Calculation of flow of highly attenuated gas around a body,taking into account interactions with the surface

The results of Monte Carlo calculations are given for the aerodynamic characteristics of different bodies in free-molecular and near-free-molecular conditions. The calculations are made for different models of the interaction between the attenuated-gas flow and the surface of the body. Analysis and comparison of the results obtained with available experimental and natural data serves as the basis for a discussion of the applicability of individual parameters of these models in practical calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 117–123, September–October, 1978.It remains to thank M. N. Kogan, V. A. Perepukhov, A. I. Erofeev, A. I. Bunimovich, L. L. Zvorykin, A. A. Pyarnpuu, and V. F. Kameko for discussions of the results and for valuable comments.     

Bifurcation and stability analysis for a non-smooth friction oscillator

Summary Friction-induced self-sustained oscillations, also known as stick-slip vibrations, occur in mechanical systems as well as in everyday life. On the basis of a one-dimensional map, the bifurcation behaviour including unstable branches is investigated for a friction oscillator with simultaneous self-and external excitation. The chosen way of mapping also allows a simple determination of Lyapunov exponents.Dedicated to Prof. Dr.-Ing. Dr.-Ing. E.h. Dr. h.c. mult. Erwin Stein on the occasion of his 65th birthday.     

Extension of joseph's criterion to the nonlinear stability of mechanical equilibria in the presence of thermodiffusive conductivity

Joseph's criterion from [1] is extended to the case of thermodiffusive conductivity for a fluid layer subject to several competing (stabilizing and destabilizing) effects. Criterion for the uniqueness and stability of all (eight) physical parameters involved was obtained. In this way, for a more realistic mathematical model, physically relevant bounds for the domain of stability are achieved.This work was performed under the auspices of G.N.F.M.-C.N.R. and I.R.M.A.-C.N.R. and was supported by M.U.R.S.T. under the grant 60% Algebra lineare ed equationi alle derivate parziali in the framework of Professor R. Pelluso's group, University of Bari, Italy.     

A deformation theory of strain gradient crystal plasticity that accounts for geometrically necessary dislocations

We propose a deformation theory of strain gradient crystal plasticity that accounts for the density of geometrically necessary dislocations by including, as an independent kinematic variable, Nye's dislocation density tensor [1953. Acta Metallurgica 1, 153-162]. This is accomplished in the same fashion as proposed by Gurtin and co-workers (see, for instance, Gurtin and Needleman [2005. J. Mech. Phys. Solids 53, 1-31]) in the context of a flow theory of crystal plasticity, by introducing the so-called defect energy. Moreover, in order to better describe the strengthening accompanied by diminishing size, we propose that the classical part of the plastic potential may be dependent on both the plastic slip vector and its gradient; for single crystals, this also makes it easier to deal with the “higher-order” boundary conditions. We develop both the kinematic formulation and its static dual and apply the theory to the simple shear of a constrained strip (example already exploited in Shu et al. [2001. J. Mech. Phys. Solids 49, 1361-1395], Bittencourt et al. [2003. J. Mech. Phys. Solids 51, 281-310], Niordson and Hutchinson [2003. Euro J. Mech. Phys. Solids 22, 771-778], Evers et al. [2004. J. Mech. Phys. Solids 52, 2379-2401], and Anand et al. [2005. J. Mech. Phys. Solids 53, 1789-1826]) to investigate what sort of behaviour the new model predicts. The availability of the total potential energy functional and its static dual allows us to easily solve this simple boundary value problem by resorting to the Ritz method.     

一种自适应轴对称FEM-SPH耦合算法及其在高速冲击模拟中的应用

为了准确、高效地模拟高速冲击问题,提出了一种自适应轴对称有限元(FEM)-光滑粒子流体动力 学(SPH)耦合算法。该算法在初始时刻全部采用FEM 计算,在动态变形过程中自动将畸变单元转化为粒 子,采用SPH 计算。该算法采用一种新的耦合算法实现单元与粒子间的高精度耦合,并应用最小内角转化准 则和单元分组转化方式实现单元向粒子的自动转化。计算了几个典型的高速冲击问题:首先,通过计算应力 波传播测试了新的单元-粒子耦合算法的精度;然后,通过计算泰勒杆问题验证了自适应耦合算法及相应程序 的正确性;最后,计算了弹体侵彻铝板和混凝土板。结果表明:自适应耦合算法计算精度好且效率高,适合模 拟高速冲击问题。     

Problemi di unicità per le equazioni di navier-stokes in domini non limitati

Sans résuméMemoria presentata da J. SerrinLavoro eseguito nell'ambito del G.N.F.M. del C.N.R.     

