Coefficient identification in Euler-Bernoulli equation from over-posed data

This is a study concerning the identification of the heterogeneous flexural rigidity of a beam governed by the steady-state Euler-Bernoulli fourth order ordinary differential equation. We use the method of Variational Imbedding (MVI) to deal with the inverse problem for the coefficient identification from over-posed data. The method is identifying the coefficient by approximating it with a piece-wise polynomial function. Several types of piece-wise polynomial functions are considered: piece-wise constant; linear spline; and cubic spline. It is observed in this study that the numerical solution of the variational problem coincides with the direct simulation of the original problem within the second order of approximation.