Development of an initially localized perturbation in the interaction of a cold beam with a dielectric

A homogeneous dielectric with a cold beam of charged particles passing through at a velocity greater than the velocity of the electromagnetic waves in the dielectric is considered. A smallperturbation instability in the form of a plane wave is built up. The structure of the perturbed state being developed from a small region of space is investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 123–128, May–June, 1978.The author is grateful to A. G. Kulikovskii and A. A. Barmin for valuable comments and remarks about this research.     

On the approximate computation of extreme eigenvalues and the condition number of nonsingular matrices

From the formulas of the conjugate gradient, a similarity between a symmetric positive definite (SPD) matrix A and a tridiagonal matrix B is obtained. The elements of the matrix B are determinedby the parameters of the conjugate gradient. The computation of eigenvalues of A is then reduced to the case of the tridiagonal matrix B. The approximation of extreme eigenvalues of A can be obtained as a by-product in the computation of the conjugate gradient ifa computational cost of O(s) arithmetic operations is added, where s is the number of iterations This computational cost is negligible compared with the conjugate gradient. If the matrix A is not SPD, the approximation of the condition number of A can be obtained from the computation of the conjugate gradient on A~T A. Numerical results show that this is a convenient and highly efficient method for computing extreme eigenvalues and the condition number of nonsingular matrices.     

Selection of prestress for optimal dynamic/control performance of tensegrity structures

This paper concerns prestress optimization of a tensegrity structure for its optimal LQR performance. A linearized dynamic model of the structure is derived in which the force-density variables that parameterize the prestress of the structure appear linearly. A feasible region for these parameters is defined in terms of the extreme directions of the prestress cone. A numerical method for computing this basis for a structure prestress cone is proposed. The problem is solved using a gradient method that provides a monotonic decrease of the objective function inside the feasible region. A numerical example of a cantilevered planar tensegrity beam is shown.     

模具冷却通道截面拓扑优化设计

本文提出一种模具冷却通道截面设计的拓扑优化方法。根据直通道的特性建立等效的温度场模型,用均匀流体速度场代替湍流流速场,构建对流换热方程,并用第三类边界条件对流道入口温度边界进行描述。建立考虑热应力的热-力耦合模型,对模具结构的热机械性能进行描述。通过引入离散体过滤法得到含圆形通道的截面拓扑,并加入几何约束解决离散体法导致的相混问题。分别以模具表面的平均温度和位移均匀性为优化目标及约束条件,构建拓扑优化列式。通过平顶模具与U型模具设计实例,验证了本文方法的可行性。设计结果表明,本文方法能够得到清晰的拓扑结构,而且优化结果满足给定的管径、管间距及管到模面距离等尺寸约束。     

Elastoplastische Stoffgleichungen für trockenen Sand

Übersicht Es werden inkrementelle Stoffgleichungen für trockenen Sand unter Berücksichtigung der Bezugsinvarianz (J 1), der Koordinateninvarianz (J 2) und der Einheiteninvarianz (J 3) entwickelt. Dabei sind die acht folgenden Stoffannahmen zugrundegelegt worden: Es liegt ein sogenannter einfacher Stoff vor (A 1), das Stoffunktional ist geschwindigkeitsunabhängig (A 2), das Stoffunktional ist stetig (A 3), die Fließgrenze hängt homogen von den Spannungen ab (A 4), im elastischen Bereich gilt das Hookesche Gesetz (A 5), die Fließregel hängt homogen von den Spannungen ab (A 6), durch Deformationszyklen kann einer Probe keine Energie entzogen werden (A 7), die Cauchy-Spannungen sind Zustandsparameter (A 8).Explizite Ausdrücke werden für isotropes Material angegeben und mit (z. T. eigenen) Versuchsergebnissen verglichen. Die Fließgrenze ist ein konvexer Kegel, der weder Kreisnoch Sechseckquerschnitt aufweist. Die Fließregel genügt nur für die deviatorischen Komponenten einer Normalitätsbedingung, während für die Volumenänderungen eine Dilatanzfunktion eingeführt wird. Je nach Dichte findet bei Gestaltänderung Kontraktion bzw. Expansion und plastische Verfestigung bzw. Entfestigung statt. Abschließend wird ein theoretisches Modell zur Erfassung anisotroper Zustände im Sand entwickelt.

