时间：2024年12月13日（周五） 16:10-17:40

Time: 16:10-17:40, Friday, December 13, 2024

地点：西湖大学云谷校区E10-205

Venue: E10-205, Yungu Campus

主持人: 西湖大学工学院 姜汉卿教授

Host: Prof. Hanqing Jiang, Chair Professor, Westlake University

语言：英文

Language: English

主讲嘉宾/Speaker：

Prof. Alberto Carpinteri

Chair Professor

Civil Engineering

Shantou University

Biography:

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  Chair Professor of Solid and Structural Mechanics, as well as the Director of the Fracture Mechanics Laboratory. During this period, he 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). After his retirement from the Politecnico di Torino in 2023, he became Chair Professor of Civil Engineering at Shantou University, Shantou-Guangdong, China.

Prof. Carpinteri was a Visiting Scientist at Lehigh University, Pennsylvania, USA (1982-1983), and was appointed as a Fellow of several Scientific Academies and Professional Institutions, 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 (1995-). He was the Head of the Engineering Division in the European Academy of Sciences (2016-2023).

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), as well as a Member of the Editorial Board of ten international journals, the Editor-in-Chief of the  International Journal “Meccanica” (Springer Nature), the Honorary Editor of the International Journal “Smart Construction & Sustainable Cities” (Springer Nature). He is the author or editor of over 1,000 publications, of which more than 500 are papers in refereed international journals (Google-Scholar H-Index=95, more than 36,000 Citations; Scopus H-Index=67, more than 17,000 Citations), and 59 are books or journal special issues.

 Prof. Carpinteri received numerous international 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 the Russian Academy of Sciences (2016), the Frocht Award from SEM (2017), the Honorary Professorship from Tianjin University (2017), the Founding Fellowship from the Indian Structural Integrity Society (2018), the “Pearl River” Professorship from Guangdong Province, Shantou University (2019), the Giuliano Preparata Medal from the International Society for Condensed Matter Nuclear Science  (2022), the George Irwin Medal from ASTM (2023), and the Honorary Professorship from Northeastern University, Shenyang (2024).

讲座摘要/Abstract:

Scope and distinctive feature of the lecture is that of proposing a new matrix- operator formulation of the Finite Element Method. The logical sequence of the topics makes it possible to introduce the complex subject with the minimum effort. The Finite Element Method is introduced on the basis of the Static-kinematic Duality in a very general, direct, and unified way. Such demonstration is totally original and is reported in the text books of the lecturer.

The mechanics of linear elastic bodies, and in particular of bars, beams, plates loaded in their middle plane, plates in flexure, arches, shells, ropes, and membranes, is studied adopting an original matrix-operator formulation, which is suitable for computational applications. The static, constitutive, and kinematic equations, once composed, provide a matrix-operator equation presenting the generalized displacement vector as its principal unknown. Constant reference is made to Duality, i.e., to the strict correspondence between Statics and Kinematics that emerges as soon as the two matrix-operators are recognised to be the adjoint of each other. In this context, it is easy to prove the mutual implication of Duality and Principle of Virtual Work. The Finite Element Method can be directly introduced as a discretization and interpolation procedure for the approximate solution of elastic problems, in both static and dynamic regimes, whatever are the dimensions of displacement vector and deformation vector, with or without intrinsic curvatures.

More in detail, after considering the case of 3-D body, for which static and kinematic matrices present only differential operators among their elements, resulting the transpose of each other (3X6 and 6X3 are the respective dimensions), the sequence continues with 1-D and 2-D cases, for which also algebraical (nondifferential) elements appear. In the case of rectilinear beam, the static matrix presents also the element –1, which is due to the well-known relationship between bending moment and shearing force (that are both internal actions), as well the kinematic matrix presents also the element +1, due to the relationship between shearing strain and rotation (where the former is a deformation and the latter a generalised displacement). In the case of curved beam, the two matrices present also the intrinsic curvature 1/r of the beam among their elements, and appear to be the transpose of each other except for the algebraical elements, which result to be the opposite of each other. We can affirm that these matrices are the adjoint of each other. The logical sequence continues with the circular plate in flexure, the cylindrical shell, the thin dome (membrane) of revolution, and the shell of revolution, the matrix of which contains the elements of the previous three structural geometries. In all these key cases, the static and kinematic matrices are the adjoint of each other.

An historical remark: the kinematic expression for the shearing strain along the meridian is easily defined according to Duality, whereas it was not in the classical treatments (Fluegge 1934, Timoshenko 1940, Novozhilov 1947).

Main conclusions:

（1）The change in algebraical sign of the nondifferential terms is due to the rule of integration by parts, which presents the sign minus before the integral just for the differential operators;

（2）The complex structure of the composite matrix-operator provided by the product of static, constitutive, and kinematic matrix-operators permits to recognise the identity between global stiffness matrix and Ritz-Galerkin matrix. In other terms, FEM strictly is a particular case of Ritz-Galerkin Method.    

讲座联系人/Contact:

工学院姜汉卿实验室 吕波

Lyubo@westlake.edu.cn