This book is intended for readers who wish to thoroughly learn the basic concepts required in understanding the
mechanics of deformation in solids. The topics covered in the book are taught at undergraduate level in courses often
named as Mechanics of Materials, Strength of Materials etc. to students of Mechanical, Civil, Applied
Mechanics and Materials engineering disciplines. However, the emphasis in such courses tend to be
more on application rather than understanding the involved concepts. Most of the books available in
the market are also designed that way. However, for students who desire to pursue higher studies or
sit in competitive exams after their undergraduate education, they will appreciate the style of the
present book. A great emphasis has been placed here on (i) deriving the theoretical concepts with full
mathematical rigor and (ii) further illustrating their application through several solved and unsolved problems.
The book will also be useful especially for Masters and PhD students working in the broad area of
Solid Mechanics and for teachers of undergraduate colleges in solidifying their grip over the subject.
The book relies heavily on the use of vectors and tensors in order to make the derivations concise
and big mathematical expressions compact which further help in elucidating the underlying physics
better. Students in second year of their college education may find it difficult to work with tensors.
Accordingly, the first chapter of the book has been carefully crafted to elucidate the various concepts
involving tensors and also introduce the mathematical language used in the book. Each chapter in the
book ends with long subjective-type solved examples to illustrate the concepts covered and further use
them in solving engineering problems. Likewise, several objective-type questions are also given at the
end of each chapter to help the readers in preparing for competitive exams. A link to my NPTEL
video lectures is also given for each section of the book in case a reader desires in learning through
video.
The various topics covered in the book are discussed according to the following outline. Chapter 1 introduces the
concepts of vectors, tensors and various mathematical operations involving them. Chapter 2 introduces the concepts
of traction vector, stress tensor, stress matrix and its transformation. In chapter 3, equilibrium equations of linear
elasticity are derived along with a discussion on boundary conditions. Chapter 4 comprehensively discusses the
various concepts involving stress tensor such as principal stress components, Mohr’s circle, stress invariants, stress
decomposition etc. In chapter 5, the concept of strain is introduced and is further generalized for arbitrary
deformation in three-dimensional solids. The mathematical formulas for various types of strains are also
derived here along with a discussion on strain compatibility conditions. Chapter 6 discusses linear
stress-strain relation in three-dimensional elastic solids for general anisotropic materials. The discussion
is later focused on isotropic materials. In chapter 7, cylindrical coordinate system is introduced and
the different components of stress and strain matrices in this coordinate system are also obtained.
The equations of elasticity are also rederived in this coordinate system. These derivations are later
used in solving various axisymmetric deformation problems such as extension, torsion and inflation of
solid and hollow cylinders. Chapter 8 discusses comprehensively beam bending - both uniform and
non-uniform as occurring in beams having symmetrical as well as unsymmetrical cross-sections. The concept
of shear center is also discussed later on and its formula is derived for thin and open cross-sections.
In chapter 9, beam theory is introduced for obtaining the transverse deflection of slender structures.
The Euler-Bernouli beam theory and the Timoshenko beam theory are both derived here. Buckling of
beams is then discussed. In chapter 10, energy methods is introduced and various concepts involving
it are discussed in detail. The chapter ends with illustrating how this method can be used to solve
complex beam deflection problems which otherwise cannot be solved using Euler-Bernouli or Timoshenko
beam theory in a conventional way. Finally, chapter 11 briefly discusses the various failure theories.
The book is a result of several years of my teaching at IIT Delhi. My own knowledge of the subject increased
manifold after rich interaction with students of IIT Delhi. I would like to express my heartfelt gratitude to my
teacher Prof. S.K. Roy Chowdhury who germinated in me the likings for Solid Mechanics while I took the
course Mechanics of Materials under him during my third semester at IIT Kharagpur. I would also
like to thank NPTEL which provided me with the platform to prepare and further decimate a video
lecture series on this topic - this immensely helped me in refining my own concepts and thinking of
alternate but simpler ways of explaining several topics. I would like to acknowledge the book Advanced
Mechanics of Solids by Prof. L.S. Srinath - few examples in the present book are taken from there
although their solutions have been prepared independently by me. I would also like to thank Prof.
Rajdip Nayek with whom I co-taught this course once and we then prepared solution to several of the
questions discussed in this book. Several of my students (especially Roushan Kumar, Siddhant Jain
and Mohit Garg) have immensely helped me in writing the book whose contributions are gratefully
acknowledged!
\begin {equation} \hspace {140mm}\text {Ajeet Kumar}\notag \end {equation}