A theory of pseudo-rigid bodies
Friday, November 5, 2004 - 4:30pm - 5:00pm
Jim Casey (University of California, Berkeley)
Bodies that are somehow capable of keeping their deformation fields homogeneous have been studied extensively in the literature. Such pseudo-rigid bodies, or Cosserat points, have been used successfully in a variety of applications. The main question addressed in this lecture is: How, in principle, can a 3-dimensional continuum, subjected to arbitrary applied loads, keep its deformation field homogeneous? The homogeneity condition is regarded as a global constraint, and a system of indeterminate reactive stresses is introduced. The remaining part of the stress tensor is specified by a constitutive equation. The reactive stresses play the same role as in rigid body dynamics. It is also shown how a pseudo-rigid body can be represented by a point moving in a 12-dimensional Euclidean space, the metric of which is determined by the radius of gyration of the body. In the presence of holonomic constraints, the configuration manifold is Riemannian, and a set of Lagrange's equations emerge as the covariant components of the governing balance equation.