有限周期梁用动力消振器抑振的特性

本文用弯曲波方法导出了多支承梁加动力消振器位移响应的普遍表达式。理论分析发现了周期结构用动力消振器抑制振动的一些新特性：（１）仅用一个动力消振器可抑制周期结构对应传递频带内的一组共振峰。被抑制的共振峰的数量与跨距的数量和消振器的布置位置有关；（２）动力消振器调谐频率与对应传递频带的第一个共振频率相关联。当动力消振器与作用在梁上的外载荷作用在同一点时，最佳调谐频率比总是大于１，否则最佳调谐频率比小于１。     

Ultrasonic tracking of acoustic radiation force-induced displacements in homogeneous media

The use of ultrasonic methods to track the tissue deformation generated by acoustic radiation force is subject to jitter and displacement underestimation errors, with displacement underestimation being primarily caused by lateral and elevation shearing within the point spread function (PSF) of the ultrasonic beam. Models have been developed using finite element methods and Field II, a linear acoustic field simulation package, to study the impact of focal configuration, tracking frequency, and material properties on the accuracy of ultrasonically tracking the tissue deformation generated by acoustic radiation force excitations. These models demonstrate that lateral and elevation shearing underneath the PSF of the tracking beam leads to displacement underestimation in the focal zone. Displacement underestimation can be reduced by using tracking beams that are narrower than the spatial extent of the displacement fields. Displacement underestimation and jitter decrease with time after excitation as shear wave propagation away from the region of excitation reduces shearing in the lateral and elevation dimensions. The use of higher tracking frequencies in broadband transducers, along with 2D focusing in the elevation dimension, will reduce jitter and improve displacement tracking accuracy. Relative displacement underestimation remains constant as a function of applied force, whereas jitter increases with applied force. Underdeveloped speckle (SNR < 1.91) leads to greater levels of jitter and peak displacement underestimation. Axial shearing is minimal over the tracking kernel lengths used in acoustic radiation force impulse imaging and thus does not impact displacement tracking.     

Boundary element formulation for 3D transversely isotropic cracked bodies

The boundary traction integral representation is obtained in elasticity when the classical displacement representation is differentiated and combined according to Hooke's law. The use of both traction and displacement integral representations leads to a mixed (or dual) formulation of the BEM where the discretization effort for crack problems is much smaller than in the classical formulation. A boundary element analysis of three‐dimensional fracture mechanics problems of transversely isotropic solids based on the mixed formulation is presented in this paper. The hypersingular and strongly singular kernels appearing in the formulation are regularized by using two terms of the displacement series expansion and one term of the traction expansion, at the collocation point. All the remaining integrals are analytically evaluated or transformed by means of Stokes' theorem into regular or weakly singular integrals, which are numerically computed. The method is general and can be used for elements of any shape including quarter‐point crack front elements. No change of co‐ordinates is required for the integration. The formulation as presented in this paper is something as clear, general and easy to handle as the classical BE formulation. It is used in combination with three‐dimensional quadratic and quarter‐point elements to obtain accurate results for several different crack problems. Cracks in boundless and finite transversely isotropic domains are studied. The meshes are simple and include only discretization of the crack and the external boundary. The obtained results are in good agreement with those existing in the literature. Copyright © 2004 John Wiley & Sons, Ltd.     

Vibrational Diver

The paper is concerned with dynamics of light solid in cavity with liquid subjected to rotational vibration in the external force field. New vibrational phenomenon – diving of a light cylinder to the cavity bottom is found. The experimental investigation of a horizontal annulus with a partition has shown that under vibration a light body situated in the upper part of the layer is displaced in a threshold manner some distance away from the boundary. In this case the body executes symmetric tangential oscillations. An increase of the vibration intensity leads to a tangential displacement of the body near the external boundary. This displacement is caused by the tangential component of the vibrational lift force, which appears as soon as the oscillations lose symmetry. In this case the trajectory of the body oscillatory motion has the form of a loop. The tangential lift force makes stable the position of the body on the inclined section of the layer and even in its lower part. A theoretical interpretation has been proposed, which explains stabilization of a quasi-equilibrium state of a light body near the cavity bottom in the framework of vibrational hydromechanics.     

