Analysis of errors caused by incomplete knowledge of material data in mathematical models of elastic media

Dr. Olli Mali

May 18, 2011, 10:30 a.m. HF 136

We study the effects that incompletely known data introduces to problems in continuum mechanics. In particular, we are interested in the case when parameters of the media in constitutive laws are not completely known.

Our analysis is based on deviation estimates, which are functionals that allow us to study the distance between an arbitrary function from the energy space and the exact solution of the problem. For the Kirchhoff-Love arch model, deviation estimates are derived for the first time. Since the data is not unique, we have a set of solutions instead of a single function. For a certain class of problems, we present estimates for the radius of the solution set, where estimates depend on the problem data and accuracy by which the data is known. For linear isotropic elasticity problem, we show that for certain type of boundary conditions the elastic energy becomes very sensitive with respect to small variations in Poisson ratio at the incompressibility limit. This phenomena may be significant enough to render quantitative analysis meaningless even relatively far from the limit.