ADVANCED MECHANICS OF MATERIALS AND APPLIED ELASTICITY PDF
In this text, the boundary value problems for computing the displacement and stress
fields in solid bodies are formulated using both their differential and integral forms (see
Chapters 13 and 14). The latter include the principle of virtual work, Castigliano’s second
theorem, the theorem of minimum total potential energy, the weighted residual equation and
the modified weighted residual equation. The last three are suitable for obtaining numerical solutions of boundary value problems with the aid of a computer, using the finite element
method presented in Chapter 15.
With the exception of Chapter 16, where an introduction to plastic analysis of structures
is presented, throughout this text, we limit our attention to bodies made from isotropic
linearly elastic materials. Moreover, with the exception of Chapter 18, where an introduction
to elastic instability of structures is presented, we assume that the magnitude of the
deformation of each material particle of the bodies, which we are considering, is such that
the change of its geometry can be approximated by its components of the strain tensor which
are related to its components of displacement by linear relations.
This assumption linearizes
the boundary value problems involving bodies made from linearly elastic materials, that is,
renders the effect linearly related to the cause and permits superposition of the results.
The author wishes to thank Dr. Nikitas Skliros for typing and laying out the final version
of the manuscript and Mr. Nassos Papoutsis for drawing and labeling the figures. Moreover,
the author wishes to thank Ms. Cleo Avrithy for checking the solution presented in the
solution manual of the problems included at the ends of Chapters 1 to 10 and Ms. Isabella
Vassilopoulou for checking the solution presented in the solution manual of the problems
included at the ends of Chapters 11 and 13 to 17.