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Seminario Dr. Bacciocchi: "Higher-order Strong and Weak Formulations for Arbitrarily Shaped Doubly-Curved Shell Structures"

12/09/2018 dalle 15:00

Dove Aula LAMC - Scuola di Ingegneria e Architettura - Viale del Risorgimento, 2 - Bologna

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Higher-order Strong and Weak Formulations for Arbitrarily Shaped Doubly-Curved Shell Structures

Michele Bacciocchi - University of Bologna

Wednesday, September, 12th 
h. 15:00
Laboratory of Computational Mechanics – LAMC (Viale Risorgimento 2, Bologna)

Abstract: The well-known three-dimensional elasticity theory represents one of the most comprehensive approach to analyze the structural behavior of doubly-curved shells. However, this approach could be extremely burdensome in terms of calculation. Consequently, two-dimensional models are introduced to reduce the computations required to obtain the solution. Among them, the Classical Shell Theory (CST) and the First-order Shear Deformation Theory (FSDT) are the most exploited approaches, due to their simplicity. Nevertheless, their inadequacy could be evident if innovative and advanced mechanical constituents are considered. For this purpose, more refined approaches are developed. These models are known as Higher-order Structural Theories (HSDTs). In general, the systems of governing equations cannot be solved analytically. Thus, a numerical method must be used to get an approximate solution. Two formulations of the same governing equations can be developed, which are the strong and weak formulations, respectively. If the strong formulation is solved, a numerical tool capable to approximate derivatives is required, since these equations are directly changed into a discrete system. On the other hand, a numerical approximation of integrals is needed when an equivalent integral formulation of lower order is solved, as in the case of the weak form. Therefore, two different numerical methods can be used to obtain the solution of these formulations. For these purposes, the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods are discussed. The accuracy, stability and reliability of the present formulations are also illustrated.