Abstract
We construct variational hierarchical two-dimensional models for elastic, prismatic shells of variable thickness vanishing at boundary. With the help of variational methods, existence and uniqueness theorems for the corresponding two-dimensional boundary value problems are proved in appropriate weighted functional spaces. By means of the solutions of these two-dimensional boundary value problems, a sequence of approximate solutions in the corresponding three-dimensional region is constructed. We establish that this sequence converges in the Sobolev space H1 to the solution of the original three-dimensional boundary value problem.
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74K20, 74K25.
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Jaiani, G., Kharibegashvili, S., Natroshvili, D. et al. Two-dimensional Hierarchical Models for Prismatic Shells with Thickness Vanishing at the Boundary. J Elasticity 77, 95–122 (2004). https://doi.org/10.1007/s10659-005-5069-5
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DOI: https://doi.org/10.1007/s10659-005-5069-5