Francesco Tornabene

Francesco Tornabene (Bologna, 13th June 1978) is an Italian Professor. His research activities are focused on the structural behaviour of doubly-curved shell structures, as well as the innovative industrial processes for the development of novel classes of materials. He is author of more than 10 books on laminated anisotropic shell structures, and more than 300 scientific publications. His name has been included in the 100000 Top Scientists List since 2019 and in the Top Italian Scientists List for the Engineering Area. In the years 2018, 2019 and 2020 he was included in the Highly Cited Researchers List. Currently, he is Professor at the University of Salento for the classes of Structural Mechanics for students of Civil and Biomedical Engineering.

Born

January 13th, 1978 Bologna, Italy

Nationality

Italian

Education

University of Bologna

Fields

Computational Mechanics; Doubly-Curved Shell Structures; Fracture Mechanics; Generalized Differential Quadrature; Innovative and Smart Materials; Structural Mechanics; Structural Stability.

Institutions

University of Salento (2018 – Present)

University of Bologna (2004-2018)

Notes

Top Italian Scientist in Engineering

Personal Information

Francesco Tornabene was born on 13 January 1978 in Bologna, where he received the high school degree at Liceo Classico San Luigi, in 1997. In 2001 he achieved a National Patent Bologna (Italy) for the Industrial Invention: Friction Clutch for High Performance Vehicles Question BO2001A00442. He received from the University of Bologna - Alma Mater Studiorum, a M.Sc. degree in Mechanical Engineering (Curriculum in Structural Mechanics), on 23/07/2003, discussing a thesis entitled: “Dynamic Behavior of Cylindrical Shells: Formulation and Solution”. In December 2003, he was admitted at the PhD course in Structural Mechanics, at the University of Bologna, reaching the first position in the competitive admission. In 2004, he received from the University of Bologna a Thesis price in memory of Carlo Felice Jodi; in 2007 he received the Ph.D. degree in Structural Mechanics at the University of Bologna, discussing the Thesis entitled “Modeling and Solution of Shell Structures Made of Anisotropic Materials”. Since 2007 to 2009 he received a research fellowship by the University of Bologna, working on the “Unified Formulation of Shell Structures Made of Anisotropic Materials. Numerical Analysis Using the Generalized Differential Quadrature Method and the Finite Element Method”. Since 2011 to 2012 he became a Junior researcher (RTD-A) within the research program entitled “Advanced Numerical Schemes for Anisotropic Materials”; since 2012 to 2018 he was an Assistant Professor and Lecturer at the Alma Mater Studiorum - University of Bologna; since 2018 to 2021 he was an Assistant Professor in Structural Mechanics and Lecturer at the University of Salento, Department of Innovation Engineering (Lecce); since 2022 up to date he is an Associate Professor at the University of Salento, Department of Innovation Engineering (Lecce). He is author of more than 260 scientific publications, and collaborates with many national or international researchers and professors worldwide, as visible from his scientific production. He is author of 11 books, see e.g. “Meccanica delle Strutture a Guscio in Materiale Composito. Il metodo Generalizzato di Quadratura Differenziale” (2012); “Mechanics of Laminated Composite Doubly-Curved Shell Structures. The Generalized Differential Quadrature Method and the Strong Formulation Finite Element Method” (2014); “Laminated Composite Doubly-Curved Shell Structures I. Differential Geometry. Higher-Order Structural Theories” (2016); “Laminated Composite Doubly-Curved Shell Structures II. Differential and Integral Quadrature. Strong Formulation Finite Element Method” (2016); “Anisotropic Doubly-Curved Shells. Higher-Order Strong and Weak Formulations for Arbitrarily Shaped Shell Structures” (2018), among many. He is member of the Editorial Board for 52 International Journals (see, e.g. Journal of Engineering, International Journal of Engineering & Applied Sciences, Composite Structures, Computers & Structures, Technologies, Journal of Applied and Computational Mechanics, Journal of Composites Science, Advanced Materials and Technologies, Heliyon, International Scholarly Research Notices, Mathematical Problems in Engineering, ISRN Mechanical Engineering, Journal of Computational Engineering, Advances in Aircraft and Spacecraft Science). He is also Editor-in-Chief for 3 International Journals: Curved and Layered Structures, Journal of Composites Science, Characterization and Application of Nanomaterials; since 2019 he is Associate Editor for the 7 International Journals such as “Mechanics Based Design of Structures and Machines”, among many. In the last years he received different important awards, see e.g. “Highly Cited Researcher by Clarivate Analytics” (years 2018, 2019, 2020), “Ambassador of Bologna Award for the organization of 21st International Conference on Composite Structures ICCS21, 4-7 September 2018, Bologna, Italy” (2019), “Member of the European Academy of Sciences” (since 2018). He collaborates as reviewer with more than 335 prestigious international journals. Since 2012, his teaching activity includes Dynamics of Structures; Computational Mechanics; Plates and Shells; Theory of Structures, Structural Mechanics. Developer and promoter of the DiQuMASPAB (Differential Quadrature for Mechanics for Mechanics of Anisotropic Shells, Plates, Arches and Beams) software, his scientific interests include the Structural Mechanics, Solid Mechanics, Innovative and Smart Materials, Computational Mechanics and Numerical Techniques, Damage and Fracture Mechanics.

