This series of 5 seminars will provide an introduction to the analysis of nonlinear problems in elasticity. Based on examples from recent research works and/or from daily life (such as the inflation of a cylindrical ballon, the shape of human hair, or the hexagonal patterns produced by the elastic Rayleigh-Taylor instability), we will derive the main methods applicable to nonlinear elasticity problems: the calculation of critical loads by a linear bifurcation analysis, the selection of buckling patterns using Koiter's method, the analysis of localized buckling using amplitude equations, etc. We will provide examples of both geometrical instabilities (as Euler's buckling) and material instabilities (as in the striction of bars and other localization phenomena).
1. Discrete nonlinear elasticity – Tuesday, April 17, 2018 at 12:00PM 115 Gates-Thomas
A quick and self-contained presentation of nonlinear elasticity is presented, for structures possessing a finite number of degrees of freedom. The different flavors of the equations of elasticity are reviewed, including those governing nonlinear equilibria, the linear(ized) theories of elasticity, the notions of elastic and geometric rigidities, buckling eigenvalue analysis, vibration analysis, etc. In this discrete setting the equations are very similar to (and much simpler than) their continuum counterpart. This introductory seminar provides a general overview of the following, more specialized topics.