A fully discrete ALE method over untwisted time–space control volumes

In this paper, a fully discrete high‐resolution arbitrary Lagrangian–Eulerian (ALE) method is developed over untwisted time–space control volumes. In the framework of the finite volume method, 2D Euler equations are discretized over untwisted moving control volumes, and the resulting numerical flux is computed using the generalized Riemann problem solver. Then, the fluid flows between meshes at two successive time steps can be updated without a remapping process in the classic ALE method. This remapping‐free ALE method directly couples the mesh motion into a physical variable update to reflect the temporal evolution in the whole process. An untwisted moving mesh is generated in terms of the vorticity‐free part of the fluid velocity according to the Helmholtz theorem. Some typical numerical tests show the competitive performance of the current method. Copyright © 2016 John Wiley & Sons, Ltd.     

Structure of wave front and organization center in excitable media

With help of establishing the moving coordinate on the wave front surface and the perturbation analysis in the boundary layer, the structures of wave front and organization center in excitable media were studied. The eikonal equation of wave front surface and general equation of organization center were obtained. These eikonal equations reveal the wave front surfaces have structures of twisted scroll wave and MObius band, the organization centers have structures of knotted and linked ring. These theoretical results not only explain the wave patterns of BZ (Belousov-Zhabotinskii) chemical reaction but also give several possibility structures of wave front surface and organization center in general excitable media.     

An exact solution in a nonlinear theory of rods

A three dimensional nonlinear equilibrium theory of elastic rods, applicable to large displacements and small strains, and accounting for extensibility and shear deformation is developed. Integrals of the governing equations are determined for the case of specified end force and moment. A class of solutions is obtained for an initially straight, untwisted rod and compared to the classical solution. The effects of extensibility and shear deformation are discussed.     

Classification of the Spatial Equilibria of the Clamped Elastica: Symmetries and Zoology of Solutions

We investigate the configurations of twisted elastic rods under applied end loads and clamped boundary conditions. We classify all the possible equilibrium states of inextensible, unshearable, isotropic, uniform and naturally straight and prismatic rods. We show that all solutions of the clamped boundary value problem exhibit a π-flip symmetry. The Kirchhoff equations which describe the equilibria of these rods are integrated in a formal way which enable us to describe the boundary conditions in terms of 2 closed form equations involving 4 free parameters. We show that the flip symmetry property is equivalent to a reversibility property of the solutions of the Kirchhoff differential equations. We sort these solutions according to their period in the phase plane. We show how planar untwisted configurations as well as circularly closed configurations play an important role in the classification. This revised version was published online in June 2006 with corrections to the Cover Date.     

General axial response of stranded wire helical springs

The large static deflection of an axially loaded helical spring formed of a twisted strand of smooth circular wires is considered. Contact between the wires in the strand may or may not be maintained upon loading, depending upon the type of construction and the type of loading. It is found that the making or breaking of wire contact within the strand has a drastic ettect upon the extension and twist of a wire and upon the extension of the strand, but has practically no effect upon the twist of the strand, and only a moderate effect upon the overall response of the spring. Limited experimental data tend to verify the theory. It is found that a good engineering approximation for the axial stiffness of a twisted m-wire spring in which contact is maintained can be made by treating the spring as m untwisted helical wires acting independently, provided the strand twist is not too severe.     

Theory of vortical helical ideal gas flows in laval nozzles

An asymptotic solution is found for the direct problem of the motion of an arbitrarily vortical helical ideal gas flow in a nozzle. The solution is constructed in the form of double series in powers of parameters characterizing the curvature of the nozzle wall at the critical section and the intensity of stream vorticity. The solution obtained is compared with available theoretical results of other authors. In particular, it is shown that it permits extension of the known Hall result for the untwisted flow in the transonic domain [1]. The behavior of the sonic line as a function of the vorticity distribution and the radius of curvature of the nozzle wall is analyzed. Spiral flows in nozzles have been investigated by analytic methods in [2–5] in a one-dimensional formulation and under the assumption of weak vorticity. Such flows have been studied by numerical methods in a quasi-one-dimensional approximation in [6, 7]. An analogous problem has recently been solved in an exact formulation by the relaxation method [8, 9]. A number of important nonuniform effects for practice have consequently been clarified and the boundedness of the analytical approach used in [2–7] is shown.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 126–137, March–April, 1978.The authors are grateful to A. N. Kraiko for discussing the research and for valuable remarks.     

