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.
Contents Generalized formulations of parabolic and hyperbolic problems Variational principles in linear elasticity Variational statements in structural mechanics Ritz method for initial-boundary value problems Variational and projection techniques with semi-discretization Integrodifferential approach to eigenvalue problems Spatial vibrations of elastic beams with convex cross-sections Double minimization in optimal control problems Semi-discrete approximations in inverse dynamic problems Modeling 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