Bestimmung von Balkenschwingungen mit Hilfe des MatrizenkalkÜls

Ohne ZusammenfassungAuszug aus der Dissertation des Verfassers, Darmstadt 1953, Referent: Prof. Dr.-Ing. K. Marguerre, Korreferent: Prof. Dr.-Ing. K. Karas.     

Instationäre Wärmespannungen in Hohlzylindern mit Kreisringquerschnitt

Ohne ZusammenfassungGekürzte Fassung einer von der Technischen Universität Berlin-Charlottenburg genehmigten Dissertation. Der Verfasser ist den beiden Berichtern, Herrn Prof. Dr.-Ing. I. Szabó und Herrn Prof. Dr.-Ing. A. Teichmann sehr zu Dank verpflichtet.     

高应变率拉伸加载下无氧铜的本构模型

为了研究材料在高应变率拉伸加载下的动态响应,利用新型爆炸膨胀环实验技术开展了无氧铜试 样环的拉伸加载实验,采用激光干涉测试技术获得了试样环拉伸变形过程的径向速度历史。数值计算发现经 典JC模型不能较好地描述无氧铜试样环的膨胀过程,于是对JC模型进行了修改:增加了应变的指数硬化项 来描述拉伸变形的累积效应;增加了应变率的线性项描述拉伸加载时的应变率效应;利用实验数据拟合了修 改后的RJC模型参数,最终较好描述了无氧铜试样环的膨胀变形过程。     

Critical thought experiment to choose the driving force for interface propagation in inelastic materials

The problem of defining the driving force for interface propagation in inelastic materials is discussed. In most publications, the driving force coincides with the Eshelby driving force, i.e. it represents a total dissipation increment on the moving interface due to all the dissipative processes (phase transition (PT) and plasticity). Recently (Levitas, V.I., 1992a. Post-bifurcation Behaviour in Finite Elastoplasticity. Applications to Strain Localization and Phase Transitions. Universität Hannover. Insititut für Baumecharik and Numerische Mechanik, [BNM-Bencht 1JP 585-LC, 92/5, Hannover; Int. J. Eng. Sci. 33 (1995) 921; Mech. Res. Commun. 22 (1995) 87; J. de Physique III 5 (1995) 173; J. De Physique III 5 (1995) 41; Int. J. Solids Struct. 35 (1998) 889], an alternative approach was developed in which the driving force represents the dissipation increment due to PT only, i.e. total dissipation minus plastic dissipation. The aim of this paper is to prove the contradictory character of application of the Eshelby driving force to inelastic materials. For this purposes, a problem on the interface propagation in a rigid–plastic half-space under homogeneous normal and shear stresses is solved using both definitions, along with the principle of the maximum the driving force. Finite strain theory is used. It appears that the first approach exhibits some qualitative contradictions, which are not observed in our approach. In particular, even for shape memory alloys, when transformation strain can be accommodated elastically (or even without internal stresses), maximization of the Eshelby driving force requires as much plasticity as possible. When applied shear stress tends to the yield stress in shear of a new phase, the driving force tends to infinity, i.e. PT has to always occur at the beginning of plastic flow. Note that in this paper plasticity means dislocation plasticity rather than plasticity due to twinning. Twinning during martensitic PT is the appearance of several martensitic variants which are in twin relation to each other. Consequently, for twinned martensite one has microheterogeneous transformation strain without plastic dissipation term, i.e. both approaches coincide.     

