Elastic rods

Abstract

Take an arbitrary plane figure S that is connected (but need not be simply connected). By moving this figure along a smooth curve c(x) so that c(x) always remains orthogonal to S and cuts its centroid, we fill some domain B in the three-dimensional Euclidean point space ɛ. (Figure 4.1). A linear elastic body occupying the domain B in its stress-free undeformed state is called an elastic rod, the curve c(x) its central line, and S its cross section.