Research Activity

Since the beginning of his academic works, Tornabene developed several structural models for the prediction of the mechanical behaviour of structures with different shapes and materials, taking into account several numerical methods including the classical Finite Element Method (FEM), the Generalized Differential Quadrature (GDQ) method and mesh-free approaches. His scientific production is focused on various research issues, primarily, structural mechanics, smart and innovative materials and computational mechanics should be mentioned. Other research activities include some innovations in the field of fracture mechanics, structural stability and experimental mechanics. Several theoretical models developed by Tornabene are implemented and distributed in the DiQuMASPAB software.

Structural Mechanics

The DiQuMASPAB software logo.

The research activity in the structural mechanics topic is focused on the mechanical analysis of plates and shells made of composite materials, due to their relevant role in civil, mechanical, architectural, aerospace and naval engineering. Shell structures, indeed, show an extraordinary efficiency in bearing the external loads, together with a high degree of resistance, good stiffness and high strength-to-weight ratio. This motivates the large interest of the scientific community since 1940 up to date on doubly-curved shells for many engineering applications.

A shell is a three-dimensional solid that can be studied with the classical theory of elasticity. However, the calculations based on this kind of theory could be computationally burdensome, because of the high number of degrees of freedom involved in the problem. The initial three-dimensional problem can be simplified by a two-dimensional model with the introduction of some proper hypotheses. In addition to the classic theory of elasticity (3D elasticity), several Higher-order Shear Deformation Theories (HSDTs), characterized by different kinematic models, have been developed and analyzed by Tornabene, based on a Carrera Unified Formulation (CUF) setting. Starting from CUF, Tornabene focused his attention on two different approaches to deal with a two-dimensional modeling of anisotropic doubly-curved shells: the Equivalent Single Layer (ESL) and the Layer-Wise (LW). The first approach uses a kinematic expansion of the generalized displacements referred to the shell mid-surface, whereas the second one considers the displacement field on the lower and upper surfaces of each layer within the laminate as primary unknowns. The intermediate kinematic quantities follow the kinematic expansion of the model.

Structures with complex geometries are considered in the works by Tornabene, including singly- and doubly-curved shells and panels, as well as degenerate structures like plates of arbitrary shape and arches. Furthermore, Tornabene studied a general procedure for the structural assessment of arbitrary shapes.

The validity of these models has been proven for the prediction of the static and dynamic behaviour of several structures for different engineering applications. An interesting aspect studied by Tornabene accounts for an efficient post-processing technique to derive the three-dimensional response of structures with a high level of accuracy starting from a computationally efficient two-dimensional approach. This procedure has been verified to provide useful results for different structural design purposes, also focusing on the delamination and fracturing processes in composite materials.

