Equations of Perturbation Growth in Aircraft Wakes

Equations for the perturbation amplitude in the vortex wake of an aircraft with a high-aspect-ratio wing are derived. The effect of the perturbing factor frequency, the proximity of the ground, and the turbulent atmosphere characteristics on the wake evolution is investigated.     

Overdetermined photoelastic solutions using least squares

The least-squares method is presented for obtaining an overdetermined solution from the various relationships available in photoelastic stress analysis. Equations are presented for incorporating the various relations into a weighted least-squares solution and advantages of this method are illustrated in two example problems. In addition to the greater accuracy possible in the overdetermined solution, the method permits weighting of the varied information and eliminates the need to separately determine the stress-optical constant. Variations of the method are discussed.     

Realization of a Given Relative Motion of two Rigid Bodies by a Two-Armed Robot

The formulation of a new task of realizing a given relative motion of two rigid bodies by means of a robot having two manipulators is given. A method for constructing the movements of two-armed robots is proposed, which consists of solving the direct and inverse problems of manipulator kinematics, taking into account additional conditions for eliminating the dangerous rapprochement of links.Equations of relationships of parameters of relative motion of the working links of the manipulators are obtained with the relative movements of their adjacent links assumed for control functions. Expressions for control functions of manipulators are obtained for the realization of a given relative motion of the general form of two rigid bodies, and also for plane motion.Pointing to the possibility of crossing the working links under the action ofmanipulators in one work area, and obtained the relationships that allow these intersections to be avoided.     

地下化学爆炸地运动信号关联探索

分析了弹性区域中应力传播的波动方程,说明该应力传播过程可以使用线性系统模型进行描述。根据系统辨识领域的脉冲响应方法,建立了应力测点的脉冲序列与源函数和响应序列之间的关系。在此基础上,建立了各测点间应力序列之间的关联响应模型,给出了采用神经网络的自适应优化方法求解关联参数的方法,并采用某次黄土介质中化学爆炸的实验数据进行了验证。将该模型用于测点数据的预测,预测值和实测值之间的误差很小。这表明,各测点间存在与测量数据无关的客观联系,仅由实验中爆炸源、测点位置和地介质力学参数分布等所决定。     

Two-dimensional photoelastic study of turbine-shell flanges

Results of a two-dimensional photoelastic study of turbine-shell flanges are reported. Equations of transition from model to prototype are given. A special loading jig for applying a uniform pressure to the boundary of a plane model is described. Pertinent aspects of the experimental technique are summarized.     

Constitutive equations for describing the elastoplastic deformation of elements of a body along small-curvature paths in view of the stress mode

Equations relating the components of the stress and strain tensors (constitutive equations) are formulated in terms of Euler coordinates. The equations describe the finite elastoplastic deformation of an isotropic body along paths of small curvature. It is assumed that the stress deviator is coaxial with the plastic-strain differential deviator. The relationships between the first and second invariants of the stress and strain tensors in the case of complex elastoplastic deformation of the body’s elements are determined from base tests on tubular specimens loaded along rectilinear paths for several values of the stress mode angle. Methods for specification of these relationships are proposed. The assumptions adopted to derive the constitutive equations are validated experimentally __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 4, pp. 62–72, April 2006.     

Motion of bed-loads under the influence of flow of a liquid

Equations are obtained for the motion of a water-soil mixture in the layer next to the base. The water-soil mixture is modeled by means of a viscous-friable medium, and the acceleration of the mixture is assumed to be small and is not taken into account. The validity of the equations is confirmed by the experimental data for the following characteristics of uniform motion of a flow: for the speed of the start of particles touching on an even bed and with allowance for inclines of a bed, and also for the flow rate of loads on an even bed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 182–185.The author is grateful to A. G. Kulikovskii, V. Ya. Shkadov, and M. É. Églit for discussing the results of the study.     

