Rigid Structures with Point-Flexibility: Elasto-statics, Dynamics, Stability and Plastic Collapse

This book deals with kinematics and statics of rigid-body systems, lumped elasticity, variational principles, dynamics, stability and bifurcation, piece-wise linear (rigid-plastic or elasto-plastic) constitutive behavior, and geometrically nonlinear behavior. The presentation of the matter is strongly innovative: all the fundamental principles and methods, which are usually discussed for continuous media (namely, the displacement and force methods, the virtual work principle, the stationarity theorems of the total potential and complementary energies), are here illustrated for naturally discrete structures. Consequently, the fundamental problem of mechanics, which, for centenary worldwide tradition, is discussed in the context of the mathematical analysis, is here brought back to the algebra environment. Due to the strong simplifications of the calculus, the learner can focus his attention on the (complex) logical architecture of the linear and nonlinear elasticity theory (and later, of limit analysis), not being distracted by the mathematical difficulties inherent partial differential equations and boundary conditions. Moreover, he easily gains insight into the mechanical behavior of structures, which clearly emerges from the numerous examples presented.

The book is mainly devoted to undergraduate students. However, it is also meant as a reading successive to classic texts on continuous systems, useful to graduate and Ph.D. students to deepen their knowledge of general principles and methods of structural mechanics.

Angelo Luongo is a professor (retired) of Solid and Structural Mechanics at L'Aquila University, Italy. He currently serves as an editor-in-chief of MDPI journal “CivilEng” and associate editor of Springer Journal "Nonlinear Dynamics." His research interests include linear and nonlinear dynamics, buckling and postbuckling, aeroelasticity, dynamic instability, perturbation methods, structural modeling. With Springer, he published the textbooks Stability and Bifurcation of Structures (2023) and Perturbation Methods and Nonlinear Phenomena (2024).

Achille Paolone is a professor of Structural Mechanics at Sapienza University of Rome, Italy. His research interests include structural dynamics, computational mechanics, structural identification and monitoring, seismic engineering, structural stability, and earthquake resistant structures. His extensive practical experience in structural engineering informs his teaching approach, connecting theoretical concepts to real-world applications.

Simona Di Nino holds a Ph.D. in Mathematics and Modeling and is currently an assistant professor of Solid and Structural Mechanics at the University of L'Aquila, Italy. Her research interests encompass linear and nonlinear dynamics, aeroelasticity, dynamic instability, perturbation methods, homogenization methods, masonry, and damage constitutive models. In 2023, she published the textbook Stability and Bifurcation of Structures with Springer.