Advanced Mechanics of Materials

Structural analysis and design today often incorporates anisotropy, inelastic strains, material non-homogeneity, material non-linearity, geometric non-linearity, shear in beams and plates, etc. These complexities were added to the classical theories of structural members over a long period of time resulting in large and baroque knowledge base that is a challenge to master for most students of mechanics. Logically synthesizing this tremendous knowledge in a single text is my primary objective for writing this book. The image shown on the front cover provides the mechanism of creating a logical framework for development of the simplest to the most advanced structural theories. Examples and post-text problems highlight the modularity of the logic and demonstrate the addition of complexities to the classical theories. The development of these advanced theories is demonstrated in two ways: the traditional differential equation approach and the variational calculus approach by which the potential energy is minimized. Problems of finite and infinite beams on elastic foundations are solved using influence functions. The last chapter on indicial notation along with variational calculus demonstrates the elegance and compactness of theory derivations covered in previous chapters. Traditional topics of three dimensional stress and strain transformation, failure theories, buckling, torsion of prismatic bars, are also covered. On my website madhuvable.org, I have posted a condensed version of this book, slides and review material. Along with my book on Intermediate Mechanics of Materials, an instructor will find all the topics that may be covered in any Advanced Mechanics of Materials course. A comparison of this book with other Advanced Mechanics of Materials books currently on the market can also be seen on the website.