An Intrinsic Geometric Formulation of the Equilibrium Equations in Continuum Mechanics. Issue 1 (21st October 2015)

• Record Type: Journal Article
• Authors: Eugster, Simon R.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 15:Issue 1(2015)
• Page Start: 289
• Page End: 290
• Publication Date: 2015-10-21
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201510135
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: The theory of invariant continuum mechanics is based on the concept that forces and stresses are defined as elements of the cotangent bundle of the configuration manifold. While body and physical space are modeled as differentiable manifolds, the infinite dimensional configuration manifold is given by all configurations of the body in the physical space. In this paper a virtual work principle is postulated which leads together with an induced traction stress and Stokes' theorem directly to the local equilibrium equations and the traction boundary conditions. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)