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JournalISSN: 0003-9527

Archive for Rational Mechanics and Analysis

About: Archive for Rational Mechanics and Analysis is an academic journal. The journal publishes majorly in the area(s): Nonlinear system & Boundary value problem. It has an ISSN identifier of 0003-9527. Over the lifetime, 4797 publication(s) have been published receiving 263480 citation(s). more


Journal ArticleDOI: 10.1007/BF00248490
Raymond D. Mindlin1Institutions (1)

2,983 Citations

Journal ArticleDOI: 10.1007/BF00276493
Jan C. Willems1Institutions (1)
Abstract: The first part of this two-part paper presents a general theory of dissipative dynamical systems. The mathematical model used is a state space model and dissipativeness is defined in terms of an inequality involving the storage function and the supply function. It is shown that the storage function satisfies an a priori inequality: it is bounded from below by the available storage and from above by the required supply. The available storage is the amount of internal storage which may be recovered from the system and the required supply is the amount of supply which has to be delivered to the system in order to transfer it from the state of minimum storage to a given state. These functions are themselves possible storage functions, i.e., they satisfy the dissipation inequality. Moreover, since the class of possible storage functions forms a convex set, there is thus a continuum of possible storage functions ranging from its lower bound, the available storage, to its upper bound, the required supply. The paper then considers interconnected systems. It is shown that dissipative systems which are interconnected via a neutral interconnection constraint define a new dissipative dynamical system and that the sum of the storage functions of the individual subsystems is a storage function for the interconnected system. The stability of dissipative systems is then investigated and it is shown that a point in the state space where the storage function attains a local minimum defines a stable equilibrium and that the storage function is a Lyapunov function for this equilibrium. These results are then applied to several examples. These concepts and results will be applied to linear dynamical systems with quadratic supply rates in the second part of this paper. more

Topics: Lyapunov function (59%), Dissipative system (58%), Linear dynamical system (58%) more

2,874 Citations

Journal ArticleDOI: 10.1007/BF00261375
Abstract: A mathematical framework is developed to study the mechanical behavior of material surfaces. The tensorial nature of surface stress is established using the force and moment balance laws. Bodies whose boundaries are material surfaces are discussed and the relation between surface and body stress examined. Elastic surfaces are defined and a linear theory with non-vanishing residual stress derived. The free-surface problem is posed within the linear theory and uniqueness of solution demonstrated. Predictions of the linear theory are noted and compared with the corresponding classical results. A note on frame-indifference and symmetry for material surfaces is appended. more

Topics: Stress (mechanics) (52%), Surface stress (52%), Surface (mathematics) (51%) more

2,357 Citations

Open accessJournal ArticleDOI: 10.1007/BF00253945
Abstract: HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Elastic materials with couple-stresses R. Toupin more

2,270 Citations

Journal ArticleDOI: 10.1007/BF00279992
John M. Ball1Institutions (1)
Topics: Convexity (64%), Linear elasticity (61%)

2,186 Citations

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Journal's top 5 most impactful authors

Morton E. Gurtin

52 papers, 8.8K citations

Bernard D. Coleman

32 papers, 3.8K citations

Avner Friedman

30 papers, 947 citations

William Alan Day

28 papers, 275 citations

Giovanni P. Galdi

26 papers, 1.3K citations

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