宽翼缘薄壁梁剪滞效应分析的变分解法

采用三个独立的广义位移w(x)、U(x)、θ(x)对宽翼缘薄壁梁的剪滞效应进行变分法分析,根据最小势能原理,建立了关于w(x)、U(x)、θ(x)的基本微分方程及相应的边界条件。计算体系总势能时考虑了剪力在剪切变形上作功。所推导的基本方程及边界条件表明,剪力滞后效应与剪切效应彼此独立。引用的算例计算结果表明,按该方法计算宽翼缘薄壁梁的挠度,能大幅度提高计算精度。     

无砟轨道端刺结构纵向位移的解析算法及应用

考虑高速铁路纵连板式无砟轨道底座板、摩擦板、端刺结构及路基土体的相互作用关系,深入分析了端刺顶部水平力的传递机理,借鉴水平荷载及弯矩共同作用下单桩承载力及变形的计算公式,推导出适用于计算端刺结构纵向受力与变形的解析算法。该方法中,底座板与摩擦板间“两布”滑动层的摩擦力假定为均匀分布,摩擦板和端刺间传递纵向力和弯矩且满足变形协调条件,路基土体对端刺侧面均匀支撑。解析算法的计算结果和基于有限元软件ANSYS 所建立的空间耦合模型具有较好的一致性,说明该文提出的解析算法正确可靠,可实现纵连板式无砟轨道端刺结构纵向位移的快速准确计算。端刺结构计算结果表明:随着大端刺深度、宽度及小端刺数量的不断增加,端刺纵向位移会不断减小,有利于减小底座板的纵向位移及土体的压缩变形。     

吊灯灯罩纸浆模塑缓冲衬垫跌落仿真

目的验证纸浆模塑缓冲衬垫是否具有缓冲性能,能否有效保护产品不受损伤。方法基于吊灯灯罩与纸浆模塑衬垫之间的装配关系,以跌落冲击为环境载荷,采用Ansys/LS-DYNA软件进行高度为1000 mm的跌落仿真分析,获取纸浆模塑缓冲衬垫应力-应变云图、加速度响应曲线等动态特征和相关参数,以此分析吊灯灯罩纸浆模塑衬垫在整个跌落过程中的作用。结果纸浆模塑衬垫凸台发生了变形,作用力由纸浆模塑衬垫向灯罩扩散;整个模型重心点的加速度小于最低点的加速度;整个模型重心点和最低点速度与位移变化符合实际情况。结论纸浆模塑缓冲衬垫通过结构的变形和破坏来吸收外界冲击能量,以及延长作用力时间起到缓冲作用,能在物流过程中对产品进行有效保护。     

Hyper-singular boundary element method for elastoplastic fracture mechanics analysis with large deformation

In this paper a two-dimensional hyper-singular boundary element method for elastoplastic fracture mechanics analysis with large deformation is presented. The proposed approach incorporates displacement and the traction boundary integral equations as well as finite deformation stress measures, and general crack problems can be solved with single-region formulations. Efficient regularization techniques are applied to the corresponding singular terms in displacement, displacement derivatives and traction boundary integral equations, according to the degree of singularity of the kernel functions. Within the numerical implementation of the hyper-singular boundary element formulation, crack tip and corners are modelled with discontinuous elements. Fracture measures are evaluated at each load increment, using the J-integral. Several cases studies with different boundary and loading conditions have been analysed. It has been shown that the new singularity removal technique and the non-linear elastoplastic formulation lead to accurate solutions.     

Identification of material parameters of the Gurson–Tvergaard–Needleman model by combined experimental and numerical techniques

To identify material parameters from suitable experiments it is prevalent to use global informations like force–displacement or force–necking curves. The quality of accordance between measured and calculated forces at given displacements can be expressed by a least-squares functional. In this contribution a non-linear optimization method will be presented, which minimizes the least-squares functional by use of a gradient based method. The gradient of this functional is calculated in a semi-analytical sensitivity analysis. To determine the derivatives of the force with respect to the material parameters, the local sensitivities on an intersection will be added together. On this intersection, the total nodal force and the external force have to be equal and the normal displacements have to be independent on the material parameters. The parameter identification is embedded in the finite element code SPC-PMHP for solving non-linear boundary and initial value problems on parallel computers. The Gurson–Tvergaard–Needleman model is used to describe the plastic deformation and damage behaviour of the ductile structural steel StE 690. The developed algorithm is applied to tensile tests with notched cylindrical bars.     

