Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/nonconvex-energy-functions-hemivariational-inequalities-and-FR5rQJfuJO
References (41)
-
K. Glashoff, J. Sprekels (1981)
An Application of Glicksberg’s Theorem to Set-Valued Integral Equations Arising in the Theory of ThermostatsSiam Journal on Mathematical Analysis, 12
-
A. Zhukov (1956)
Plastic deformations of isotropic metals in combined loadingIzv. Akad. Nauk. SSSR OTN, 12
-
W. Olszak, Z. Mróz, P. Perzyna, R. Sankaranarayanan (1963)
Recent trends in the development of the theory of plasticity -
A. P. Robertson, W. Robertson (1967)
Topologische Vectorräume -
A. C. Palmer, G. Maier, D. C. Drucker (1967)
Normality relations and convexity of yield surfaces for unstable materials of structural elementsTrans. ASME, 24
-
G. Rieder, U. Heise, U. Pahnke, H. Antes, H. Glahn, V. Kompiš (1976)
Berechnung von elastischen Spannungen in beliebig krummlinig berandeten Scheiben und Platten -
P. Panagiotopoulos (1981)
Dynamic and incremental variational inequality principles, differential inclusions and their applications to co-existent phases problemsActa Mechanica, 40
-
C. Lanczos (1949)
The variational principles of mechanics -
J. Moreau (1968)
La notion de sur-potentiel et les liaisons unilatérales en élastostatique -
B. Halphen, Q. Nguyen (1975)
Sur les matériaux standard généralisés, 14
-
I. Salençon, Agustin Tristán-Lopez (1980)
Analyse de la stabilité des talus en sols cohérents anisotropesC. R. Acad. Sci. B, 290
-
J. P. Crouzeix (1977)
Lectures Notes in Economics, Vol. 144 -
U. Heise (1978)
Application of the singularity method for the formulation of plane elastostatical boundary value problems as integral equationsActa Mechanica, 31
-
G. Maier (1967)
On elastic-plastic structures with associated stress-strain relations allowing for work softeningMeccanica, 2
-
P. Germain (1973)
Cours de mécanique des milieux continus -
J. Aubin, F. Clarke (1979)
Shadow Prices and Duality for a Class of Optimal Control ProblemsSiam Journal on Control and Optimization, 17
-
R. Rockafellar (1979)
La théorie des sous-gradients et ses applications à l'optimisation : fonctions convexes et non convexes -
G. Hamel (1967)
Theoretische Mechanik -
H. Ziegler (1963)
Some extremum principles in irreversible thermodynamics with applications to continuum mechanicsProgress in Solid Mechanics, 4
-
G. Duvaut, J. Lions (1973)
Les inéquations en mécanique et en physiqueMathematics of Computation, 27
-
P. D. Panagiotopoulos (1981)
Superpotentials in the sense of F.H. Clarke and applicationsMech. Res. Comm., 8
-
J. Crouzeix (1977)
Conjugacy in quasiconvex analysis -
F. Clarke (1975)
Generalized gradients and applicationsTransactions of the American Mathematical Society, 205
-
P. Germain (1973)
The Role of Thermodynamics in Continuum Mechanics -
A. Green, P. Naghdi (1965)
A general theory of an elastic-plastic continuumArchive for Rational Mechanics and Analysis, 18
-
E. Tonti (1973)
Variational methods in engineering -
G. Fichera (1972)
Boundary value problems in elasticity with unilateral constraints -
J. Toland (1979)
A duality principle for non-convex optimisation and the calculus of variationsArchive for Rational Mechanics and Analysis, 71
-
A. A. Ilyushin (1960)
On the increment of plastic deformation and yield functionPrikl. Math. Mech., 24
-
J. Mandel (1972)
Plasticité classique et viscoplasticité -
P. Panagiotopoulos (1981)
Non-convex superpotentials in the sense of F.H. Clarke and applicationsMechanics Research Communications, 8
-
H. J. Grootenboer, S. F. C. H. Leijten, J. Blauuwendraad (1981)
Numerical models for reinforced concrete structures in plane stressHeron, 26
-
A. Palmer, G. Maier, D. Drucker (1967)
NORMALITY RELATIONS AND CONVEXITY OF YIELD SURFACES FOR UNSTABLE MATERIALS OR STRUCTURAL ELEMENTS.Journal of Applied Mechanics, 34
-
P. D. Panagiotopoulos (1977)
A systematic approach to the search for variational principles for bilateral and unilateral problemsZAMM, 57
-
J. J. Moreau (1974)
New Variational Techniques in Mathematical Physics -
J. Warga (1975)
Necessary conditions without differentiability assumptions in optimal controlJournal of Differential Equations, 18
-
R. Rockafellar (1980)
Generalized Directional Derivatives and Subgradients of Nonconvex FunctionsCanadian Journal of Mathematics, 32
-
H. Brézis (1973)
Operateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert -
P. Panagiotopoulos (1975)
A nonlinear programming approach to the unilateral contact-, and friction-boundary value problem in the theory of elasticityIngenieur-Archiv, 44
-
J. Mandel (1973)
Thermodynamics and Plasticity -
E. Tonti (1973)
A Systematic Approach to the Search for Variational Principles
- Publisher
- Springer Journals
- Copyright
- Copyright © 1983 by Springer-Verlag
- Subject
- Engineering; Theoretical and Applied Mechanics; Classical and Continuum Physics; Solid Mechanics; Solid Mechanics; Vibration, Dynamical Systems, Control; Engineering Thermodynamics, Heat and Mass Transfer
- ISSN
- 0001-5970
- eISSN
- 1619-6937
- DOI
- 10.1007/BF01170410
- Publisher site
- See Article on Publisher Site
Abstract
The purpose of the present paper is the derivation of certain new classes of variational principles for material laws and boundary conditions resulting from nonconvex, generally nondifferentiable, potentials. To this end two recently defined notions are employed the “generalized gradient” of Clarke and the “derivate container” of Warge. Several general classes of problems are discussed and the respective variational forms called here hemivariational inequalities are derived. For the respective static problems the equivalence of these forms to the “substationarity” of the potential and complementary energy is discussed. Finally an integral inclusion formulation for certain classes of static problems is presented.
Journal
Acta Mechanica – Springer Journals
Published: Jan 31, 2005