2011/06/01 by Frank L. Schadt, Frank Schadt, Schadt, Frank
Engineering · Mathematics · Physics and Astronomy · #Dynamics and Control of Mechanical Systems #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods for differential equations #Quantum chaos and dynamical systems #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1106.0130
openalex publication_date 2011/06/01 · arxiv created 2011/06/07 · arxiv updated 2011/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper presents a reformulation of some of the most basic entities and equations of linear elasticity - the stress and strain tensor, the Cauchy Navier equilibrium equations, material equations for linear isotropic bodies - in a modern differential geometric language using differential forms and lie derivatives. Similar steps have been done successfully in general relativity, quantum physics and electrodynamics and are of great use in those fields. In Elasticity Theory, however, such a modern differential geometric approach is much less common. Furthermore, existing reformulations demand a vast knowledge of differential geometry, including nonstandard entities such as vector valued differential forms and the like. This paper presents a less general but more easily accessible approach to using modern differential geometry in elasticity theory than those published up to now.