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

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 mathematicsGives a comprehensive overview of bifurcation of linear and nonlinear structures, in static and dynamic fieldsContains a chapter in which many problems are solved, either analytically or numerically, and results commented

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

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.

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

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 mathematicsGives a comprehensive overview of bifurcation of linear and nonlinear structures, in static and dynamic fieldsContains a chapter in which many problems are solved, either analytically or numerically, and results commented

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

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.