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Finite element approximation of a prestressed shell model. (English) Zbl 1446.74209

Summary: 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.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K25 Shells
74G22 Existence of solutions of equilibrium problems in solid mechanics
74G30 Uniqueness of solutions of equilibrium problems in solid mechanics
65N15 Error bounds for boundary value problems involving PDEs
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