2015
DOI: 10.1002/mma.3451
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On a model of a flexural prestressed shell

Abstract: 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 solution… Show more

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Cited by 5 publications
(15 citation statements)
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“…The main advantage of using global coordinates is the fact that less regularity for the chart φ is needed. The main goal of the present paper is to introduce a penalized version of the model obtained in Marohnic and Tambača and to show that the solution of this penalized problem converges to the solution of the original problem as the penalization parameter tends to zero. We further perform a robust finite element approximation of the penalized version that is based on a regularity assumption on the solution.…”
Section: Introductionmentioning
confidence: 99%
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“…The main advantage of using global coordinates is the fact that less regularity for the chart φ is needed. The main goal of the present paper is to introduce a penalized version of the model obtained in Marohnic and Tambača and to show that the solution of this penalized problem converges to the solution of the original problem as the penalization parameter tends to zero. We further perform a robust finite element approximation of the penalized version that is based on a regularity assumption on the solution.…”
Section: Introductionmentioning
confidence: 99%
“…This paper is organized as follows: in Section , we briefly recall the geometry of the surface as well as the prestressed model presented in Marohnic and Tambača and we point out that the model is not necessarily positive. Section is devoted to the well‐posedness of the variational problem.…”
Section: Introductionmentioning
confidence: 99%
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“…shell model; undrained and fixed stress split; iterative numerical method; existence of solutions 1) formulate a linear quasi-static model of poroelastic shells (of Naghdi type), 2) formulate two iterative sequences of solutions of the problems associated to the formulated poroelastic shell model (one of the sequences is related to the 'undrained split' iterative method and the other to the 'fixed stress split' iterative method, which are usually applied in geomechanics), 3) prove the convergence of these sequences to the solution of the formulated poroelastic shell model.The proposed model is closely related to the poroelastic shell models derived asymptotically from the three-dimensional Biot's equations in [2,3].There are many different shell theories that can be found in the literature. Within the classical elasticity, we mention the membrane shell model, the flexural shell model, the generalized membrane shell model, the Koiter model (see references [4][5][6][7] or [8]), the Naghdi shell model (see references [9,10]) and the newly introduced models of the Koiter and Naghdi type (see references [11,12], a very similar model already appears in [13]), which are well defined for Lipschitz middle surfaces. All these models are two-dimensional models (defined on a two-dimensional domain) and describe behavior of three-dimensional elastic bodies that are thin in one direction.In geomechanics, there are many examples of elastic bodies which are saturated by a fluid, see e.g., references [14,15].…”
mentioning
confidence: 99%
“…There are many different shell theories that can be found in the literature. Within the classical elasticity, we mention the membrane shell model, the flexural shell model, the generalized membrane shell model, the Koiter model (see references [4][5][6][7] or [8]), the Naghdi shell model (see references [9,10]) and the newly introduced models of the Koiter and Naghdi type (see references [11,12], a very similar model already appears in [13]), which are well defined for Lipschitz middle surfaces. All these models are two-dimensional models (defined on a two-dimensional domain) and describe behavior of three-dimensional elastic bodies that are thin in one direction.…”
mentioning
confidence: 99%