Stability and Bifurcation of Structures

This book overcomes the separation existing in literature between the static and the dynamic bifurcation worlds. It brings together buckling and post-buckling problems with nonlinear dynamics, the bridge being represented by the perturbation method, i.e., a mathematical tool that allows for solving static and dynamic problems virtually in the same way.

The book is organized as follows: Chapter one gives an overview; Chapter two illustrates phenomenological aspect of static and dynamic bifurcations; Chapter three deals with linear stability analysis of dynamical systems; Chapter four and five discuss the general theory and present examples of buckling and post-buckling of elastic structures; Chapter six describes a linearized approach to buckling, usually adopted in the technical literature, in which pre-critical deformations are neglected; Chapters seven to ten, analyze elastic and elasto-plastic buckling of planar systems of beams, thin-walled beams and plate assemblies, respectively; Chapters eleven to thirteen, illustrate dynamic instability phenomena, such as flutter induced by follower forces, aeroelastic bifurcations caused by wind flow, and parametric excitation triggered by pulsating loads. Finally, Chapter fourteen discusses a large gallery of solved problems, concerning topics covered in the book. An Appendix presents the Vlasov theory of open thin-walled beams.

The book is devoted to advanced undergraduate and graduate students, as well as engineers and practitioners. The methods illustrated here are immediately applicable to model real problems.

The Book

• Introduces, in a simple way, complex concepts of bifurcation theory, by making use of elementary mathematics
• Gives a comprehensive overview of bifurcation of linear and nonlinear structures, in static and dynamic fields

• Contains a chapter in which many problems are solved, either analytically or numerically, and results commented

  Introduces, in a simple way, complex concepts of bifurcation theory, by making use of elementary mathematics Gives a comprehensive overview of bifurcation of linear and nonlinear structures, in static and dynamic fields Contains a chapter in which many problems are solved, either analytically or numerically, and results commented

  Autorentext
  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.

  Inhalt
  Phenomenological aspects of the bifurcation of structures.- Linear stability and bifurcation.- Buckling and postbuckling of conservative systems.- The buckling theory of the pre-stressed structures.- Buckling of planar beams.- Buckling of open thin-walled beams.- Buckling of plates and prismatic shells.- Dynamic instability induced by follower forces.- Aeroelastic stability.- Parametric excitation.