Conservation laws and conjugate solutions in the elasticity of simple materials and materials with couple stress

Journal of Elasticity

Volumn 51, Issue 1, 1998, Pages 1-22

  Nikitin, Evgeny ^a   Zubov, Leonid M ^b  

^a RUTGERS UNIVERSITY   (United States)

^b SOUTHERN FEDERAL UNIVERSITY   (Russian Federation)

Author keywords

Conservation laws; Cosserat continuum; Noether's Theorem

Indexed keywords

CONTINUUM MECHANICS; DEGREES OF FREEDOM (MECHANICS); DIFFERENTIAL EQUATIONS; ELASTICITY; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; ROTATION; STRESSES; TENSORS; THEOREM PROVING; ENERGY CONSERVATION; ENERGY STORAGE; STRESS ANALYSIS;

CONSERVATION LAWS; COSSERAT CONTINUUM; ELASTIC MATERIALS; NOETHER'S THEOREM; CONJUGATE SOLUTION; CONSERVATION LAW; COUPLE STRESS; NOETHER THEOREM;

MATERIALS SCIENCE; ELASTICITY;

EID: 0032288087     PISSN: 03743535     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1007569315660     Document Type: Article

References (10)

1. R. A. Toupin, Theories of elasticity with couple-stress. Archive for Rational Mechanics and Analysis 17 (1964), 85-112.
2. A.E. Green and J.E. Adkins, Large Elastic Deformations and Non-linear Continuum Mechanics. Oxford University Press (1960).
3. R.T. Shield, Inverse deformation results in finite elasticity. ZAMP 18 (1967), 490-500.
4. D.E. Carlson and R.T. Shield, Inverse deformation results for elastic materials. ZAMP 20 (1969), 261-263.
5. L.M. Zubov, Conjugate solutions in the nonlinear theory of elasticity. Doklady Akademii Nauk 324 (Number 2) (1992), 282-286 (Russian); translation in, Soviet Physics Doklady 37 (Number 5) (1992), 261-263.
6. L.M. Zubov, Conjugate solutions in the nonlinear theory of elasticity. Doklady Akademii Nauk 324 (Number 2) (1992), 282-286 (Russian); translation in, Soviet Physics Doklady 37 (Number 5) (1992), 261-263.
7. J.K. Knowles and E. Sternberg, On a class of conservation laws in linearized and finite elastostatics. Archive for Rational Mechanics and Analysis 44 (1972), 187-211.
8. P.J. Olver, Applications of Lie Groups to Differential Equations. Graduate Texts in Mathematics 107. Springer-Verlag (1986).
9. L.M. Zubov, Variational principles and invariant integrals for nonlinearly elastic bodies with couple stress, Izvestiya Akademii Nauk SSSR Mehanika Tverdogo Tela 25 (Number 6) (1990), 10-16 (Russian); translation in, Mechanics of Solids 25 (Number 2) (1990), 7-13.
10. L.M. Zubov, Variational principles and invariant integrals for nonlinearly elastic bodies with couple stress, Izvestiya Akademii Nauk SSSR Mehanika Tverdogo Tela 25 (Number 6) (1990), 10-16 (Russian); translation in, Mechanics of Solids 25 (Number 2) (1990), 7-13.