共查询到20条相似文献,搜索用时 15 毫秒
1.
Alexander Mielke Adrien Petrov 《Journal of Mathematical Analysis and Applications》2008,348(2):1012-1020
This paper discusses the convergence of kinetic variational inequalities to rate-independent quasi-static variational inequalities. Mathematical formulations as well as existence and uniqueness results for kinetic and rate-independent quasi-static problems are provided. Sharp a priori estimates for the kinetic problem are derived that imply that the kinetic solutions converge to the rate-independent ones, when the size of initial perturbations and the rate of application of the forces tend to 0. An application to three-dimensional elastic-plastic systems with hardening is given. 相似文献
2.
Adrien Petrov 《PAMM》2007,7(1):4060003-4060004
In this note, a priori estimates for the kinetic problem are obtained that imply, that the kinetic solutions converge to the quasi-static ones, when the size of initial perturbations and the rate of application of the forces tend to 0. An application to three-dimensional elastic-plastic systems with hardening is given. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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J. A. C. Martins N. V. Rebrova V. A. Sobolev 《Mathematical Methods in the Applied Sciences》2006,29(6):741-750
A concept of stability of quasi‐static paths is discussed in this paper that takes into account the existence of fast (dynamic) and slow (quasi‐static) time scales in the evolution of many mechanical systems. The proposed concept is essentially a continuity property with respect to the smallness of the initial perturbations (as in Lyapunov stability) and the smallness of the quasi‐static loading rate (that plays the role of the small parameter in singular perturbation problems). A related concept of attractiveness is also proposed. Several examples illustrate the relevance of the definitions. Sufficient conditions for attractiveness or for instability of quasi‐static paths of smooth systems are proved. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
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Mihai Bostan Vanessa Lleras 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1820-1833
The subject matter of this paper is the asymptotic behaviour of quasi-static variational inequalities, as regards physical parameters like the friction coefficient, compliance coefficient, etc. By convex duality, the quasi-static problems can be recast into the forms of standard evolution problems, whose study relies on well-known methods. In this framework the stability with respect to small friction coefficients reduces to long time behaviour for evolution problems. 相似文献
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《Journal of Applied Mathematics and Mechanics》1998,62(2):281-288
A formulation of a quasi-static problem of the mechanics of elastic-plastic bodies with loss-of-strength zones and boundary conditions of contact type: is given which enables the properties of the loading system to be taken into account. With certain constraints on the constitutive relations and using a condition for stability of the softening process in a local zone, theorems are proved on the uniqueness of the solution of the boundary-value problem and on the maximum and minimum of the functionals when the kinematically or statically possible and actual fields are the same. The corresponding generalized variational principles are given. 相似文献
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线性硬化材料中稳恒扩展裂纹尖端场的粘塑性解 总被引:1,自引:0,他引:1
采用弹粘塑性力学模型,对线性硬化材料中平面应变扩展裂纹尖端场进行了渐近分析.假设人工粘性系数与等效塑性应变率的幂次成反比,通过量级匹配表明应力和应变均具有幂奇异性,奇异性指数由粘性系数中等效塑性应变率的幂指数唯一确定.通过数值计算讨论了Ⅱ型动态扩展裂纹尖端场的分区构造随各材料参数的变化规律.结果表明裂尖场构造由硬化系数所控制而与粘性系数基本无关.弱硬化材料的二次塑性区可以忽略,而较强硬化材料的二次塑性区和二次弹性区对裂尖场均有重要影响.当裂纹扩展速度趋于零时,动态解趋于相应的准静态解;当硬化系数为零时便退化为HR(Hui-Riedel)解. 相似文献
7.
S.V. Morgunov 《Journal of Applied Mathematics and Mechanics》2012,76(2):250-252
Linear elastic systems with a finite number of degrees of freedom, the initial equations of motion of which are constructed using the finite element method or other discretization methods, are considered. Since, in applied dynamics problems, the motions are usually investigated in a frequency range with an upper bound, the degrees of freedom of the initial system of equations are split into dynamic and quasi-dynamic degrees. Finally, the initial system of equations is split into a small number of differential equations for the dynamic degrees of freedom and into a system of algebraic equations for determining the quasi-static displacements, represented in the form of a matrix series. The number of terms of the series taken into account depends on the accuracy required. 相似文献
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根据Илюшин微小弹塑性变形理论,本文导出了幂硬化不可压缩材料平面应变问题的基本方程. 另外,本文提出了这些基本方程的两种解法,即位移函数-应力法和应力函数-应变法.举了两个实例来说明这两个方法的应用. 相似文献
10.
