This comprehensive textbook compiles cutting-edge research on beams and circular plates, covering theories, analytical solutions, and numerical solutions of interest to students, researchers, and engineers working in industry. Detailing both classical and shear deformation theories, the book provides a complete study of beam and plate theories, their analytical (exact) solutions, variational solutions, and numerical solutions using the finite element method.

Beams and plates are some of the most common structural elements used in many engineering structures. The book details both classical and advanced (i.e., shear deformation) theories, scaling in complexity to aid the reader in self-study, or to correspond with a taught course. It covers topics including equations of elasticity, equations of motion of the classical and first-order shear deformation theories, and analytical solutions for bending, buckling, and natural vibration. Additionally, it details static as well as transient response based on exact, the Navier, and variational solution approaches for beams and axisymmetric circular plates, and has dedicated chapters on linear and nonlinear finite element analysis of beams and circular plates.

Theories and Analyses of Beams and Axisymmetric Circular Plates will be of interest to aerospace, civil, materials, and mechanical engineers, alongside students and researchers in solid and structural mechanics.

chapter 1|26 pages

Mechanics Preliminaries

chapter 2|34 pages

Energy Principles and Variational Methods

chapter 3|90 pages

The Classical Beam Theory

chapter 5|82 pages

Third-Order Beam Theories

chapter 6|52 pages

Classical Theory of Circular Plates

chapter 7|40 pages

First-Order Theory of Circular Plates

chapter 8|20 pages

Third-Order Theory of Circular Plates

chapter 9|72 pages

Finite Element Analysis of Beams

chapter 10|38 pages

Finite Element Analysis of Circular Plates