General Concepts of Stress and Strain

In extending the direct method of stress analysis presented in previous modules to geometrically more complex structures, it will be convenient to have available somewhat more general mathematical statements of the kinematic, equilibrium, and constitutive equations; this is the objective of the present chapter. These equations also form the basis for more theoretical methods in stress analysis, as well as for numerical approaches such as the finite element method. We will also seek to introduce some of the notational schemes used widely in the technical literature for such entities as stress and strain. Depending on the specific application, both index and matrix notations can be very convenient; these are described in a separate module.