Maqola

Conservation laws of linear elasticity in stress formulations

Shaofan LiDepartment of Civil and Environmental Engineering, University of California, Berkeley, CA 94720, USA ()Anurag GuptaDepartment of Civil and Environmental Engineering, University of California, Berkeley, CA 94720, USA ()Xanthippi MarkenscoffDepartment of Applied Mechanics and Engineering Science, University of California, San Diego, La Jolla, CA 92093, USA

2004en

ABI

Annotatsiya

In this paper, we present new conservation laws of linear elasticity which have been discovered. These newly discovered conservation laws are expressed solely in terms of the Cauchy stress tensor, and they are genuine, non–trivial conservation laws that are intrinsically different from the displacement conservation laws previously known. They represent the variational symmetry conditions of combined Beltrami–Michell compatibility equations and the equilibrium equations. To derive these conservation laws, Noether's theorem is extended to partial differential equations of a tensorial field with general boundary conditions. By applying the tensorial version of Noether's theorem to Pobedrja's stress formulation of three–dimensional elasticity, a class of new conservation laws in terms of stresses has been obtained.

Hali tarjima qilinmagan

Identifikatorlar

DOI: 10.1098/rspa.2004.1347

Iqtiboslar va manbalar

9 ta iqtibos0 ta foydalanilgan manba

Koʻrsatkichlar — AkademScholar