Estimation of elastic parameters in a nonlinear elliptic model of a plate

摘要

We consider the estimation of an elastic parameter in a nonlinear von Karman model of large deformations of a thin plate with uniform cross-section but with variable Young's modulus. It is well known that these equations may possess multiple solutions, and thus the parameter-to-state mapping is no longer well defined. In spite of this, it is still possible to give meaning to a regularized output-least-squares formulation of the parameter estimation problem. We introduce a model error function and determine conditions under which a solution and its differentiability may be analyzed locally. We also discuss stability and the application of the augmented Lagrangian method in this case. If the conditions are not satisfied, we provide an analysis of the penalty method applied to the problem. Finally, we report the results of numerical experiments.