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Raja, J.
- Justification of the Asymptotic Analysis of Linear Shallow Shells
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Authors
Affiliations
1 Department of Mathematics, Indian Institute of Space Science and Technology, Valiamala P.O, Trivandrum-695 547, IN
1 Department of Mathematics, Indian Institute of Space Science and Technology, Valiamala P.O, Trivandrum-695 547, IN
Source
The Journal of the Indian Mathematical Society, Vol 81, No 3-4 (2014), Pagination: 335-356Abstract
Two dimensional model of linearly elastic shallow shells is derived in [1] under suitable scalings on the unknowns and the data. In this paper we justify the scalings used in [1] to derive the two dimensional shallow shell model.Keywords
Elasticity, Shallow Shells.
References
- S. Busse, P. G. Ciarlet and B. Miara, Justification d'un modele lineaire bi-dimensional de coques "faiblment courbees" en coordonnees curvilignes, M2 N A, 31 (1997), 409-434.
- P. G. Ciarlet, Plates and junctions in elastic multistructures, An asymptotic analysis, Masson, Paris, 1990.
- P. G. Ciarlet and P. Destuynder, A justification of the two dimensional plate model, J. Mechanique, 18 (1978), 315-344.
- P. G. Ciarlet and P. Destuynder, A justification of a non-linear model in plate theory model, Camp. Methods in App!. Mech. Engrg, 17/18, (1979), 227-258.
- P. G. Ciarlet and S. Kesavan, Two-dimensional approximation of three-dimensional eigenvalue problem in plate theory, Camp. Methods in App!. Mech. Engrg., 26 (1981), 145-172.
- P. G. Ciarlet and V. Lads, Asymptotic analysis of linearly elastic shells. I. Justification of membrane shell equation, Arch. Rational Mech. Ana!., 136 (1996), 119-16l.
- P. G. Ciarlet and V. Lads, Asymptotic analysis of linearly elastic shells, III Justification of Koiter's shell equations, Arch.Rationa!.Mech.Ana!',136 (1996), 191-200.
- P. G. Ciarlet, V. Lads and B. Miara, Asymptotic analysis of linearly elastic shells. II.Justification of flexural shell equations, Arch. Rational Mech. Ana!., 136 (1996), 162190.
- P. G. Ciarlet and B. Miara, Justification of the two-dimensional equations of a linearly elastic shell, Comm. Pure and App!. Math; 45 (1992), 327-360.
- S. Kesavan and N. Sabu, Two dimensional approximation of eigenvalue problem in shallow shells, Math. Mech. Solids, 4, 441-460.
- S. Kesavan and N. Sabu, Two-dimensional approximation of eigenvalue problem for flexural shells, Chinese Annals Maths., 21 B (2000), 1-16.
- H. Le Dret, Problems Variationnels dans les Multi-Bomains, Modelisation des jonctions et Applications, 1991, Masson, Paris.
- J. L. Lions, Perturbations Singulieres dans les Problems aux limites et en Controle Optimal. Lecture Notes in Math., Va!. 323, Springer-verlag, Berlin, 1973.
- B. Miara, Justification of the asymptotic analysis of elastic plates, I. linear case, Asymptotic analysis, 9 (1994), 47-60.
- B. Miara, Justification of the asymptotic analysis of elastic plates, I. Non linear case, Asymptotic analysis, 9 (1994), 119-134.
- N. Sabu, Vibrations of piezoelectric flexural shells: Two dimensional approximation, J. Elasticity, 68 (2000), 145-165.
- N. Sabu., Vibrations of piezoelectric shallow shells: Two dimensional approximation, Proc. Indian Acad. Sci;(Math Sci), 113 (2003), 333-352.
- Justification of the Asymptotic Analysis of Linear Slender Rods
Abstract Views :199 |
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Authors
Affiliations
1 SCL, Chandigarh, IN
2 Department of Mathematics, IIST, Trivandrum-695 547, IN
1 SCL, Chandigarh, IN
2 Department of Mathematics, IIST, Trivandrum-695 547, IN
Source
The Journal of the Indian Mathematical Society, Vol 83, No 1-2 (2016), Pagination: 181-197Abstract
One dimensional model of linearly elastic slender rods is derived by Trabucho and Viano using asymptotic expansion method under suitable scalings on the unknowns and the data and later Le Dret had proved the convergence of the scaled solution to the one dimensional model under the same scalings on the unknowns and data. In this paper we justify the scalings used by them to derive the one dimensional model.Keywords
Elasticity, Rods, Asymptotics.References
- S. Busse, P. G. Ciarlet and B. Miara; Justication d'un modele lineaire bi-dimensional de coques faiblment courbees"en coordonnees curvilignes, M2NA; 31(3) 1997, 409-434.
- P. G. Ciarlet and P. Destuynder, A justication of the two dimensional plate model, J. Mechanique, 18 (1978), 315-344.
- P. G. Ciarlet and P. Destuynder, A justication of a non-linear model in plate theory model, Comp. Methods in Appl. Mech. Engrg, 17/18 (1979), 227-258.
- P. G. Ciarlet and J. L. Lions, Hand book of Numerical Analysis, Volume 4, Finite element method (part 2), Numerical method of solids (part 2)
- P. G. Ciarlet and V. Lods, Asymptotic analysis of linearly elastic shells. I. Justication of membrane shell equation, Arch. Rational Mech. Anal., 136 (1996), 119-161.
- P. G. Ciarlet and V. Lods, Asymptotic analysis of linearly elastic shells, III Justication of Koiter's shell equations, Arch. Rational. Mech. Anal., 136, 1996, 191-200.
- P. G. Ciarlet, V. Lods and B. Miara, Asymptotic analysis of linearly elastic shells. II.Justication of exural shell equations, Arch. Rational. Mech. Anal., 136 (1996), 162-190.
- J. L. Lions, Perturbations Singulieres dans les Problems aux limites et en Controle Optimal, Lecture Notes in Math., Vol. 323 Springer-Verlag, Berlin, 1973.
- B. Miara, Justication of the asymptotic analysis of elastic plates, I. linear case, Asymptotic analysis, 9 (1994), 47-60.
- B. Miara, Justication of the asymptotic analysis of elastic plates, I. Non linear case, Asymptotic analysis, 9 (1994), 119-134.
- H. Le Dret, Convergence of displacements and stresses in linearly elastic slender rods as the thickness goes to zero, Asymptotic analysis, 10 (1995), 367-402.
- L. Trabucho and J. M. Viano, Une justication des equations de la thermo-elaste des poutres a section variable par des methodes asymptotiques, RAIRO Anal, Numerique, 18 (1984), 347-376.