Equilibrium states of an elastic conducting rod in a magnetic field

Our principal concern is an analysis of the equilibrium states of a nonlinearly elastic conducting rod in a magnetic field. We assume hyperelasticity so the equilibria formally appear as critical points of a potential energy functional on the strains. Fairly standard methods give existence of a minimum (not necessarily unique) with e.g., L₂-regularity. The assumptions imposed on the functional preclude the use of the usual techniques for justification of the formal necessary conditions for optimality. A new general technique is developed to justify these conditions; it then follows that minimizers satisfy the equilibrium conditions in the classical sense. (A feature of this technique is that the variations considered are homotopies so one can consider minimization within a homotopy class.) In the symmetric case, which admits trivial (straight and untwisted) solutions, we show that nontrivial solutions also exist if the field is strong enough.     

Neuere Ergebnisse zur Knickung verwundener Stäbe

Übersicht Die vorliegende Arbeit behandelt die Stabilität verwundener Stäbe unter konservativer, kontinuierlich und gleichmäßig verteilter Belastung für alle möglichen Lagerungsfälle. Für die verwundenen Stäbe ergibt sich eine höhere Kuicklast als für die unverwundenen. Die Knicklasten werden graphisch und in Faustformeln als Funktion des Verwindungswinkels und des Verhältnisses der Biegesteifigkeiten dargestellt. Die Grundfunktionen und die Eigenfunktionen der erhaltenen Eigenwertaufgaben werden untersucht und ihre numerische Ermittlung wird beschrieben. Die für die Berechnung der Eigenwerte benutzten Methoden werden bezüglich Arbeitsaufwand und Genauigkeit miteinander verglichen.

---

Summary The stability of twisted columns under a conservative, continuously and homogeneously distributed load is investigated. All possible ways of supporting the column are considered. In all cases the critical load is found to be higher for the twisted columns than for the untwisted ones. The critical loads are given by graphs and approximation formulae as functions of the angle of twisting and of the ratio of the bending rigidities. The fundamental functions and the eigenfunctions of the obtained eigenvalue-problems are investigated and their numerical determination described. The methods used for the calculation of the eigenvalues are compared with each other with regard to the expenditure of work and to the obtained accuracy.

---

---

Der Verfasser dankt der Deutschen Forschungsgemeinschaft für die Unterstützung der vorliegenden Arbeit.     

Rectangular tensile sheet with a center notch root crack

This paper deals with the rectangular tensile sheet with a center notch crack. Such a crack problem is called a center notch crack problem for short. By using a hybrid displacement discontinuity method (a boundary element method) proposed recently by Yan, two center notch models are analyzed in detail. By changing the geometrical forms and parameters of the center notch, and by comparing the SIFs of the center notch crack problem with those of the center cracked plate tension specimen (CCT), which is a model frequently used in fracture mechanics, the effect of the geometrical forms and parameters of the center notch on the stress intensity factors (SIFs) of the center cracked plate tension specimen, is revealed. Some geometric characterestic parameters are introduced here, which are used to formulate the notch length and the branch crack length, which are to be determined in mechanical machining of the center cracked plate tension specimen. So we can say that the geometric characterestic parameters and the formulae used to determine the notch length and the branch crack length presented in this paper perhaps have some guidance role for mechanical machining of the center cracked plate tension specimen. In addition, the numerical investigation proves that the conventional angular notched specimen is much less sensitive to the size of notch than is the circular notched specimen.     