Mixed boundary value problem of simple support type in plane elasticity

Summary A general solution of a mixed boundary value problem in the plane elasticity is obtained for the boundary condition; one of two displacement components and one of two external force components are given on a part of the boundary. The part of the boundary is a straight line. A mapping function of a sum of fractional expressions and the complex stress functions are used. A closed solution can be obtained. As an example, a semi-infinite plate with a simple support on a part of the boundary is analyzed. The analysis is carried out for the states before and after the crack initiation at an end of the simple support. The loading condition is that the constant tensile load applies on the simple support. The stress distribution, the stress intensity factor and the resultant moment on the simple support are obtained.With 6 Figures     

Stationary singular points induced by discontinuous external forces in one-dimensional materials with internal variables

It is shown that in one-dimensional materials with internal variables a discontinuous external force induces a stationary singular point at which the second deformation gradient is discontinuous. An explicit formula for the growth and decay of the discontinuity is obtained. The creep compliance for the material can be determined by observing the variation of the discontinuity induced by a discontinuous external force which is the unit function of time.     

Elastic large deflection analysis of plates subjected to uniaxial thrust using meshfree Mindlin-Reissner formulation

A meshfree approach for plate buckling/post-buckling problems in the case of uniaxial thrust is presented. A geometrical nonlinear formulation is employed using reproducing kernel approximation and stabilized conforming nodal integration. The bending components are represented by Mindlin–Reissner plate theory. The formulation has a locking-free property in imposing the Kirchhoff mode reproducing condition. In addition, in-plane deformation components are approximated by reproducing kernels. The deformation components are coupled to solve the general plate bending problem with geometrical non-linearity. In buckling/post-buckling analysis of plates, the in-plane displacement of the edges in their perpendicular directions is assumed to be uniform by considering the continuity of plating, and periodic boundary conditions are considered in assuming the periodicity of structures. In such boundary condition enforcements, some node displacements/rotations should be synchronized with others. However, the enforcements introduce difficulties in the meshfree approach because the reproducing kernel function does not have the so-called Kronecker delta property. In this paper, the multiple point constraint technique is introduced to treat such boundary conditions as well as the essential boundary conditions. Numerical studies are performed to examine the accuracy of the multiple point constraint enforcements. As numerical examples, buckling/post-buckling analyses of a rectangular plate and stiffened plate structure are presented to validate the proposed approach.     

Shear and bending deformation of rigid-plastic circular plates by central pressure pulse

The dynamic plastic deformation of simply supported and clamped circular plates to a central pressure pulse is investigated theoretically. The plate material is assumed to be rigid-perfectly plastic and to obey a yield criterion which retains the transverse shear force as well as bending moments. Various patterns of deformation are obtained for a wide range of parameters which combine plastic bending and shear sliding. The dependence of the final central deflection and shear displacement on the relative shear strength, the load magnitude and the loaded area are discussed for a short duration pressure pulse. The influence of boundary conditions on shear and bending deformation is examined.     

The symplectic approach for two-dimensional thermo-viscoelastic analysis

This paper presents an exact symplectic approach for two dimensional isotropic viscoelastic solids subjected to external force and temperature boundary conditions. With the use of the state space method and the Laplace transform, all general solutions of the governing equations are obtained analytically. By applying the inverse integral transform, the time domain adjoint symplectic relationships between the general solutions are established. Therefore, the problems of the particular solution and the boundary conditions can be analysed either in the Laplace domain or directly in the time domain. As its applications, the boundary condition problems are discussed in the numerical calculations. The results show that, due to the displacement constraints and the temperature influence, local effects are distinct near the boundary, and the effects decay rapidly with the distance from the boundary.     

内置碟簧自复位联肢剪力墙参数设计与滞回性能研究

为了减小结构的震后残余变形,有效地避免墙肢破坏,该文提出并设计了一种内置碟簧装置的自复位联肢剪力墙(SC-CSW)。SC-CSW主要通过碟簧装置中的摩擦耗散地震能量,碟簧提供恢复力。建立了预压小于摩擦的SC-CSW1、预压大于摩擦的SC-CSW2及普通联肢剪力墙的有限元模型,对比分析了三者的承载能力、变形能力、耗能能力和自复位能力,结果表明：加载位移达到弹塑性层间位移限值时,SC-CSW1的累积耗能比普通联肢剪力墙降低28.03%,但其延性比普通联肢剪力墙提高至少2.94倍,能更好的满足大震下的位移需求; SC-CSW2的累积耗能比SC-CSW1降低15.83%,但其承载力提高,且最大残余位移比仅为0.09%,基本消除了残余变形,能满足结构功能可恢复的需求。     

