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| Author(s): |
Jorge Carvalho Costa
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Paulo. |
| Institution: | Universidade de São Paulo (USP). Escola Politécnica (EP/BC) |
| Defense date: | 2010-09-10 |
| Examining board members: |
Paulo de Mattos Pimenta;
Carlos Manuel Tiago Tavares Fernandes;
Sergio Persival Baroncini Proença
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| Advisor: | Paulo de Mattos Pimenta |
| Abstract | |
The Finite Element Method is the most spread numerical analysis tool, applied to a wide range of structural theories. However, for the study of shells and other problems, some of its deficiencies have stimulated research in other methods for solving the derived Partial Differential Equations. The present work uses one of those alternatives, the Element Free Galerkin Method, for the study of shells. It begins with the observation of the approximation used in the method, Moving Least Squares and Multiple-Fixed Least Squares. Then, it establishes a formulation that combines the Reissner-Mindlin moderately thick plate theory with plane elasticity, and uses the proponed approximation to analyze such plates and stabs. Afterwards, it demonstrates a geometrically exact shell theory that accounts for initial curvatures as a stress-free deformation from a flat reference configuration. Such theory precludes the use of curvilinear coordinates and, subsequently, the use of objects such as Cristoffel symbols, as all integrations and impositions are done in the flat reference configuration, in an orthogonal frame. The essential boundary conditions are imposed in a eak statement, rendering a hybrid displacement functional that provides the necessary conditions for the use of Moving Least Squares. This works main objective is the particularization of this theory for the small displacement and strains assumption (geometrical linearity), keeping the consistent definition of generalized stresses and strains, while allowing the imposition of the discretized weak form through a system of linear equations. Lastly, numerical simulations are carried out to assess the methods efficiency and accuracy. (AU) | |
| FAPESP's process: | 09/04525-5 - Linear Analysis of Shells with Meshless Methods |
| Grantee: | Jorge Carvalho Costa |
| Support Opportunities: | Scholarships in Brazil - Master |