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Summary Incremental constitutive equations for dry sand satisfying the frame invariance (J 1), the coordinate invariance (J 2) and the unit invariance (J 3) are developed from the following constitutive assumptions: sand is a simple material (A 1), the constitutive functional is velocity independent (A 2), the constitutive functional is continuous (A 3), the flow condition is a homogeneous function of stress (A 4), within the elastic range Hooke's law holds (A 5), the flow rule is a homogeneous function of stress (A 6), it is impossible to drag energy from a sample by cyclic deformation (A 7), the Cauchy stresses are state parameters (A 8).Explicit expressions are given for isotropic material and compared with (partly new) test results. The flow condition is a convex cone, being neither hexagonal nor circular. The flow rule satisfies a normality condition for the deviatoric components, whereas a dilatancy function is introduced for volume changes. Depending on density deformation is accompanied by contraction and plastic hardening or expansion and softening, respectively. Finally, a theoretical model for anisotropic states in sand is proposed.

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Gekürzte Fassung einer von der Fakultät für Bauingenieur- und Vermessungswesen der Universität (TH) Karlsruhe genehmigten Habilitationsschrift.     

Stress analysis of a flexible ring plate with circumferentially varying stiffness in a magnetic field

A problem of magnetoelasticity for a ring plate of variable stiffness is solved. A governing system of nonlinear differential equations is derived. It describes the stress–strain state of flexible conductive plates in nonstationary mechanical and electromagnetic fields. A numerical example is given. The stress state of a flexible plate of variable stiffness in a magnetic field is analyzed     

On the motion stability of an airplane on a runway under wind loading

A nonlinear mathematical model is constructed for an airplane in high-speed plane-parallel motion along a runway when the airplane's weight exceeds slightly the lift of its wings in the presence of a cross wind. The airplane is considered a two-weight mechanical object. A system of second-order equations is obtained that describes the airplane's behavior. A system of three phase variables is suggested in which the dynamics of transverse motion is described by a set of three second-order equations. A stationary solution of this system is obtained. A stability criterion for the plane-parallel motion of the airplane is established using the Routh-Hurwitz criterion. Analysis of the data of other authors indicates that the mathematical model is adequate for some objects of aviation technology. Translated from Prikladnaya Mekhanika, Vol. 35, No. 10, pp. 101–107, October, 1999.     

Simple waves of a seven-dimensional subalgebra of all translations in gas dynamics

A differentially invariant solution of rank 1 for gas dynamics equations is considered in a seven-dimensional subalgebra of all translations including Galilean translations. Exact solutions with a uniformly accelerated plane of the level of invariant functions are obtained. A nonisentropic wave depends on two arbitrary functions and constants. A general solution of an isentropic simple wave depends on the constants only.     

Stokes flow due to fundamental singularities before a plane boundary

A representation for the velocity and pressure fields in three-dimensional Stokes flow was presented in terms of a biharmonic function A and a harmonic function B. This representation was used to establish a general theorem for the calculation of Stokes flow due to fundamental singularities in a region bounded by a stationary no-slip plane boundary. Collins‘s theorem for axisymmetric Stokes flow before a rigid plane follows as a special case of the theorem. A few illustrative examples are given to show its usefulness.     

Axial compression of circular cylindrical bar with coaxial subsurface cylindrical crack of finite length

A fracture stability of a circular cylindrical bar with a coaxial surface cylindrical crack subjected to an axial compression is considered. A state of subcritical initial strain is assumed. A non-classical fracture criterion is based on a local stability loss near the defect. The theory of integral Fourier transforms and series expansions are used to reduce these problems to a system of paired integral equations and then to a system of linear algebraic equations with respect to the contraction parameter.     

Finite-dimensional approximation to global minimizers in functional spaces with R-convergence

A new concept of convergence (R-convergence) of a sequence of measures is applied to characterize global minimizers in a functional space as a sequence of approximate solutions in finite-dimensional spaces. A deviation integral approach is used to find such solutions. For a constrained problem, a penalized deviation integral algorithm is proposed to convert it to unconstrained ones. A numerical example on an optimal control problem with non-convex state constraints is given to show the effectiveness of the algorithm.     

Polarization of a plasma in an electric field

A study has been made of the electrostatic polarization of a plasma in an applied electric field, i. e., the process of charge separation in the case when a steady current flow through the plasma is excluded.The authors are deeply grateful to G. A. Lyubimov and S. A. Regirer for useful discussion.     