Innovative and Smart Materials

Through-the-thickness variation of the volume fraction in a layered FGM structure.

One of the most interesting research aspects developed by Tornabene relies on the investigation of advanced innovative materials, with a particular attention to granular composites like Functionally Graded Materials (FGMs), characterized by a smooth variation of the mechanical properties. In 2009, Tornabene proposed a five-parameter enhanced law to define the through-the-thickness distribution of the FGM volume fraction, including different existing models from literature as subcases. Thanks to his studies, it has been shown that a combined composite material can assume improved dynamic properties with respect to the original constituents, differently from a mere intermediate structural response. Moving from FGMs, Tornabene has also focused on reinforcements with Carbon Nanotubes (CNTs), taking into account the effects of different nanofiber agglomerations.

The development of enhanced materials has always played a key role in Tornabene research. In last recent years, he developed some structural models of laminated structures made of lattice layers, characterized by a typical softcore behaviour. Furthermore, original studies on the so-called Variable Angle Tow (VAT) composites have been improved in order to account for a three-dimensional variation of the material properties within structures, even in presence of different defects and porosities.

Computational Mechanics and Numerical Techniques

Tornabene is known in the scientific academy for his extensive use of advanced numerical methods for the solution of several structural models. More specifically, he adopted the GDQ approach developed by Shu for the solution of several linear and nonlinear problems including the statics, dynamics, and fracture mechanics.

The main issue solved by Tornabene in these studies stems form the possibility to solve differential problems directly in a strong form for structures characterized by an arbitrary shape. More specifically, the Strong Formulation Finite Element Method (SFEM) developed by the author accounts for a decomposition of the physical domain and the direct application of the GDQ numerical technique within each discretized element, mapped in the computational space. This strong form approach differs from classical finite element procedures defined in a weak form. Several practical applications on the static and dynamic behavior of plates, membranes, plane stress and strain states can be found in literature, showing the stability and reliability of this numerical technique, against higher demanding approaches from literature.

Other research topics

The scientific production by Tornabene also accounts for the effect of singularities and inclusions within materials and structures. Above all, he applied several numerical techniques like the GDQ and the Extended Finite Element Method (XFEM) for the study of cracking processes within anisotropic materials. Furthermore, he studied some issues related to the delamination phenomena in composite materials. Above all, he focused his attention on the numerical optimization of some fracture mechanics models with a reduced computational effort, to study heterogeneous materials and standard composite specimens.

Tornabene is currently working on the structural modelling of smart materials, taking into account any possible coupling effect in multifield problems.

Curiosity

Francesco Tornabene is an estimator of J.R.R. Tolkien and of The Lord of the Rings saga. For this reason, he has been named by his students with the nickname “The Lord of the Shells and Beyond” because of his readings and primary research topic. To this purpose, at the beginning of his most important book on shell structures the writes: “One Book for the Lord of the Shells on his differential throne. One Book to rule all the shells, one Book to find them, one Book to bring them and all in the theory bind them. In the land of Shell-wood where the Truth lies”

Titles and Awards

• 35th position in the Top Italian Scientists List for the Engineering Area, January 2017.
• Member of the International Research Centre on Mathematics and Mechanics of Complex Systems, June 2018.
• Member of the European Academy of Sciences, July 2018.
• Highly Cited Researcher by Clarivate Analytics, November 2018.
• Ambassador of Bologna Award, 7 February 2019.
• Added to the 100000 Top Scientists List, August 2019.
• Highly Cited Researcher by Clarivate Analytics, November 2019.
• Highly Cited Researcher by Clarivate Analytics, November 2020.

List of Selected Publications

In the following some selected references from the Tornabene scientific production are reported. The complete scientific production of Tornabene can be found in the most popular international scientific databases. Furthermore, Tornabene presented his results in a series of national and International Conferences, and he has been invited for some plenary lectures for his studies.

