动态像面法测量水面落点位置及误差分析

为了测量弹丸水面落点的位置, 建立了基于CCD相机动态像面的测量模型。该模型通过CCD相机辅助采集相关点位的图像信息, 对水面落点的位置函数以及误差进行了研究。首先, 利用空间几何获得靶船上三定点相对于测量船的方位、俯仰信息。接着, 结合t时刻观测图像上定点的像面坐标, 运用底片常数模型建立像面坐标和角度信息两套参量之间的关系函数, 从而得到目标落点的方位、俯仰信息, 再利用异面交会法计算出目标落点位置。最后, 分析了目标落点位置的误差来源(质心误差, 位置误差)、误差以及各误差源与位置坐标之间的关系。实验结果表明:在测量船位置精度达到0.05 m, 图像质心定位精度达到0.5 pixel时, 在最小交会误差的情况下, 目标落点的位置测量误差分别为2.8, 4.9, 4.3 m。     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅴ)——POLAR THERMOMECHANICAL CONTINUA

The purpose is to reestablish rather complete basic balance equations and boundary conditions for polar thermomechanical continua based on the restudy of the traditional theories of micropolar thermoelasticity and thermopiezoelectricity. The equations of motion and the local balance equation of energy rate for micropolar thermoelasticity are derived from the rather complete principle of virtual power. The equations of motion, the balance equation of entropy and all boundary conditions are derived from the rather complete Hamilton principle. The new balance equations of momentum and energy rate which are essentially different from the existing results are presented. The corresponding results of micromorphic thermoelasticity and couple stress elastodynamics may be naturally obtained by the transition and the reduction from the micropolar case, respectively. Finally, the results of micropolar thermopiezoelectricity are directly given. Contributed by DAI Tian-min, Original Member of Editorial Committee, AMM Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001) Biography: DAI Tian-min (1931-)     

Geometry and differentiability requirements in multibody railroad vehicle dynamic formulations

The dynamic equations of multibody railroad vehicle systems can be formulated using different sets of generalized coordinates; examples of these sets of coordinates are the absolute Cartesian and trajectory coordinates. The absolute coordinate based formulations do not require introducing an intermediate track coordinate system since all the absolute coordinates are defined in the global system. On the other hand, when the trajectory coordinates are used, a track coordinate system that follows the motion of a body in the railroad vehicle system is introduced. This track coordinate system is defined by the track geometry and the distance traveled by the body along the track centerline. The configuration of the body with respect to the track coordinate system is defined using five coordinates; two translations and three Euler angles. In this paper, the formulations based on the absolute and trajectory coordinates are compared. It is shown that these two sets of coordinates require different degrees of differentiability and smoothness. When an elastic contact formulation is used to study the wheel/rail dynamic interaction, there are significant differences in the order of the derivatives required in both formulations. In fact, as demonstrated in this study, in the absence of a contact constraint formulation, higher order derivatives with respect to geometric parameters are still required when the equations are formulated using the trajectory coordinates. The formulation of the constraints used in the analysis of the wheel/rail contact is discussed and it is shown that when the absolute coordinates are used, only third order derivatives need to be evaluated. The relationship between the track frame used in railroad vehicle dynamics and the Frenet frame used in the theory of curves to describe the curve geometry is also discussed in this paper. Based on the analysis presented in this paper, the advantages and drawbacks of a hybrid method which employs both the absolute and trajectory coordinates and planar contact conditions in order to reduce the number of contact constraints and relax the differentiability requirements are discussed. In this method, the absolute coordinates are used to formulate the equations of motion of the railroad vehicle system. The absolute coordinate solution can be used to determine the trajectory coordinates and their time derivatives. Using the trajectory coordinates, the motion of the body in the vehicle with respect to the track coordinate system can be predicted and used in the formulation of the planar contact model.     

Modeling of Shear-Induced Diapycnal Mixing in Frontal Systems

Three shear-induced mixing models are examined and applied to oceanic frontal systems. These are a simple diagnostic model, a one-dimensional kinematical model and a two-dimensional geostrophic model. All of these are process-oriented models in isopycnic coordinates, with diapycnal mixing depending on the gradient Richardson number and mixing rapidly developing in subcritical flows. In the first model an initial subcritical condition is specified and mixing is allowed to redistribute the vertical density flux. In the second model the dynamics is specified ad hoc to simulate a frontal system which leads to subcritical conditions and we are left to solve the mass conservation equation. In the final model a two-dimensional density-depth field is forced through an externally imposed deformation velocity field and we solve both the mass and momentum conservation equations. In this last model diapycnal mixing controls the mass conservation equation while the momentum equations consist in cross-stream geostrophic balance. All three models produce mixed regions which probably correspond to some of the fine structure density-depth steps that are observed in geophysical flows. The very simple diagnostic and kinematical models have the merit of providing a clear picture of the physical mechanism that produces the density-depth steps, but the potential complexity of the solution is only appreciated when incorporating the dynamics, such as in the geostrophic model.     

On the Spectral Representation of Stretch and Rotation

By means of Sylvester's spectral representation of tensor-valued functions, a representation is derived for the finite stretch and rotation associated with the polar decomposition of a given deformation gradient. This revised version was published online in August 2006 with corrections to the Cover Date.     

