The Hamiltonian Structure of Nonlinear Elasticity: The Convective Representation of Solids, Rods, and Plates,
Abstract
It is our belief that a thorough understanding of the mathematical underpinnings of elasticity is crucial to its analytical and numerical implementation. For example, in the analysis of rotating structures, if one attempts to couple geometrically inexact models, obtained by linearization or other approximations to rotating rigid bodies, one can easily get serious artificial softening effects that can significantly alter numerical results; see Simo and Vu-Quoc for a discussion (compare equations of that paper). In this paper, we consider geometrically exact models, such as the Kirchhoff-Love-Reissner-Antman model for rods and its counterpart for plates and shells. These models take into account shear and torsion as well as the usual bending effects in traditional rod and plate models. Our purpose is to systematically develop the Hamiltonian structure for the dynamics of these models in the convective representation. The convective representation is chosen for its computational convenience and for our planned coupling of these models to the dynamics of rigid body motion, as in Krishnaprasad and Marsden. One of the topics that is of importance in the foundations of elasticity is a geometric formulation of the equations in Hamiltonian form.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1986
- Accession Number
- ADA187200
Entities
People
- Jerrold E. Marsden
- Juan C. Simo
- P.S.Krishnaprasad
Organizations
- Stanford University