Linearizability and critical period bifurcations of a generalized Riccati system

In this paper, we investigate the isochronicity and linearizability problem for a cubic polynomial differential system which can be considered as a generalization of the Riccati system. Conditions for isochronicity and linearizability are found. The global structure of systems of the family with an isochronous center is determined. Furthermore, we find the order of weak center and study the problem of local bifurcation of critical periods in a neighborhood of the center.     

近断层地震动作用下地铁车站中柱减震效果研究

为研究近断层地震动作用下地铁车站中柱减震效果,本文首先从PEER强震数据库中选取我国台湾集集大地震中典型近断层地震动记录,进行了近断层地震动频谱特性分析。然后,以某地铁车站为背景,分别建立中柱安装橡胶隔振支座和没有安装橡胶隔振支座的土-地铁车站结构相互作用体系有限元模型。在此基础上,选取4条具有明显脉冲特性的近断层地震动记录和El Centro波作为输入,对土-地铁车站结构相互作用体系进行了地震反应分析,对比分析了减震模型和原型结构的位移响应和应力响应等结果,探讨了近断层地震动作用下地铁车站中柱的减震效果。结果表明:近断层脉冲型地震动具有较大的加速度、速度和位移时程幅值,并有明显的速度脉冲效应,0.1～1Hz的低频成分丰富;在地铁车站中柱柱端安装橡胶支座后,改变了车站结构的传力机制,使得顶板的内力及变形不能有效的传递到中柱上,起到了非常明显的减震效果;中柱增设橡胶支座后结构整体刚度变小,车站结构侧墙内力和水平变形较原型结构有明显增大。     

Nonlinear analysis of a rub-impact rotor supported by turbulent couple stress fluid film journal bearings under quadratic damping

This work reports a numerical study undertaken to investigate the dynamic response of a rotor supported by two turbulent flow model journal bearings with nonlinear suspension and lubricated with couple stress fluid under quadratic damping. This may be the first time that analysis of rotor-bearing system considered the quadratic damping effect. The dynamic response of the rotor center and bearing center are studied. The analysis methods employed in this study are inclusive of the dynamic trajectories of the rotor center and bearing center, power spectra, Poincaré maps and bifurcation diagrams. The maximum Lyapunov exponent analysis is also used to identify the onset of chaotic motion. The modeling results provide some useful insights into the design and development of rotor-bearing system for rotating machinery that operates at highly rotational speed and highly nonlinear regimes.     

Sensitivity analysis for a type of statically stable sailcrafts

Two types of sensitivities are proposed for statically stable sailcrafts.One type is the sensitivities of solar-radiation-pressure force with respect to position of the center of mass,and the other type is the sensitivities of solar-radiation-pressure force with respect to attitude.The two types of sensitivities represent how the solar-radiationpressure force changes with the position of mass center and the attitude.Sailcrafts with larger sensitivities undergo larger error of the solar-radiation-pressure force,leading to larger orbit error,as demonstrated by simulation.Then as a case study,detailed formulas are derived to calculate the sensitivities for sailcrafts with four triangular sails.According to these formulas,in order to reduce both types of sensitivities,the angle between opposed sails should not be too large,and the center of mass should be as close to the axis of symmetry of the four sails as possible and as far away from the center of pressure of the sailcraft as possible.     

Bifurcation of limit cycles,classification of centers and isochronicity for a class of non-analytic quintic systems

Inspired by Llibre and Vallls (in J. Math. Anal. Appl. 357:427–437, 2009), the conditions of center and isochronous center at the origin for a class of non-analytic quintic systems are studied in this paper. By a transformation, we first transform the systems into analytic systems, then sufficient and necessary conditions for the origin of the systems being a center are obtained. The fact that 11 limit circles could be bifurcated is proved. A complete classification of the sufficient and necessary conditions is given for the origin of the systems being an isochronous center.     

