Italian Workshop on
Shell and Spatial Structures
Funicularity in elastic domes: Coupled effects of shape and thickness
Alberto Carpinteri, Federico Accornero (Politecnico di Torino, Italy)
An historical overview is presented concerning the theory of shell structures and thin domes. Early conjectures proposed by, among others, French, German, and Russian Authors are discussed [1,2]. Static and kinematic matrix operator equations are formulated explicitly in the case of shells of revolution and thin domes [3,4]. It is realized how the static and kinematic matrix operators are one the adjoint of the other, and then it is rigorously demonstrated through the definition of stiffness matrix and the application of virtual work principle. In this context, any possible omission present in the previous approaches becomes evident. As regards thin shells of revolution (thin domes), the elastic problem results to be internally statically-determinate, in analogy to the case of curved beams, being characterized by a system of two equilibrium equations in two unknowns. Thus, the elastic solution can be obtained, just based on the equilibrium equations and independently of the shape of the membrane itself. The same cannot be affirmed for the unidimensional elements without flexural stiffness (ropes). Generally speaking, the static problem of elastic domes is governed by two parameters, the constraint reactions being assumed to be tangential to meridians at the dome edges: the shallowness ratio and the thickness of the dome. On the other hand, when the dome thickness tends to zero, the funicularity emerges and prevails, independently of the shallowness ratio or the shape of the dome. When the thickness is finite, an optimal shape is demonstrated to exist, which minimizes the flexural regime if compared to the membranal one.
References
[1] A. Carpinteri, F. Accornero, “Static-kinematic duality in the shells of revolution: Historical aspects and present developments”, Archive of Applied Mechanics, Vol. 89, pp. 2313–2320, 2019.
[2] K.E. Kurrer, The History of the Theory of Structures. From Arch Analysis to Computational Mechanics, Ernst & Sohn, Berlin, 2008.
[3] A. Carpinteri, "Static-kinematic duality in beams, plates, shells and its central role in the finite element method ", Curved and Layered Structures, Vol. 4, pp. 38-51, 2017.
[4] A. Carpinteri, Advanced Structural Mechanics, CRC, New York, 2017.
Alberto Carpinteri
Alberto Carpinteri received his Doctoral Degrees in Nuclear Engineering cum Laude (1976) and in Mathematics cum Laude (1981) from the University of Bologna (Italy). After two years at the Consiglio Nazionale delle Ricerche, he was appointed Assistant Professor at the University of Bologna in 1980.
He moved to the Politecnico di Torino in 1986 as a full professor, and became the Chair of Solid and Structural Mechanics, as well as the Director of the Fracture Mechanics Laboratory. During this period, he has held different positions of responsibility, among which: Head of the Department of Structural Engineering (1989-1995), and Founding Director of the Post-graduate School of Structural Engineering (1990-2014).
Prof. Carpinteri was a Visiting Scientist at Lehigh University, Pennsylvania, USA (1982-1983), and was appointed as a Fellow of several Academies and Professional Societies, among which: the European Academy of Sciences (2009-), the International Academy of Engineering (2010-), the Turin Academy of Sciences (2005-), the American Society of Civil Engineers (1996-). He is presently the Head of the Engineering Division in the European Academy of Sciences (2016-).
Prof. Carpinteri was the President of different Scientific Associations and Research Institutions: the International Congress on Fracture, ICF (2009-2013), the European Structural Integrity Society, ESIS (2002-2006), the International Association of Fracture Mechanics for Concrete and Concrete Structures, lA-FraMCoS (2004-2007), the Italian Group of Fracture, IGF (1998-2005), the National Research Institute of Metrology, INRIM (2011-2013).
Prof. Carpinteri was appointed as a Member of the Congress Committee of the International Union of Theoretical and Applied Mechanics, IUTAM (2004-2012), a Member of the Executive Board of the Society for Experimental Mechanics, SEM (2012-2014), a Member of the Editorial Board of fifteen international journals, the Editor-in-Chief of the journal “Meccanica” (Springer, IF=1.949), and is the author or editor of over 900 publications, of which more than 400 are papers in refereed international journals (Scopus H-Index=51, more than 9000 Citations) and 54 are books or journal special issues.
Prof. Carpinteri received numerous Honours and Awards: the Robert L'Hermite Medal from RILEM (1982), the Griffith Medal from ESIS (2008), the Swedlow Memorial Lecture Award from ASTM (2011), the Inaugural Paul Paris Gold Medal from ICF (2013), the Doctorate Honoris Causa in Engineering from theRussian Academy of Sciences (2016), the Frocht Award from SEM (2017), the Honorary Professorship from Tianjin University (2017), and the Founding Fellowship from the Indian Structural Integrity Society (2018), among others.