弹性力学中Fredholm积分方程组解法的表达通式及其讨论

本文采用覆盖域的概念,给出受外力作用的任意形状弹性体采用Fredhikm积分方程组解法的统一表达式,而且就含洞的无限大体且远场应力不为零,边界上有集中力作用等特殊情况进行讨论并给出相应的表达式,对边界上作用力和覆盖域边界上作用力之间在合力和合力矩上的关系也作了讨论,文中给出的算例表明,对于一些简单情况可以求得解析解。而对于需要采用数值解的问题,本文工作具有精度高、收敛快的优点。     

DIFFERENTIAL-ALGEBRAIC APPROACH TO COUPLED PROBLEMS OF DYNAMIC THERMOELASTICITY

An efficient numerical approach for the general thermomechanical problems was developed and it was tested for a two-dimensional thermoelasticity problem. The main idea of our numerical method is based on the reduction procedure of the original system of PDEs describing coupled thermomechanical behavior to a system of Differential Algebraic Equations (DAEs) where the stress-strain relationships are treated as algebraic equations. The resulting system of DAEs was then solved with a Backward Differentiation Formula (BDF) using a fully implicit algorithm. The described procedure was explained in detail, and its effectiveness was demonstrated on the solution of a transient uncoupled thermoelastic problem, for which an analytical solution is known, as well as on a fully coupled problem in the two-dimensional case.     

A shadow-moiré method with continuously variable sensitivity

This paper presents a shadow moiré method whereby the isostathmics (contours of surface depth) can be studied with continuously variable sensitivity. In the method the sensitivity is varied by simply rotating the grating in front of the object surface. Equations interpreting the isostathmics are derived, and an experimental demonstration is included.     

Shear measurement using strain gages under large deformation and rotation

The measurement of shear strain under finite deformation and large rotation by using electrical-resistance metallic foil strain gages is studied both analytically and experimentally. Equations for calculating shear strain and axial and circumferential stretches are derived based on the kinematics of general tension-torsion deformation mode. These equations are applied to analyzing pure torsion experimental data. Comparison is made between results obtained with strain gages and a rotary transducer. It is shown that, in case of large rotation, one simple equation can be used to calculate the shear strain up to 30 percent with adequate accuracy.     

Thickness-variation analog for nonhomogeneous plane-elasticity problems

This investigation was undertaken to show that the experimental study of the stress distribution in plane nonhomogeneous bodies may be accomplished by using models of varying thickness. Fabrication of models makes the experimental analysis of heterogeneous plane bodies difficult. Equations of elasticity are given which show that models with thickness variation should give the same results as those with a comparable variation in Young's modulus. Experimental results are given for the thickness-variation analog of the classical inclusion problem of varying modulus. These results are compared with the known theoretical results of the classical problem.     

On the Secondary Instability of Three-Dimensional Boundary Layers

One of the possible transition scenarios in three-dimensional boundary layers, the saturation of stationary crossflow vortices and their secondary instability to high-frequency disturbances, is studied using the Parabolized Stability Equations (PSE) and Floquet theory. Starting from nonlinear PSE solutions, we investigate the region where a purely stationary crossflow disturbance saturates for its secondary instability characteristics utilizing global and local eigenvalue solvers that are based on the Implicitly Restarted Arnoldi Method and a Newton–Raphson technique, respectively. Results are presented for swept Hiemenz flow and the DLR swept flat plate experiment. The main focuses of this study are on the existence of multiple roots in the eigenvalue spectrum that could explain experimental observations of time-dependent occurrences of an explosive growth of traveling disturbances, on the origin of high-frequency disturbances, as well as on gaining more information about threshold amplitudes of primary disturbances necessary for the growth of secondary disturbances. Received 13 July 1998 and accepted 7 July 2000     

水下爆炸气泡运动的理论研究

在适当深度的无黏、无旋的流体中对水下爆炸气泡运动特性进行理论研究。综合运用势流理论、能量方程以及拉格朗日方程建立气泡在不可压缩流体中的运动方程。并以此为基础,考虑重力、浮力以及阻力等多种因素对气泡运动特性的影响,通过引入新的边界积分方程,结合分析力学中完整非保守系统的Hamilton原理建立气泡在可压缩流体中的运动微分方程,并对微分方程进行求解。将方程的数值解与MSC.DYTRAN非线性有限元软件的计算结果以及经验公式进行对比,方程数值解与二者都具有较好的一致性。结果表明,基于非保守系统可压缩流体建立的气泡运动方程正确、可行,相关的理论研究和计算具有一定参考价值。     

