other. The present method for aerodynamic analysis and its results can form a basis for evaluating aerodynamic performance of large-scale offshore wind turbine rotors.     

A function theory for thin elastic shells

It is well known in the theory of elastic shells that a first order approximation using the shell thickness as an expansion parameter leads to the membrane theory of shells. The membrane equations have as solutions thegeneralized analytic functions. These functions have been exhaustively studied by Ilya N. Vekua [6], [7] and his students. R.P. Gilbert and J. Hile [3] introduced an extension of these systems to include elliptic systems of 2n equations in the plane and named the solutions of these systemsgeneralized hyperanalytic functions.It is shown in this paper that the next order approximation to the shell, which permits, moreover, the introduction of bending, may be described in terms of the generalized hyperanalytic functions. It is strongly suspected that the higher order approximations may also be described in terms of corresponding hypercomplex systems.