Blended skip entry guidance for low-lifting lunar return vehicles

A skip entry guidance algorithm blending numerical predictor-corrector and nominal trajectory tracking is presented for lunar return vehicles.The guidance is decoupled into longitudinal and lateral channels.A piecewise bank-vs-energy magnitude profile and a sign profile are adopted in the skip phase.A magnitude parameter is used to adjust the predicted downrange,and a pseudo-crossrange at the beginning of the final phase is selected as the lateral control variable.Prediction biases of both channels are nullified by a false position iteration algorithm.An on-line estimation and modeling method is introduced to compensate for aerodynamic and atmospheric uncertainties.A nominal trajectory for the final phase is generated based on actual reenter conditions,and the obtained nominal trajectory is tracked by a linear feedback law.A lateral corridor is used to manage the lateral state.The proposed guidance algorithm is assessed using three-degree-of-freedom Monte Carlo analyses,and the results show a satisfactory and robust performance under highly stressful dispersions.     

Correlation of finite strain measures

A numerical scheme for correlating any two finite strain measures is given, and situations in which such a scheme might be used are introduced. A check is established by comparison with the Reiner-Hanin solution of the Almansi-to-Hencky conversion. A numerical example is provided.     

Simulation of transient gas flows in networks

A technique is presented for calculating the transient flow in high pressure transportation systems where both simple systems (without compressors) and systems with compressors have been taken into consideration. A partial differential equation characterizing the dynamic gas flow through a pipeline and a numerical scheme for its solution are considered. A method of computing node pressures is also characterized.     

A vanishing diffusion process in unsaturated soils

A model for simulating water flow and air flow in unsaturated soils is presented herein. Drainage from a one-dimensional soil column is specifically investigated. A mathematical analysis of the equations reveals that, due to a vanishing diffusion process, the gradient of the water degree of saturation is infinite at the water table. Moreover, this discontinuity propagates at a velocity that satisfies a local non-linear equation involving only the properties of the material. A numerical simulation of this problem serves to confirm the results obtained.     

Motion of the interface of two fluids with formation of a region of two-phase flow

A study is made of the problem of the displacement of one fluid by another with the formation of a region of combined flow in the case of an elastic flow regime in the region of the displaced fluid. A self-similar solution is constructed for the flow equations averaged with respect to the vertical coordinate. A numerical algorithm is developed for determining the saturation in the region of the mixture, the pressure, and also the position and shape of the interface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 8, pp. 78–83, October–December, 1981.We thank A. A. Barmin for a helpful discussion of the work.     

Kinematic model for long streamers. self-similar description of the streamer evolution

A nonlinear diffusion equation describing a long streamer is obtained using a kinematic approach. A self-similar solution of the one-dimensional problem of the unsteady evolution of the charge-density wave is obtained. The main features of the process are analyzed. It is established that the obtained analytical formulas can be used to analyze experimental and computer modeling data for a long spark. A comparison of these data shows that the self-similar solution can be used to describe the deceleration of the streamer.     

低碳贝氏体微观组织形态对冲蚀磨损性能的影响

通过热处理改变低碳贝氏体钢中的奥氏体及其转变物(下称M/A)分布形态,调整钢响应载荷时的微观应力集中位置,并用弹塑性力学理论揭示了贝氏体钢较高的抗冲蚀磨损性能的力学机理.对比研究了相同化学成分贝氏体、珠光体和马氏体的冲蚀磨损性能,发现珠光体和马氏体因强度、韧塑性无法达到最佳匹配,其抗冲蚀磨损性能均不如贝氏体.在贝氏体钢中,粒状M/A贝氏体的应力集中位置使得冲蚀裂纹显著地向试样心部扩展,降低了抗冲蚀磨损能力.薄膜状M/A贝氏体的应力集中位置不利于表面裂纹向试样心部生长,实现了较高的抗冲蚀磨损性能.     

A problem for diffusion with relaxation in polymers

A nonlinear problem for penetrant diffusion with relaxation in polymers is considered. A numerical approach to solving this type of problems is developed. The proposed numerical scheme based on a finite element domain approximation and a time difference method can be used for numerical simulation of the considered penetrant diffusion in 2-D and 3-D domains. A numerical procedure and a corresponding computer code are created and tested for some examples in 1-D and 2-D domains.