Contents

1. A One-Dimensional Beam Metamodel.2. Straight Beams.3. Curved Beams.4. Internally Constrained Beams.5. Flexible Cables.6. Stiff Cables.7. Locally-Deformable Thin-Walled Beams.8. Distortion-Constrained Thin-Walled Beams.

Contents

1. A One-Dimensional Beam Metamodel.2. Straight Beams.3. Curved Beams.4. Internally Constrained Beams.5. Flexible Cables.6. Stiff Cables.7. Locally-Deformable Thin-Walled Beams.8. Distortion-Constrained Thin-Walled Beams.

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

This concise text introduces the reader to the use of perturbation methods, able to investigate nonlinear phenomena in continuous (not only discrete) mechanical systems. Distinct from the classic books on perturbation methods, the algorithms are directly illustrated for continuous systems, referring to a very simple case-study as well as to a metamodel, for which Statics, Buckling, Dynamics and Bifurcation behavior are quickly analyzed. Moreover, fundamental mechanical aspects are discussed in dealing with applications. Concepts herein are reinforced with worked examples at the end the book, relevant to several continuous systems. 

Contents

1. A One-Dimensional Beam Metamodel.2. Straight Beams.3. Curved Beams.4. Internally Constrained Beams.5. Flexible Cables.6. Stiff Cables.7. Locally-Deformable Thin-Walled Beams.8. Distortion-Constrained Thin-Walled Beams.

Contents

1. A One-Dimensional Beam Metamodel.2. Straight Beams.3. Curved Beams.4. Internally Constrained Beams.5. Flexible Cables.6. Stiff Cables.7. Locally-Deformable Thin-Walled Beams.8. Distortion-Constrained Thin-Walled Beams.

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

This concise text introduces the reader to the use of perturbation methods, able to investigate nonlinear phenomena in continuous (not only discrete) mechanical systems. Distinct from the classic books on perturbation methods, the algorithms are directly illustrated for continuous systems, referring to a very simple case-study as well as to a metamodel, for which Statics, Buckling, Dynamics and Bifurcation behavior are quickly analyzed. Moreover, fundamental mechanical aspects are discussed in dealing with applications. Concepts herein are reinforced with worked examples at the end the book, relevant to several continuous systems.