Scientific Articles

• Tornabene, F. (2009). Free vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution. Computer Methods in Applied Mechanics and Engineering, 198(37-40), 2911-2935.

• Tornabene, F., Fantuzzi, N., Ubertini, F., & Viola, E. (2015). Strong formulation finite element method based on differential quadrature: a survey. Applied Mechanics Reviews, 67(2).

• Tornabene, F., Viola, E., & Inman, D. J. (2009). 2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures. Journal of Sound and Vibration, 328(3), 259-290.

• Tornabene, F., Fantuzzi, N., Bacciocchi, M., & Viola, E. (2016). Effect of agglomeration on the natural frequencies of functionally graded carbon nanotube-reinforced laminated composite doubly-curved shells. Composites Part B: Engineering, 89, 187-218.

• Tornabene, F., Fantuzzi, N., Viola, E., & Batra, R. C. (2015). Stress and strain recovery for functionally graded free-form and doubly-curved sandwich shells using higher-order equivalent single layer theory. Composite Structures, 119, 67-89.

• Tornabene, F., Fantuzzi, N., Viola, E., & Carrera, E. (2014). Static analysis of doubly-curved anisotropic shells and panels using CUF approach, differential geometry and differential quadrature method. Composite Structures, 107, 675-697.

• Tornabene, F., & Ceruti, A. (2013). Free-form laminated doubly-curved shells and panels of revolution resting on Winkler-Pasternak elastic foundations: a 2-D GDQ solution for static and free vibration analysis.

• Tornabene, F., & Viola, E. (2009). Free vibration analysis of functionally graded panels and shells of revolution. Meccanica, 44(3), 255-281.

• Tornabene, F., Bacciocchi, M., Fantuzzi, N., & Reddy, J. N. (2019). Multiscale approach for three‐phase CNT/polymer/fiber laminated nanocomposite structures. Polymer composites, 40(S1), E102-E126.

• Tornabene, F., & Reddy, J. N. (2013). FGM and laminated doubly-curved and degenerate shells resting on nonlinear elastic foundations: a GDQ solution for static analysis with a posteriori stress and strain recovery. Journal of Indian Institute of Science, 93(4), 635-688.

National Monographs

• F. Cesari, F. Tornabene (2011) - Esercizi di Meccanica delle Strutture: I Materiali Compositi, Pitagora, Bologna. ISBN: 88-371-1844-9.

• F. Tornabene (2012) - Meccanica delle Strutture a Guscio in Materiale Composito. Il metodo Generalizzato di Quadratura Differenziale, Esculapio, Bologna. ISBN: 978-88-7488-527-5.

• F. Tornabene, R. Dimitri (2015) - Stabilità dell’Equilibrio Elastico, Esculapio, Bologna. ISBN: 978-88-7488-845-0.

• F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola (2015) - Strutture a Guscio in Materiale Composito I. Geometria Differenziale. Teorie di Ordine Superiore, Esculapio, Bologna. ISBN: 978-88-7488-855-9. ISSN: 2421-2822.

• F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola (2015) - Strutture a Guscio in Materiale Composito II. Quadratura Differenziale e Integrale. Elementi Finiti in Forma Forte, Esculapio, Bologna. ISBN: 978-88-7488-856-6. ISSN: 2421-2822.

• F. Tornabene (2017) - Teoria delle Strutture a Guscio in Materiale Composito, Esculapio, Bologna. ISBN: 978-88-9385-000-1. ISSN: 2421-2822.

International Monographs

• F. Tornabene, N. Fantuzzi (2014) - Mechanics of Laminated Composite Doubly-Curved Shell Structures. The Generalized Differential Quadrature Method and the Strong Formulation Finite Element Method, Esculapio, Bologna. ISBN: 978-88-7488-687-6.

• F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola (2016) - Laminated Composite Doubly-Curved Shell Structures I. Differential Geometry. Higher-Order Structural Theories, Esculapio, Bologna. ISBN: 978-88-7488-957-0. ISSN: 2421-2822.

