On modeling elastic bodies with defects
In this paper, the author considers some mathematical analysis problems on the equilibrium for 2D elastic bodies with thin defects, which are characterized with a damage parameter. Solution existence of the problems considered is proved, and different equivalent problem formulations are proposed. Dependence of solutions on the damage parameter and the defect length is investigated. The author derives a formula for the derivative of the energy functional with respect to the defect length and prove that the formula can be written in the form of an invariant integral. An optimal control problem is investigated with a cost functional equal to the derivative of the energy functional with respect to the defect length, and the damage parameter being a control function.
scientific article; zbMATH DE number 6855321