An inverse problem for estimation of bending stiffness in Kirchhoff–Love plates

This work deals with the development of a numerical method for solving an inverse problem for bending stiffness estimation in a Kirchhoff–Love plate from overdetermined data. The coefficient is identified using a technique called the Method of Variational Imbedding, where the original inverse problem is replaced by a minimization problem. The Euler–Lagrange equations for minimization comprise higher-order equations for the solution of the displacement and an equation for the bending stiffness. The correctness of the embedded problem is discussed. A difference scheme and a numerical algorithm for solving the parameter identification problem are developed. Numerical results for the obtained values of the bending stiffness as an inverse problem are presented.