Andrianov I.V., Awrejcewicz J., Danishevs’kyy V.V., Ivankov A.O. Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions

Wiley, 2014. — 288 p. — ISBN: 1118725190.The first part of this book introduces the theory and application of asymptotic methods and includes a series of approaches that have been omitted or not rigorously treated in the existing literature. These lesser known approaches include the method of summation and construction of the asymptotically equivalent functions, methods of small and large delta, and the homotopy perturbations method.
The second part…
Key features:
-Includes analytical solving of mixed boundary value problems
-Introduces modern asymptotic and summation procedures
-Presents asymptotic approaches for nonlinear dynamics of rods, beams and plates
-Covers statics, dynamics and stability of plates with mixed boundary conditions
-Explains links between the Adomian and homotopy perturbation approaches
Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions is a comprehensive reference for researchers and practitioners working in the field of Mechanics of Solids and Mechanical Engineering, and is also a valuable resource for graduate and postgraduate students from Civil and Mechanical Engineering.Asymptotic Approaches
Asymptotic Series and Approximations
Some Nonstandard Perturbation Procedures
Summation of Asymptotic Series
Some Applications of PA
Matching of Limiting Asymptotic Expansions
Dynamical Edge Effect Method
Continualization
Averaging and Homogenization
Computational Methods for Plates and Beams with Mixed Boundary ConditionsNatural Vibrations of Beams and Plates
Nonlinear Vibrations of Rods, Beams and Plates
SSS of Beams and Plates
Forced Vibrations of Beams and Plates
Stability of Beams and Plates
Some Related Problems
Links between the Adomian and Homotopy Perturbation Approaches