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Lie Group Symmetry Analysis for Granular Media Stress Equations by I. Kenneth Johnpillai; Scott W. McCue; James M. Hill is a Mathematics article available to read on EtoBox.

What is Lie Group Symmetry Analysis for Granular Media Stress Equations about?

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb-Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction φ and gravity g) it is found there are three

Who reads Lie Group Symmetry Analysis for Granular Media Stress Equations?

Author

I. Kenneth Johnpillai; Scott W. McCue; James M. Hill

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-247X)

Published

2005

Language

EN

Field

Mathematics (Physical Sciences)