Kinematics

In three-dimensional continuum mechanics, the integral-gradient theorem, which is the basis of Green's transformation, often called “the divergence theorem,” is a tool of central importance. All the shapes of bodies should be such as to make the integral-gradient theorem apply whenever the fields integrated are smooth to the degrees ordinarily assumed. The first statement in the theorem makes the sets of finite perimeter a Boolean algebra with respect to intersection and union. This chapter discusses a theorem that relates sets of finite perimeter directly to the integral-gradient theorem. The chapter presents a local analysis of the equilibrium and motion of continuous media. © 1977, Academic Press, Inc.