This monograph covers new variational and projection methods to study the dynamics within solid structures. To cope with the underlying initial-boundary value problems, the method of integrodifferential relations is employed. Applications and examples in physics, mechanics and control engineering range from natural vibrations or forced motions of elastic and viscoelastic bodies to heat and mass transfer processes. ContentsGeneralized formulations of parabolic and hyperbolic problemsVariational principles in linear elasticityVariational statements in structural mechanicsRitz method for initial-boundary value problemsVariational and projection techniques with semi-discretizationIntegrodifferential approach to eigenvalue problemsSpatial vibrations of elastic beams with convex cross-sectionsDouble minimization in optimal control problemsSemi-discrete approximations in inverse dynamic problemsModeling and control in mechatronics
Georgy V. Kostin and Vasily V. Saurin, Institute for Problems in Mechanics, Russia.
"The book is well written and includes numerical examples at the end of each chapter. The book will be useful to teachers, students and researchers."Girish Kumar Ramaiah in: Zentralblatt MATH 1406.74001 "In summary, this book will be of interest to researchers in theoretical and computational solid mechanics. It is perhaps less appropriate for a crystallography audience."Gregory Chirikjian in: Acta Cryst. (2019). A75, 657