Ciarlet Mathematical Elasticity Pdf 15

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Patrick Ciarlet,Philippe G. Ciarlet, Oana Iosifescu, Stefan Sauter and Jun Zou(2011)Lagrange multipliers in intrinsic elasticityMathematical Models and Methods inAppliedSciences, 21, p. 651-666 (DOI) preprint.pdf

Patrick Ciarlet and PhilippeG. Ciarlet (2009)Direct computation of stresses in planarlinearized elasticityMathematical Models and Methods inAppliedSciences, 19, p. 1043-1064 (DOI) preprint.pdf(264K)

Patrick Ciarlet andPhilippe G. Ciarlet(2008)A new approach for approximating linearelasticity problemsC. R. Acad. Sci. Paris, Ser. I, 346, p.351-356 (DOI) preprint.pdf(224K)

Patrick Ciarlet andPhilippe G. Ciarlet (2005)Another approach to linearizedelasticityand a new proof of Korn's inequalityMathematical Models and Methods inAppliedSciences, 15, p. 259-271 (DOI) article.pdf(224K)

Philippe G. Ciarlet (born 14 October 1938) is a French mathematician, known particularly for his work on mathematical analysis of the finite element method. He has contributed also to elasticity, to the theory of plates and shells and differential geometry.

Philippe Ciarlet is a former student of the École Polytechnique and the École des ponts et chaussées. He completed his PhD at Case Institute of Technology in Cleveland in 1966 under the supervision of Richard S. Varga. He also holds a doctorate in mathematical sciences from the Faculty of Sciences of Paris (doctorate under the supervision of Jacques-Louis Lions in 1971).

Plate modeling by asymptotic analysis and singular disturbance techniques: Philippe Ciarlet is also well known for his leading role in justifying two-dimensional models of linear and non-linear elastic plates from three-dimensional elasticity; in particular, he established convergence in the linear case,[11][12] and justified two-dimensional non-linear models, including the von Kármán and Marguerre-von Karman equations, by the asymptotic development method.[13]

Modeling, mathematical analysis and numerical simulation of "elastic multi-structures" including junctions: This is another entirely new field that Philippe Ciarlet has created and developed, by establishing the convergence of the three-dimensional solution towards that of a "multidimensional" model in the linear case, by justifying the limit conditions for embedding a plate.[14][15]

Modeling and mathematical analysis of "general" shells: Philippe Ciarlet established the first existence theorems for two-dimensional linear shell models, such as those of W.T. Koiter and P.M. Naghdi,[16] and justified the equations of the "bending" and "membrane" shell;[17][18][19] he also established the first rigorous justification of the "shallow" two-dimensional linear shell equations and of Koiter equations, using asymptotic analysis techniques; he also obtained a new theory of existence for non-linear shell equations.

Non-linear elasticity: Philippe Ciarlet proposed a new energy function that is polyconvex (as defined by John Ball), and has proven to be very effective because it is "adjustable" to any given isotropic elastic material;[20] he has also made important and innovative contributions to the modelling of contact and non-interpenetration in three-dimensional non-linear elasticity.[21] He also proposed and justified a new non-linear Koiter-type model for non-linearly elastic hulls.

Intrinsic methods in linearized elasticity: Philippe Ciarlet has developed a new field, that of the mathematical justification of "intrinsic" methods in linearized elasticity, where the linearized metric tensor and the linearized tensor of curvature change are the new, and only, unknowns:[25] This approach, whether for three-dimensional elasticity or for plate and shell theories, requires an entirely new approach, based mainly on the compatibility conditions of Saint-Venant and Donati in Sobolev spaces.

Intrinsic methods in non-linear elasticity: Philippe Ciarlet has developed a new field, that of the mathematical justification of "intrinsic" methods in non-linear elasticity. This approach makes it possible to obtain new existence theorems in three-dimensional non-linear elasticity.[26] 2b1af7f3a8