Analysis of melt spinning transients in Lagrangian coordinates

Transients in melt spinning of isothermal power law and Newtonian fluids were found to be governed by an extremely simple partial differential equation ² ( ^1/n )/() = 0 in Lagrangian coordinates where is the cross-sectional area,n the power law exponent, the time and the the time at which a fluid molecule constituting the spinline left the spinneret. The general integral ^1/n =f() +g () of the above governing equation containing two arbitrary functions represents physically attainable spinline transients. Hitherto unknown analytical transient solutions of the above governing equation were obtained for the response of isothermal constant tension spinlines to a stepwise change in tension, spinneret hole area, extrusion speed or extrusion viscosity and for the starting transient in gravitational spinning. Linearized perturbation solutions and the stability limit of the spinline derived from the above new found nonlinear solutions were in agreement with previous findings and the above nonlinear response of the spinline to a step increase in the spinneret hole area was found to be equivalent to Orowan's tandem cylinder model of dent growth in filament stretching.     

Finite multiplicative plasticity for small elastic strains with linear balance equations and grain boundary relaxation

This paper is concerned with the formulation of a phenomenological model of finite elasto-plasticity valid for small elastic strains for initially isotropic polycrystalline material. As a basic we assume the multiplicative split of the deformation gradient into elastic and plastic part. A key feature of the model is the introduction of an independent field of 'elastic' rotations which eliminate the remaining geometrical nonlinearities coming from finite elasticity in the presence of small elastic strains. In contrast to micro-polar theories an evolution equation for is presented which relates to making use of a new device found by the author to perform the polar decomposition asymptotically. The model is shown to be invariant under both change of frame and rotation of the so called intermediate configuration. The corresponding equilibrium equations at frozen plastic and viscoelastic configuration constitute then a linear, elliptic system with nonconstant coefficients which makes this model amenable to a rigorous mathematical analysis. The introduced hysteresis effects within the elastic region are related to viscous elastic rotations of the grains of the polycrystal due to internal friction at the grain boundaries and constitute as such a rate dependent transient texture effect. The inclusion of work hardening will be addressed in future work. Received March 07, 2002 / Published online February 17, 2003 RID="*" ID="*"Communicated by Kolumban Hutter, Darmstadt     

A geometrically exact Cosserat shell-model including size effects,avoiding degeneracy in the thin shell limit. Part I: Formal dimensional reduction for elastic plates and existence of minimizers for positive Cosserat couple modulus

This contribution is concerned with a consistent formal dimensional reduction of a previously introduced finite-strain three-dimensional Cosserat micropolar elasticity model to the two-dimensional situation of thin plates and shells. Contrary to the direct modelling of a shell as a Cosserat surface with additional directors, we obtain the shell model from the Cosserat bulk model which already includes a triad of rigid directors. The reduction is achieved by assumed kinematics, quadratic through the thickness. The three-dimensional transverse boundary conditions can be evaluated analytically in terms of the assumed kinematics and determines exactly two appearing coefficients in the chosen ansatz. Further simplifications with subsequent analytical integration through the thickness determine the reduced model in a variational setting. The resulting membrane energy turns out to be a quadratic, elliptic, first order, non degenerate energy in contrast to classical approaches. The bending contribution is augmented by a curvature term representing an additional stiffness of the Cosserat model and the corresponding system of balance equations remains of second order. The lateral boundary conditions for simple support are non-standard. The model includes size-effects, transverse shear resistance, drilling degrees of freedom and accounts implicitly for thickness extension and asymmetric shift of the midsurface. The formal thin shell membrane limit without classical h ³-bending term is non-degenerate due to the additional Cosserat curvature stiffness and control of drill rotations. In our formulation, the drill-rotations are strictly related to the size-effects of the bulk model and not introduced artificially for numerical convenience. Upon linearization with zero Cosserat couple modulus we recover the well known infinitesimal-displacement Reissner-Mindlin model without size-effects and without drill-rotations. It is shown that the dimensionally reduced Cosserat formulation is well-posed for positive Cosserat couple modulus by means of the direct methods of variations along the same line of argument which showed the well-posedness of the three-dimensional Cosserat bulk model [72].Received: 16 April 2004, Accepted: 3 May 2004, Published online: 17 September 2004     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅵ)—CONSERVATION LAWS OF MASS AND INERTIA

The purpose is to reestablish the coupled conservation laws, the local conservation equations and the jump conditions of mass and inertia for polar continuum theories. In this connection the new material derivatives of the deformation gradient, the line element, the surface element and the volume element were derived and the generalized Reynolds transport theorem was presented. Combining, these conservation laws of mass and inertia with the balance laws of momentum, angular momentum and energy derived in our previous papers of this series, a rather complete system of coupled basic laws and principles for polar continuum theories is constituted on the whole. From this system the coupled nonlocal balance equations of mass, inertia, momentum, angular momentum and energy may be obtained by the usual localization. Contributed by DAI Tian-min, Original Member of Editorial Committee, AMM Foundation items: the National Natural Science Foundation of China (10072024); the Research Foundation of Liaoning Education Committee (990111001) Biography: DAI Tian-min (1931≈)     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (Ⅵ)—CONSERVATION LAWS OF MASS AND INERTIA

IntroductionThisworkisadirectcontinuationandasupplementofRefs .[1～8] .InRefs.[1～8]thecoupledbalancelawsandequationsofmomentum ,angularmomentumandenergyaswellasthenewHamiltonprinciple,principleofvirtualpowerandNoethertheoremhavebeenpresented .However,thecoupledconservationlawsofmassandinertiahavenotbeenreestablishedyet.Thepurposeofthispaperistoreestablishtheconservationlawsandequationsofmassandinertiaandtocombinethemwiththecoupledbalancelawsandequationsofmomentum ,angularmomentum ,energyand…