Flexural - Torsional Nonlinear Analysis of Timoshenko Beam-Column of Arbitrary Cross Section by BEM

In this paper a boundary element method is developed for the nonlinear flexural - torsional analysis of Timoshenko beam-columns of arbitrary simply or multiply connected constant cross section, undergoing moderate large deflections under general boundary conditions. The beam-column is subjected to the combined action of an arbitrarily distributed or concentrated axial and transverse loading as well as to bending and twisting moments. To account for shear deformations, the concept of shear deformation coefficients is used. Seven boundary value problems are formulated with respect to the transverse displacements, to the axial displacement, to the angle of twist (which is assumed to be small), to the primary warping function and to two stress functions and solved using the Analog Equation Method, a BEM based method. Application of the boundary element technique yields a system of nonlinear equations from which the transverse and axial displacements as well as the angle of twist are computed by an iterative process. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. Numerical examples with great practical interest are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. The influence of both the shear deformation effect and the variableness of the axial loading are remarkable.     

变截面连续箱梁桥剪力滞及剪切变形双重效应分析的传递矩阵法

基于能量原理,考虑箱梁截面底板、顶板、悬臂板剪滞翘曲幅度一般各不相同的影响和轴力自平衡条件,计入腹板剪切变形,导出了箱梁的平衡控制微分方程组、边界条件;给出了该方程组在均布荷载作用下的初参数解,提出一种研究变截面连续箱梁桥剪力滞后效应的传递矩阵法。建立了相应的场矩阵和点矩阵,从而实现了变截面连续箱梁桥内力、应力及位移的一维递推求解。数值算例与模型试验及已有文献结果对比表明:该文方法计算精度好、效率高,为求解连续箱梁、变截面箱梁的剪力滞问题提供了强有力的计算手段。     

Further study on the refined theory of rectangle deep beams

Based on the refined theory for narrow rectangular deep beams, two different displacement boundary conditions of the fixed end of a cantilever beam are used to study the deformation of the beam. One is the conventional simplified displacement boundary condition, and the other is a new boundary condition determined by the least squares method. Three load cases are investigated, which are a transverse shear force at the free end of the beam, a uniformly distributed load at the top surface, and a linearly distributed load at the top surface, respectively. Solutions are given for both the refined theory and the Timoshenko beam theory and are compared with the known solutions from the elastic theory and results by the finite element method. It is shown that the solutions of the refined theory coincide with those of the elastic theory; the solutions from the Timoshenko theory by using the two different displacement boundary conditions are the same; the refined theory by using the new boundary condition provides better results than using the conventional boundary condition and also better than those of the Timoshenko beam theory.     

基于微小形变测量的旋翼天平高精度测力校准系统

旋翼天平原位校准中,校准力精确加载是提高校准精度的重要因素。校准装置结构形变会给校准力加载造成误差,影响校准精度。针对这一问题,设计了旋翼天平测力校准系统。该系统采用激光三角法实现微小位移测量,通过测量立方靶块空间位置变化,计算力加载点位移;建立数学模型,分析结构形变对校准力加载影响,测量校准力。经实验,该系统可以消除结构形变影响,准确测量校准力,提高校准力加载精度。     

A three‐scale compressible microsphere model for hyperelastic materials

This paper presents a seminumerical homogenization framework for porous hyperelastic materials that is open for any hyperelastic microresponse. The conventional analytical homogenization schemes do apply to a limited number of elementary hyperelastic constitutive models. Within this context, we propose a general numerical scheme based on the homogenization of a spherical cavity in an incompressible unit hyperelastic solid sphere, which is denoted as the mesoscopic representative volume element (mRVE). The approach is applicable to any hyperelastic micromechanical response. The deformation field in the sphere is approximated via nonaffine kinematics proposed by Hou and Abeyaratne (JMPS 40:571‐592,1992). Symmetric displacement boundary conditions driven by the principal stretches of the deformation gradient are applied on the outer boundary of the mRVE. The macroscopic quantities, eg, stress and moduli expressions, are obtained by analytically derived pointwise geometric transformations. The macroscopic expressions are then computed numerically through quadrature rules applied in the radial and surface directions of the sphere. A three‐scale compressible microsphere model is derived from the developed seminumerical homogenization framework where the micro‐meso transition is based on the nonaffine microsphere model at every point of the mRVE. The numerical scheme developed for the derivation of macroscopic homogenized stresses and moduli terms as well as the modeling capability of the three‐scale microsphere model is investigated through representative boundary value problems.