Mechanics of Elastic Solids

An alternative approach to solving boundary value problems in elasticity is explored: variational methods.The power of the principles of minimum potential energy and complementary energy is effectively demonstrated through illustrative examples of beam bending and Saint-Venant torsion, showcasing a selfconsistent approach to simplifying complex three-dimensional elasticity problems into more manageable two-dimensional or even one-dimensional models.Their direct applications to numerical solutions are illustrated via the Rayleigh-Ritz method.Mathematical tools, including index notation for tensors and two-and threedimensional integration by parts, are integrated into the chapters, emphasizing their applications over their mathematical intricacies.The rules for generalizing one-dimensional integration by parts to higher dimensions are provided.The second and third authors have utilized these lecture notes on the Mechanics of Elastic Solids as teaching materials in courses titled "Advanced Solid Mechanics" for graduate students.