The Complementing Condition in Elasticity

Author

Lavanya Ramanan, University of Tennessee - KnoxvilleFollow

Date of Award

5-2014

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Henry C. Simpson

Committee Members

Mike Frazier, Jochen Denzler

Abstract

We consider a boundary value problem of nonlinear elasticity on a domain [omega] in R³ [3-dimensional space] and compute the Complementing Condition for the linearized equations at a point X₀ [x zero] on boundary of omega. We assume a stored energy function depending on the first and third invariants of the deformation F and that the strong-ellipticity condition holds in [omega] . A surface traction boundary condition is imposed at X_0.
The Complementing Condition is calculated from a system of 3 second-order ordinary differential equations (0 less than and equal to t less than infinity) with boundary conditions at t = 0 and constant coefficients; the condition is satisfied if and only if the only bounded exponential solution is trivial. We compute the Complementing Condition in terms of parameters in W.

Recommended Citation

Ramanan, Lavanya, "The Complementing Condition in Elasticity. " Master's Thesis, University of Tennessee, 2014.
https://trace.tennessee.edu/utk_gradthes/2748