Mechanics of Laminated Composite Doubly-Curved Shell Structures: The Generalized Differential Quadrature Method and the Strong Formulation Finite Element Method

This manuscript comes from the experience gained over ten years of study and research on shell structures and on the Generalized Differential Quadrature method. The title, Mechanics of Laminated Composite Doubly-Curved Shell Structures, illustrates the theme followed in the present volume. The present study aims to analyze the static and dynamic behavior of moderately thick shells made of composite materials through the application of the Differential Quadrature (DQ) technique. A particular attention is paid, other than fibrous and laminated composites, also to "Functionally Graded Materials" (FGMs). They are non-homogeneous materials, characterized by a continuous variation of the mechanical properties through a particular direction. The GDQ numerical solution is compared, not only with literature results, but also with the ones supplied and obtained through the use of different structural codes based on the Finite Element Method (FEM). Furthermore, an advanced version of GDQ method is also presented. This methodology is termed Strong Formulation Finite Element Method (SFEM) because it employs the strong form of the differential system of equations at the master element level and the mapping technique, proper of FEM. The connectivity between two elements is enforced through compatibility conditions.

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About the Author :
FRANCESCO TORNABENE was born in Bologna, January 13, 1978. School-leaving examination in a classical liceo achieved at Liceo Classico San Luigi in Bologna in 1997. Patent for Industrial Invention: Friction Clutch for High Performance Vehicles Question BO2001A00442 filed on 13/07/2001 in National Patent Bologna (Italy). Assignees: Alma Mater Studiorum - University of Bologna. Degree in Mechanical Engineering (Course of Studies in Structural Mechanics) obtained at the Alma Mater Studiorum - University of Bologna on 23/07/2003. Thesis Title (in Italian): Dynamic Behavior of Cylindrical Shells: Formulation and Solution. First position obtained in the competition for admission to the PhD in Structural Mechanics at the Alma Mater Studiorum - University of Bologna in December 2003. Winner of the scholarship, Carlo Felice Jodi for a degree in Structural Mechanics in 2004. Adjunct Professor (Tutor Contract) for activities of supporting the teaching of Scienza delle Costruzioni (Structural Mechanics) L, for the course in Civil Engineering, at Alma Mater Studiorum - University of Bologna, a.a. 2005/2006. Adjunct Professor (Tutor Contract) for activities to support the teaching of Scienza delle Costruzioni (Structural Mechanics) L, for the course in Civil Engineering, at Alma Mater Studiorum - University of Bologna, a.a. 2007/2008. PhD in Structural Mechanics at the Alma Mater Studiorum - University of Bologna on 31/05/2007. PhD Thesis Title the (in Italian): Modeling and Solution of Shell Structures Made of Anisotropic Materials. Owner of the research grant entitled: Unified Formulation of Shell Structures Made of Anisotropic Materials. Numerical Analysis Using the Generalized Differential Quadrature Method and the Finite Element Method from January 2007 to January 2009 at the Alma Mater Studiorum - University of Bologna. Adjunct Professor (Tutor Contract) for activities to support the teaching of Mechanical Design and Laboratory T C.I., for the Degree in Mechanical Engineering, at Alma Mater Studiorum - University of Bologna, a.a. 2010/2011. Winner of the Senior research grant entitled: Design for Recycling Methodologies Applied to the Nautical Field from February 2011 to October 2011 at the Alma Mater Studiorum - University of Bologna. Junior researcher for the research program entitled: Advanced Numerical Schemes for Anisotropic Materials from December 2011 to January 2012 at the Alma Mater Studiorum - University of Bologna. Research Activities in collaboration with Foreign University Professors. Author of the book (in Italian) entitled: Mechanics of Shell Structures Made of Composite Materials. The Generalized Differential Quadrature Method, Esculapio, Bologna, 2012. Member of the Editorial Board of Journal of Computational Engineering and ISRN Mechanical Engineering since 2013. Member of Scientific Committee, Promoter and Secretary of CIMEST Center, Center for Studies and Research on the Identification of Materials and Structures - "Michele Capurso" - at the Department DICAM of the Alma Mater Studiorum - University of Bologna, since 2005. Professor of Dynamics of Structures since 2012 and of Computational Mechanics since 2013. Assistant Professor at the Alma Mater Studiorum - University of Bologna since 2012. Author of more than seventy research papers since 2005. ​ NICHOLAS FANTUZZI was born in Bologna, June 16, 1984. School-leaving examination in a scientific liceo achieved at Liceo Scientifico Augusto Righi in Bologna in 2003. Bachelor's degree in Civil Engineering (Course of Studies in Structural Engineering) obtained at the Alma Mater Studiorum - University of Bologna on 16/10/2006, grade 110/110 cum laude. Thesis title (in Italian): On the Behavior of Cylindrical Vaults. Master degree in Civil Engineering (Course of Studies in Structural Engineering) obtained at the Alma Mater Studiorum - University of Bologna on 16/01/2009, grade 110/110 cum laude. Thesis title (in Italian): Curvature Effect on the Behavior of Shells with Anisotropic Material. First position obtained in the competition for admission to the PhD in Structural Engineering and Hydraulics at the Alma Mater Studiorum - University of Bologna in December 2009. PhD in Structural Engineering and Hydraulics at the Alma Mater Studiorum - University of Bologna on 31/05/2013. PhD Thesis title: Generalized Differential Quadrature Finite Element Method Applied to Advanced Structural Mechanics. Owner of the research grant entitled: About Shell Structures Made of Anisotropic Materials. Unified Formulation and Numerical Analysis since June 2013 at the Alma Mater Studiorum - University of Bologna. Winner of the "ICCS17 Ian Marshall's Award for Best Student Paper" with the work entitled: Static Analysis of Doubly-Curved Anisotropic Shells and Panels Using CUF Approach, Differential Geometry and Differential Quadrature Method by F. Tornabene, N. Fantuzzi, E. Viola and E. Carrera, published in Composite Structures 107, 675-697 (2014). Adjunct Professor (Tutor Contract) for activities to support the teaching of Second Level Master in "Design of Oil & Gas plants", for ENI Corporate University, at Alma Mater Studiorum - University of Bologna, since 2010. Member of Scientific Committee, Promoter and Secretary of CIMEST Center, Center for Studies and Research on the Identification of Materials and Structures - "Michele Capurso" - at the Department DICAM of the Alma Mater Studiorum - University of Bologna, since 2011. ​