Finite element approximation of a prestressed shell model | Zendy

Rezzag Bara Rayhana | Zendy; Nicaise Serge | Zendy; Merabet Ismail | Zendy

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Finite element approximation of a prestressed shell model

Author(s) -

Rezzag Bara Rayhana,

Nicaise Serge,

Merabet Ismail

Publication year - 2020

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.6196

Subject(s) - mathematics , discretization , uniqueness , finite element method , a priori and a posteriori , constraint (computer aided design) , mixed finite element method , shell (structure) , mathematical analysis , mathematical optimization , geometry , materials science , composite material , philosophy , physics , epistemology , thermodynamics

This work deals with the finite element approximation of a prestressed shell model formulated in Cartesian coordinates system. The considered constrained variational problem is not necessarily positive. Moreover, because of the constraint, it cannot be discretized by conforming finite element methods. A penalized version of the model and its discretization are then proposed. We prove existence and uniqueness results of solutions for the continuous and discrete problems, and we derive optimal a priori error estimates. Numerical tests that validate and illustrate our approach are given.

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