• F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola (2016) - Laminated Composite Doubly-Curved Shell Structures II. Differential and Integral Quadrature. Strong Formulation Finite Element Method, Esculapio, Bologna. ISBN: 978-88-7488-958-7. ISSN: 2421-2822.

• F. Tornabene, N. Fantuzzi (2017) - Theory of Laminated Composite Doubly-Curved Shell Structures, Esculapio, Bologna. ISBN: 978-88-9385-001-8. ISSN: 2421-2822.

• F. Tornabene, N. Fantuzzi, M. Bacciocchi (2018) - DiQuMASPAB: Differential Quadrature for Mechanics of Anisotropic Shells, Plates, Arches and Beams. User Manual, Esculapio, Bologna. ISBN: 978-88-938-5063-6. ISSN: 2421-2822.

• F. Tornabene, M. Bacciocchi (2018) - Anisotropic Doubly-Curved Shells - Higher-Order Strong and Weak Formulations for Arbitrarily Shaped Shell Structures, Esculapio, Bologna. ISBN: 978-88-9385-080-3. ISSN: 2421-2822.

Curatorships

• E. Viola, F. Tornabene (2007) - Dynamical Analysis of Spherical Shell Structural Elements Using the First-order Shear Deformation Theory, Mechanical Vibration: Where do we stand?, CISM Courses and Lectures no. 488, 17-41, ed. by I. Elishakoff, Springer - Wien, New York.

• A.J.M. Ferreira, E. Viola, F. Tornabene (2015) - International Conference on Shells, Plates and Beams Esculapio, Bologna. ISBN: 978-88-7488-886-3. ISSN: 2421-2822.

• A.J.M. Ferreira, A.M.A. Neves, E. Viola, F. Tornabene, N. Fantuzzi (2016) - 2nd International Conference on Mechanics of Composites, Esculapio, Bologna. ISBN: 978-88-7488-963-1. ISSN: 2421-2822.

• A.J.M. Ferreira, A.M.A. Neves, E. Viola, F. Tornabene, N. Fantuzzi (2016) - 19th International Conference on Composite Structures, Esculapio, Bologna. ISBN: 978-88-7488-977-8. ISSN: 2421-2822.

• A.J.M. Ferreira, E. Viola, F. Tornabene, N. Fantuzzi (2017) – 3rd International Conference on Mechanics of Composites, Esculapio, Bologna. ISBN: 978-88-9385-029-2. ISSN: 2421-2822.

• A.J.M. Ferreira, W. Larbi, J.-F. Deu, F. Tornabene, N. Fantuzzi (2017) - 20th International Conference on Composite Structures, Esculapio, Bologna. ISBN: 978-88-9385-041-4. ISSN: 2421-2822.

• A.J.M. Ferreira, F. Tornabene, N. Fantuzzi, E. Viola (2018) – 21th International Conference on Composite Structures, Esculapio, Bologna. ISBN: 978-88-9385-079-7. ISSN: 2421-2822.

• F. Tornabene, R. Dimitri (2021) - Advanced Theoretical and Computational Methods for Complex Materials and Structures, MDPI 2021. ISBN: 978-3-0365-1118-4 (Hbk), ISBN: 978-3-0365-1119-1 (PDF).

• S. Chakraverty, F. Tornabene, J.N. Reddy (2021) - Modeling and Computation in Vibration Problems, Volume 1: Numerical and Semi-Analytical Methods, IOP 2021. ISBN: 978-0-7503-3481-5.

• S. Chakraverty, F. Tornabene, J.N. Reddy (2021) - Modeling and Computation in Vibration Problems: Soft Computing and Uncertainty, IOP Publishing Ltd 2021. ISBN: 978-0-7503-3485-3.

• F. Tornabene, R. Dimitri (2022) - Recent Advances in Theoretical and Computational Modeling of Composite Materials and Structures, MDPI 2022. ISBN: 978-3-0365-4261-4 (Hbk), ISBN: 978-3-0365-4262-1 (PDF).