Beginning of plastic yielding in a stress concentration zone

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 147–152, May–June, 1991.     

The plastic yielding of double notched bars due to pure bending

Conclusion It is believed that all practical cases of notch shapes are covered by the above analysis. The experiments are in favour of the upper bound solution, though, for practical cases, the mean value derived from the limit analysis differs very little from that of the bounds, and it can be used with confidence.Further tests, however, are needed to confirm the deformation pattern. It is also believed that this analysis will furnish useful informations on the study on the mechanism of fracture.     

控制理论在地下工程施工姿态控制中的应用

由于地下工程涉及的不确定性因素多、施工环境的复杂变异性，使得对沉井这样的地下工程的施工在保证均匀下沉、防止突沉和控制终沉上难度较大。本文采用H∞控制理论，考虑了沉井下沉力学模型的不确定性以及外部干扰的影响，设计H∞控制器，并用一工程实例进行数值模拟计算。将计算结果与经验控制的结果进行比较。对比结果表明，H∞能有效地保证沉井的下沉姿态，为地下工程的施工控制研究提供一种有效的新方法。     

Microscopic modelling of volume expansion and pressure dependence of plastic yielding in crystalline solids

Summary The present paper deals with a nonlinear finite element procedure for the macroscopic rate-independent analysis of micromechanics of crystalline solids undergoing finite elastic-plastic deformations including plastic volume expanding effects. Particular attention is focused on deviations from the Schmid law of the critical resolved shear stress to model different stress-deflection behavior in uniaxial tension and compression tests. Numerical simulations of elastic-plastic boundary-value problems should demonstrate the efficiency of the algorithm and discuss the influence of different model parameters on stress-carrying and deformation behavior observed experimentally. Accepted for publication 3 June 1997     

Shakedown theory for elastic plastic kinematic hardening bodies

Shakedown static and kinematic theorems for elastic–plastic (generally nonlinear) kinematic hardening solids are derived in classical (path-independence) spirit with new constructions. The generally plastic-deformation-history-dependent hardening curve is assumed to be limited by the initial yield stress and ultimate yield strength, and to obey a positive hysteresis postulate for closed plastic cycles, but else can be arbitrary and unspecified. The theorems reveal that the shakedown of structures is not affected by the particular form of the hardening curve, but just by the initial and ultimate yield stresses. While the ultimate yield strength is clearly defined macroscopically and attached to the incremental collapse mode with unbounded plastic deformations, the initial yield stress, which is responsible for the bounded cyclic plasticity collapse mode, should not be taken as the convenient one at a fixed amount of plastic deformation (0.2%), but is suggested to be taken as low as the fatigue limit to preserve the classical load-history-independence spirit of the shakedown theorems. Otherwise, for our pragmatic application purpose, it may be given empirical values between the low fatigue limit and high ultimate yield stresses according to particular loading processes considered, which may range anywhere between the high-cycle and low-cycle ones. The theorems appear as simple as those of Melan and Koiter for perfect plasticity but applied to the much larger class of more realistic kinematic hardening materials.     

Asymptotic theory of turbulent separation

The flow of an incompressible fluid in the viscous wall sublayer of a turbulent boundary layer in the neighborhood of a point of separation is considered. On the basis of an asymptotic analysis of the Reynolds equations and without the use of any hypotheses about their closure it is shown that at large Reynolds numbers the velocity profile satisfies the well-known “half-power law,” and as a result of a large self-induced pressure gradient separation is preceded by the appearance of reverse flows in a thin viscous sublayer.     

Asymptotic theory of nonstationary separation

Nonstationary separation of a laminar boundary layer in a incompressible fluid is studied on the basis of asymptotic analysis of the Navier-Stokes equations at large Reynolds numbers. The case when the point of separation moves upstream is considered. It is shown that under certain restrictions on the acceleration with which the motion of the point of separation occurs the local solution depends on the time as on a parameter. As in the stationary case, the separation occurs spontaneously under the influence of the large local pressure gradient. An important difference is however that the mechanism of nonstationary separation is inviscid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 21–32, November–December, 1979.I thank A. I. Ruban for great interest and assistance in the work, and also O. S. Ryzhov for a number of helpful comments.     

Asymptotic theory of separation flows

A review is given of the results of theoretical investigations of the separation of laminar and turbulent boundary layers in an incompressible fluid obtained on the basis of matched asymptotic expansions valid at large Reynolds numbers (Re). The global picture of the separation flow behind a body of finite size as Re is investigated.Paper presented at Fifth All-Union Symposium on Theoretical and Applied Mechanics, Alma-Ata, 1981.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 20–30, March–April, 1982.     

Quadratic programming and theory of elastic-perfectly plastic structures

Summary For elastic perfectly plastic discretized structures acted upon by given loads and dislocations, it is shown, under holonomic constitutive laws or no local unloading hypothesis, that the formulation of the analysis problem in terms of finite (not incremental) stresses, is amenable to the Kuhn-Tucker conditions of a quadratic program. Then it is readily derived a generalized form of the principle of Haar and Kármán, together with an extremum theorem for displacements and plastic strains, which is the dual of the preceding one. As special cases of this theorems known variational principles follow, which thus turn out to be related in pairs by the duality notion as understood in programming theory. Also the statical and kinematical theorems of limit analysis are proved by means of the unitary conceptual framework supplied by quadratic programming.

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Sommario Con riferimento a strutture discretizzate idealmente elastoplastiche, soggette a dati carichi e distorsioni, si mostra che nell'ipotesi di olonomia dei legami costitutivi o di assenza di ritorni elastici, la formulazione del problema strutturale negli sforzi finiti (non incrementali) è riducibile alle condizioni di Kuhn e Tucker di un programma quadratico. Se ne deducono direttamente una forma generalizzata del principio di Haar e Kármán ed un teorema di estremo negli spostamenti e nelle deformazioni plastiche, duale al precedente. Dai due teoremi discendono come casi speciali noti principi variazionali, che cosi risultano collegati in coppie dalla nozione di dualitá propria della teoria delle ottimizzazioni.Si mostra come anche i teoremi statico e cinematico del calcolo a rottura trovano una nuova dimostrazione nell'inquadramento teorico unitario fondato sulla programmazione quadratica.

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The results presented here form part of a series of studies supported by the C.N.R. (National Research Council).