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On a model of a flexural prestressed shell. (English) Zbl 1333.74056

Summary: We derive a linearized prestressed elastic shell model from a nonlinear Kirchhoff model of elastic plates. The model is given in terms of displacement and micro-rotation of the cross-sections. In addition to the standard membrane, transverse shear, and flexural terms, the model also contains a nonstandard prestress term. The prestress is of the same order as flexural effects; hence, the model is appropriate when flexural effects dominate over membrane ones. We prove the existence and uniqueness of the solutions by Lax-Milgram theorem and compare solution with the solution of the standard shell model via numerical examples.

MSC:

74K25 Shells
74B15 Equations linearized about a deformed state (small deformations superposed on large)

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