聚能罩压垮图象的计算机处理

本文探讨了聚能罩压垮照片的数字图象处理技术。认为利用图象处理的方法,不但可以减少实验数据的判读误差,提高清晰度,而且还可以得到其它方法很难得到的边界曲线方程。     

Wedge and twist disclinations in second strain gradient elasticity

The aim of this paper is to study disclinations in the framework of a second strain gradient elasticity theory. This second strain gradient elasticity has been proposed based on the first and second gradients of the strain tensor by Lazar et al. [Lazar, M., Maugin, G.A., Aifantis, E.C., 2006. Dislocations in second strain gradient elasticity. Int. J. Solids Struct. 43, 1787–1817]. Such a theory is an extension of the first strain gradient elasticity [Lazar, M., Maugin, G.A., 2005. Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity. Int. J. Eng. Sci. 43, 1157–1184] with triple stress. By means of the stress function method, the exact analytical solutions for stress and strain fields of straight disclinations in an infinitely extended linear isotropic medium have been found. An important result is that the force stress, double stress and triple stress produced by wedge and twist disclinations are nonsingular. Meanwhile, the corresponding elastic strain and its gradients are also nonsingular. Analytical results indicate that the second strain gradient theory has the capacity of eliminating all unphysical singularities of physical fields.     

Special solutions of the Boussinesq-equations for free convection flows in a vertical gap

The free convection in a vertical gap is generalized to realize new analytical solutions of the Boussinesq-equations. The steady and time-dependent solutions for the temperature and velocity distribution are discussed in detail depending on the mass flux in vertical direction. The range of existence for flows with and without back flow is obtained. The transient behaviour of the solutions during the time-dependent development displays interesting physical behaviour.Dedicated to Prof. Dr.-Ing., Dr. techn. E.h. Jürgen Zierep to his 75. birthday.     

Phase averaged velocity field in an axisymmetric jet subject to a sudden velocity decrease

An unsteady transient axisymmetric turbulent jet was studied experimentally. The initial flow perturbation consisted of a sudden and large decrease in the ejection velocity. The temporal evolution of the mean and fluctuating unsteady velocity field was measured by using X hot-wire probes. In the jet far field, adaptation of the externally imposed unsteadiness to the local jet time scale is confirmed quantitatively. The main features of the phase averaged velocity field are presented and comments are made about the instantaneous state of the turbulence energetics. Transient mean radial velocities are deduced and an important increase of the instantaneous rate of entraining external fluid into the jet is found. Finally, we show that the pressure effect due to radial impusle terms plays an important role in the propagation of the mean perturbation. The longitudinal adaptation of the perturbation time scale driven by the local jet time scale provides a turbulent flow that is intermediate to quasi-static flows and rapidly distorted flows.We wish to thank Professor H. Fiedler and Professor M. Wolfshtein for their helpful comments about this work. We have benefited greatly from discussions with Dr. H.J. Nuglisch, Professor E.K. Longmire and Dr. A. Sevrain and of the technical support of G. Couteau and J.F. Alquier.     

Two- and three-dimensional instabilities in the film blowing process

We examine the film blowing process (FBP), which is widely used for manufacturing biaxially stretched films of polymeric materials. The viscoelastic property of the material is taken into account by employing the Upper Convected Maxwell, the Oldroyd-B or the Phan-Thien and Tanner constitutive model. In contrast to all previous theoretical works, which followed the now classical method developed by Pearson and Petrie [J.R.A. Pearson, C.J.S. Petrie, The flow of a tubular film. Part 1. Formal mathematical representation, J. Fluid Mech. 40 (1) (1970) 1–19; J.R.A. Pearson, C.J.S. Petrie, The flow of a tubular film. Part 2. Interpretation of the model and discussion of solutions, J. Fluid Mech. 42 (3) (1970) 609–625], we analyze the process by starting with the general three-dimensional mass and momentum balances and by formally and systematically applying the thin-film approximation. This procedure results in two-dimensional dynamic balances in both the axial and azimuthal directions. Although these balances are highly non-linear and more complicated than the original momentum balance, they are reduced by one spatial dimension and, more importantly, they are more general than the classical ones, whereas they are developed in a rigorous and straightforward manner. When we assume axial symmetry and steady state, we recover the earlier model equations. However, this new methodology allows us to examine not only axisymmetric, but also non-axisymmetric disturbances to this base flow and to retain the time derivatives in all the governing equations. This procedure is an extension of our earlier one used to study transient annular extrusion [K. Housiadas, J. Tsamopoulos, Unsteady flow of an axisymmetric annular film under gravity, Phys. Fluids 10 (10) (1998) 2500–2516; K. Housiadas, J. Tsamopoulos, Unsteady extrusion of a viscoelastic annular film: I. General model and its numerical solution, J. Non-Newton. Fluid Mech. 88 (3) (2000) 229–259], which also involved the thin-film approximation and three moving interfaces, but under the assumption of axial symmetry. Viscous, elastic, inertial, gravitational and capillary forces are included in our model. The base state is computed using finite differences to simultaneously predict bubble shape, film thickness, velocity, pressure and polymer extra-stress profiles. Subsequently, its linear stability is examined to two- and three-dimensional disturbances by solving the full eigenvalue problem to determine the stability regions of the process. It is shown that under typical operating conditions the bubble becomes unstable first to non-axisymmetric disturbances, although two-dimensional instability is also predicted by our model, in agreement with recent experiments.     

