Book Synopsis
This set of lecture notes and worked example problems covers topics in the application of variational and energy methods in mechanics. These are scalar based principles, as contrasted with vector approaches based on Newton’s 2nd Law. The Principle of Virtual Work is the foundation of the variational based approaches. Equilibrium and deformation equations based on virtual work and stationary potential energy are developed with applications to rods, bars, beams, frames, etc. Approximate solution methodologies derived from these techniques (e.g. Rayleigh Ritz and Finite Elements) are covered. An introduction to the use of the Calculus of Variations for continuous systems is included. These notes were developed for a one semester senior or beginning graduate level class in engineering. The author is Dr. John L. Turner, an adjunct professor at the University of Arizona.