A derivation of the compatibility conditions for a continuum with rigid structure undergoing finite deformations is proposed. The geometry of the Lie group of frame changes is used. The compatibility conditions are deduced by requiring the involutiveness of a distribution associated to the strain: their relationship with the Maurer-Cartan equations of the group of frame changes is demonstrated. Applications to micropolar and Cauchy continua are given.
Teresi, L., Tiero, A. (1997). Lie Groups and the Compatibility Conditions for Continua with Rigid Structure. INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 35(12/13), 1195-1202 [10.1016/S0020-7225(97)00105-5].
Lie Groups and the Compatibility Conditions for Continua with Rigid Structure
TERESI, Luciano;
1997-01-01
Abstract
A derivation of the compatibility conditions for a continuum with rigid structure undergoing finite deformations is proposed. The geometry of the Lie group of frame changes is used. The compatibility conditions are deduced by requiring the involutiveness of a distribution associated to the strain: their relationship with the Maurer-Cartan equations of the group of frame changes is demonstrated. Applications to micropolar and Cauchy continua are given.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
