Nonlinear Mechanics of Shells and Plates in Composite, Soft and Biological Materials

This book presents the most recent advances on the mechanics of soft and composite shells and their nonlinear vibrations and stability, including advanced problems of modeling human vessels (aorta) with fluid-structure interaction. It guides the reader into nonlinear modelling of shell structures in applications where advanced composite and complex biological materials must be described with great accuracy. To achieve this goal, the book presents nonlinear shell theories, nonlinear vibrations, buckling, composite and functionally graded materials, hyperelasticity, viscoelasticity, nonlinear damping, rubber and soft biological materials. Advanced nonlinear shell theories, not available in any other book, are fully derived in a simple notation and are ready to be implemented in numerical codes. The work features a blend of the most advanced theory and experimental results, and is a valuable resource for researchers, professionals and graduate students, especially those interested in mechanics, aeronautics, civil structures, materials, bioengineering and solid matter at different scales.

1. Classical nonlinear theories of elasticity of plates and shells; 2. Classical nonlinear theories of doubly curved shells; 3. Composite, sandwich, and functionally graded materials; 4. Nonlinear shell theory with thickness deformation; 5. Hyperelasticity of soft biological and rubber materials; 6. Nonlinear dynamics; 7. Viscoelasticity and damping; 8. Vibrations of rectangular plates; 9. Nonlinear stability and vibration of FGM rectangular plates under static and dynamic loads; 10. Nonlinear static and dynamic response of rectangular plates in rubber and biomaterial; 11. Vibrations of isotropic and laminated composite circular cylindrical shells; 12. Effect of boundary conditions on nonlinear vibrations of circular cylindrical shells; 13. Nonlinear static and dynamic response of a blood-filled and pressurized human aorta; 14. Nonlinear vibrations and stability of doubly curved shallow shells; 15. Nonlinear stability of circular cylindrical shells under static and dynamic axial loads.

Marco Amabili is Canada Research Chair Professor in Vibrations at the Department of Mechanical Engineering, McGill University, Montreal. Considered one of the most distinguished scientists in his field of research, he is the author of over 430 papers, many of which are published in prestigious refereed international journals, including Nature Communications, as well as the book Nonlinear Vibrations and Stability of Shells and Plates (Cambridge, 2008). Professor Amabili is a Fellow of the American Society of Mechanical Engineers and is a recipient of the Christophe Pierre Research Excellence Award from McGill University.