空心光纤网络埋入复合材料中性能影响的研究

空心光纤网络可用来进行复合材料力学性能的监测,同时又可对材料的损伤进行自修复。空心光纤网络与复合材料性能的影响主要有三方面：1）复合材料对空心光纤的影响;2）空心光纤对复合材料的影响;3）空心光纤与复合材料力学性能的匹配。本文测试了三种规格的空心光纤埋入复合材料中受到的影响,依据国家有关的复合材料测试标准,对树脂基复合材料埋与不埋大直径空心光纤进行了对比实验,并论证了光纤与材料力学性能匹配点存在的必然性。从而为空心光纤网络用于复合材料的自诊断与自修复提供了研究的依据。     

On the choice of physically realizable parameters when studying the dynamics of spherical and ellipsoidal rigid bodies

The paper presents necessary and sufficient conditions whose must be satisfied by the main geometric and dynamic parameters of spherical, ellipsoidal, or parabolic rigid bodies for their physical realization. The main parameters are both the geometric characteristics of the body boundary (radius of the sphere, semiaxes of the ellipsoid, principal curvatures at the vertex, and the paraboloid center location on its symmetry axis) and the body mass and dynamic characteristics (body mass, displacement of the body center of mass from the center on the paraboloid symmetry axis or from the sphere or ellipsoid center of symmetry, the orientation of the principal central axes of inertia with respect to the principal geometric axes of the shell, and the values of the principal central moments of inertia). The physical realization is understood as the existence of an actual distribution of positive masses inside the sphere, ellipsoid, or paraboloid for which the above-listed characteristics of the body are equal to the chosen ones. Several examples from earlier-published papers dealing with the dynamics of spherical, ellipsoidal, or parabolic bodies with physically unrealizable parameters are given.     

On the stress singularities generated by anisotropic eigenstrains and the hydrostatic stress due to annular inhomogeneities

The problems of singularity formation and hydrostatic stress created by an inhomogeneity with eigenstrain in an incompressible isotropic hyperelastic material are considered. For both a spherical ball and a cylindrical bar with a radially symmetric distribution of finite possibly anisotropic eigenstrains, we show that the anisotropy of these eigenstrains at the center (the center of the sphere or the axis of the cylinder) controls the stress singularity. If they are equal at the center no stress singularity develops but if they are not equal then stress always develops a logarithmic singularity. In both cases, the energy density and strains are everywhere finite. As a related problem, we consider annular inclusions for which the eigenstrains vanish in a core around the center. We show that even for an anisotropic distribution of eigenstrains, the stress inside the core is always hydrostatic. We show how these general results are connected to recent claims on similar problems in the limit of small eigenstrains.     

Stability of high-frequency periodic motions of a heavy rigid body with a horizontally vibrating suspension point

The motion of a heavy rigid body one of whose points (the suspension point) executes horizontal harmonic high-frequency vibrations with small amplitude is considered. The problem of existence of high-frequency periodic motions with period equal to the period of the suspension point vibrations is considered. The stability conditions for the revealed motions are obtained in the linear approximation. The following three special cases of mass distribution in the body are considered; a body whose center of mass lies on the principal axis of inertia, a body whose center of mass lies in the principal plane of inertia, and a dynamically symmetric body.     

Attitude dynamics of a cylinder floating in immiscible fluids

This study elaborates the attitude dynamics of a cylinder floating in two immiscible fluids. A cubic polyno- mial was derived based on the attitude angle, weight, center of gravity, and the density ratio of fluids. The numerical solution was validated by experimental data. Under prescribed constraints for the physical model, we have found that multiple solutions exist for cases with no radially biased center of gravity. When the center of gravity is biased, the attitude angles change abruptly around some critical values, which is related to the density ratio. Moreover, the attitude angles are less sensitive to the varying density ratios when the cylinder is heavier. The results also reveal that the cylinder tends to be vertical for nearly the whole range of density ratios when the center of gravity is slightly biased radially.