This book by the late R D Mindlin is destined to become a classic introduction to the mathematical aspects of two-dimensional theories of elastic plates. It systematically derives the two-dimensional theories of anisotropic elastic plates from the variational formulation of the three-dimensional theory of elasticity by power series expansions. The uniqueness of two-dimensional problems is also examined from the variational viewpoint. The accuracy of the two-dimensional equations is judged by comparing the dispersion relations of the waves that the two-dimensional theories can describe with prediction from the three-dimensional theory. Discussing mainly high-frequency dynamic problems, it is also useful in traditional applications in structural engineering as well as provides the theoretical foundation for acoustic wave devices.
Sample Chapter(s)
Chapter 1: Elements of the Linear Theory of Elasticity (416 KB)
Contents:
- Elements of the Linear Theory of Elasticity
- Solutions of the Three-Dimensional Equations
- Infinite Power Series of Two-Dimensional Equations
- Zero-Order Approximation
- First-Order Approximation
- Intermediate Approximations
Readership: Researchers in mechanics, civil and mechanical engineering and applied mathematics.