Crystal plasticity finite element modelling of low cycle fatigue in fcc metals

A new dislocation-based model for low cycle fatigue in fcc metals at a length scale smaller than the feature size of the dislocation structures is presented. It uses the crystal plasticity finite element method and dislocation densities as internal variables. Equations for the dipole distance distribution, for the double cross slip mechanism and a new dislocation multiplication law are introduced, which can predict the emergence of vein and channel structures starting from a randomly perturbed dislocation distribution. The characteristics of these structures in copper and aluminium, as well as the mechanical properties, are compared with experiments. Compared with existing density-based theories, the capability to reproduce dislocation patterning is a significant step forward.     

Equations of motion for mechanical systems: A unified approach

This paper presents a unified framework from which emerge the Lagrange equations, the Gibbs-Appell Equations and the Generalized Inverse Equations for describing the motion of constrained mechanical systems. The unified approach extends the applicability of the first two approaches to systems where the constraints are non-linear functions of the generalized velocities and are not necessarily independent. Furthermore, the approach leads to the Explicit Gibbs-Appell Equations.     

Analytical and numerical solutions of the Local Inertial Equations

Neglecting the convective terms in the Saint-Venant Equations (SVE) in flood hydrodynamic modelling can be done without a loss in accuracy of the simulation results. In this case the Local Inertial Equations (LInE) are obtained. Herein we present two analytical solutions for the Local Inertial Equations. The first is the classical instantaneous Dam-Break Problem and the second a steady state solution over a bump. These solutions are compared with two numerical schemes, namely the first order Roe scheme and the second order MacCormack scheme. Comparison between analytical and numerical results shows that the numerical schemes and the analytical solution converge to a unique solution. Furthermore, by neglecting the convective terms the original numerical schemes remain stable without the need for adding entropy correction, artificial viscosity or special initial conditions, as in the case of the full SVE.     

Vibrations of a body in a bounded volume of viscous fluid

The problem of the vibrations of a body in a bounded volume of viscous fluid has been studied on a number of occasions [1–4]. The main attention has been devoted to determining the hydrodynamic characteristics of elements in the form of rods. Analytic solution of the problem is possible only in the simplest cases [2]. In the present paper, in which large Reynolds numbers are considered, the asymptotic method of Vishik and Lyusternik [5] and Chernous' ko [6] is used to consider the general problem of translational vibrations of an axisymmetric body in an axisymmetric volume of fluid. Equations of motion of the body and expressions for the coefficients due to the viscosity of the fluid are obtained. It is shown that in the first approximation these coefficients differ only by a constant factor and are completely determined if the solution to the problem for an ideal fluid is known. Examples are given of the determination of the “viscous” added mass and the damping coefficient for some bodies and cavities. In the case of an ideal fluid, general estimates are obtained for the added mass and also for the influence of nonlinearity. Ritz's method is used to solve the problem of longitudinal vibrations of an ellipsoid of revolution in a circular cylinder. The hydrodynamic coefficients have been determined numerically on a computer. The theoretical results agree well with the results of experimental investigations.     

Investigation of changes in the spherical shell shape under the action of pulsed loading due to contact interaction with a rigid block

An axisymmetric problem of high strains in a spherical lead shell enclosed into an aluminum “spacesuit” under the action of pulsed loading is considered. The shell straining is described with the use of equations of mechanics of elastoviscoplastic media in Lagrangian variables, and the kinematic relations are determined in the current state metrics. Equations of state are taken in the form of equations of the flow theory with isotropic hardening. The problem is solved numerically by using the variational difference method and the “cross” explicit scheme of integration with respect to time. The influence of the yield stress as a function of the strain rate on changes in the shell shape is studied for different values of loading. The calculated final shape and residual strains are demonstrated to be in good agreement with experimental data.