This paper is addressed to some questions concerning the exponential stability and its robustness measure for linear time-varying differential-algebraic systems of index 1. First, the Bohl exponent theory that is well known for ordinary differential equations is extended to differential-algebraic equations. Then, it is investigated that how the Bohl exponent and the stability radii with respect to dynamic perturbations for a differential-algebraic system depend on the system data. The paper can be considered as a continued and complementary part to a recent paper on stability radii for time-varying differential-algebraic equations [N.H. Du, V.H. Linh, Stability radii for linear time-varying differential-algebraic equations with respect to dynamic perturbations, J. Differential Equations 230 (2006) 579-599]. 相似文献
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This paper deals with the stability of linear time-varying systems involving switches through time between different parameterizations of a dynamic linear time-varying system. Graph theory is used to describe the combinations of possible switches of the various sets of parameterizations which ensure the stability of the configurations. Each graph vertex is associated with a particular parameterization while edges (arcs) are associated with switches between the graphs (directed graphs or digraphs). An axiomatic framework is first established concerned with previously known stability results from systems theory related to the achievement of stability when switches between several parameterizations of a dynamic system take place. The axiomatic context is then used to obtain stability results mainly based on the topology of the links between the various configurations associated with a state-trajectory as well as on the nature of the vertices related to the stability of the various isolated parameterizations. 相似文献
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Igor V. Evstigneev Thorsten Hens Klaus Reiner Schenk-Hopp�� 《Mathematics and Financial Economics》2011,5(3):185-202
This paper introduces and analyzes an evolutionary model of a financial market with a risk-free asset. Focus is on the study
of local stability of the wealth dynamics through the application of recent results on the linearization and stability of
random dynamical systems (Evstigneev et al. Proc Am Math Soc 139:1061–1072, 2011). Conditions are derived for the linearization of the model at an equilibrium state which ensure local convergence of sample
paths to this equilibrium. The paper also shows that the concept of local stability is closely related to the notion of evolutionary
stability. A locally evolutionarily stable investment strategy in the evolutionary model with a risk-free asset is derived,
extending previous research. The method illustrated here is applicable for the analysis of manifold economic and financial
dynamic models involving randomness. 相似文献
16.
The network approach to the modelling of complex technical systems results frequently in a set of differential-algebraic systems that are connected by coupling conditions. A common approach to the numerical solution of such coupled problems is based on the coupling of standard time integration methods for the subsystems. As a unified framework for the convergence analysis of such multi-rate, multi-method or dynamic iteration approaches we study in the present paper the convergence of a dynamic iteration method with a (small) finite number of iteration steps in each window. Preconditioning is used to guarantee stability of the coupled numerical methods. The theoretical results are applied to quasilinear problems from electrical circuit simulation and to index-3 systems arising in multibody dynamics. 相似文献
17.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(11):1307-1313
In a previous Note dealing with bifurcated solutions of the quasi-static equilibrium problem of an elastic-plastic compressed beam, we established that the loading axis contains, on the fundamental branch, successive intervals completely filled with points where the velocity answer is not unique. This Note shows that there exists actually a bifurcated branch tangent to any of these non trivial velocities. The branches are the solutions of Cauchy problems whose initial data are the corresponding points of the fundamental branch. From these problems, we deduce the monotonicity of the branches, and their regularity, depending on the regularity of the cross-section. 相似文献
18.
V. V. Bolotin 《Mechanics of Composite Materials》2001,37(5-6):367-380
A survey of the literature and state of the art of the mechanical aspects of delaminations in laminate composite structures is presented. Surface and internal delaminations of various origin, shape, and location are discussed. The origination, stability, and postcritical behavior of delaminations under quasi-static, cyclic, and dynamic loads are analyzed. Some problems for further investigations are discussed. 相似文献
19.
A New Multiobjective Dynamic Routing Method for Multiservice Networks: Modelling and Performance 总被引:1,自引:0,他引:1
There are potential advantages in formulating the routing problems in modern multiservice networks as multiple objective problems. This paper presents a novel hierarchical bi-level multiobjective dynamic routing model for multiservice networks. It is based on a bi-objective shortest path algorithm, with dynamically adapted soft-constraints, to compute alternative paths for each node pair and on a heuristic to synchronously select alternative routing plans for the network in a dynamic alternative routing context. It is a routing method which periodically changes alternative paths as a function of periodic updates of certain QoS related parameters obtained from real-time measurements. The performance of the proposed routing method is compared with two reference dynamic routing methods namely RTNR and DAR by means of a discrete-event simulator.A previous short version of this work was presented at INOC’03 (International Network Optimisation Conference). Work partially supported by programme POSI of the III EC programme cosponsored by FEDER and national funds. 相似文献
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This paper is a survey of reachability and controllability results for discrete-time positive linear systems. It presents a variety of criteria in both algebraic and digraph forms for recognising these fundamental system properties with direct implications not only in dynamic optimization problems (such as those arising in inventory and production control, manpower planning, scheduling and other areas of operations research) but also in studying properties of reachable sets, in feedback control problems, and others. The paper highlights the intrinsic combinatorial structure of reachable/controllable positive linear systems and reveals the monomial components of such systems. The system matrix decomposition into monomial components is demonstrated by solving some illustrative examples. 相似文献