Nonsteady-state thermal convection in a spherical cavity

Three-dimensional axisymmetrical convection in a spherical cavity is examined. The general heat-transfer condition is stipulated on the boundary of the spherical cavity. A method of finite differences is used for the solution.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 118–124, July–August, 1970.The authors thanks G. Z. Gershuni and E. M. Mukhovitskii for their help in this work.     

Parametric study of the interaction of bridges and moving vehicles

In this paper we develop a mathematical model for the analysis of the dynamic response of a bridge structure as it interacts with moving vehicles. The vehicles are modeled both for fixed axle distances (e.g. Cooper Loadings) and for variable axle distances (e.g. multi-vehicles). We then generate an algorithm to solve the resulting equations of motion. Results obtained using our theoretical model are shown to compare very well with measured field data.Associate Professor of Mech. Eng.Professor of Mech. Eng.Associate Professor of Civil Eng.     

弹头侵彻明胶的运动模型

为探讨弹头在肌肉组织中的运动规律,以明胶作为组织模拟物,结合明胶力学性质,在区别攻角和 偏角的情况下,建立同时考虑水平和垂直方向弹头侵彻明胶的二维运动模型。以7.62mm 普通弹和5.8mm 普通弹为杀伤元,根据龙格-库塔法原理对运动模型进行数值计算。同时,对2种弹丸侵彻明胶实验数据进行 了对比分析。分析结果表明,该二维运动模型能够准确合理的描述2种弹丸侵彻明胶的运动过程,具有一定 通用性,可为弹药设计和战伤救治提供理论参考。     

Non-Newtonian flow at lowest order,the role of the Reiner–Rivlin stress

In 1963 Giesekus [H. Giesekus, Die simultane Translations- und Rotationsbewegung einer Kugel in einer elastikoviskosen Flüssigkeit, Rheol. Acta 3 (1962) 59–71] showed that a Stokes velocity field also satisfies the equilibrium equation for the flow of a restricted form of the second order fluid. The same result was found by Tanner [R.I. Tanner, Plane creeping flows of incompressible second order fluids, Phys. Fluids 9 (1966) 1246–1247] in 1966 in the context of plane flow for which the restrictions on the second order fluid are not relevant. Tanner [R.I. Tanner, Some extended Giesekus-type theorems for non-Newtonian fluids, Rheol. Acta 28 (1989) 449–452] later showed that the velocity field for the inertialess, plane flow of the generalized Newtonian fluid is also the velocity field for the flow of a special form of the Criminale–Ericksen–Filbey (CEF) stress system [W.O. Criminale Jr., J.L. Ericksen, G.L. Filbey Jr., Steady flow of non-Newtonian fluids, Arch. Rat. Mech. 1 (1958) 410–417]. In this paper it will be shown that the results of Giesekus and Tanner are special cases of a more general theorem in which the velocity field, in any dimension, of the equilibrium Reiner–Rivlin problem also satisfies the corresponding problem for the materially steady stress system (a generalization of the CEF system) provided the coefficients of the Reiner–Rivlin stress [M. Reiner, A mathematical theory of dilatancy, Am. J. Math. 67 (1945) 350–362; R.S. Rivlin, The hydrodynamics of non-Newtonian fluids, Proc. R. Soc. Lond. 193 (1948) 260–281] are derivable from a strain-rate potential. As with the Giesekus–Tanner theorems the new theorem holds generally for velocity boundary conditions, but in some cases, such as the free jet, stress boundary conditions can be imposed.     

Problems of dynamic fracture mechanics with allowance for contact of the crack edges

S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine. Kharkov Institute of Highway Engineering. Translated from Prikladnaya Mekhanika, Vol. 31, No. 1, pp. 3–36, January, 1995.