Existence of an optimal size of a delaminated rigid inclusion embedded in the Kirchhoff-Love plate

Boundary value problems

Nyurgun Lazarev¹ 

[1] North-Eastern Federal University, Yakutsk, Russia

关键词: crack;    plate;    rigid inclusion;    nonpenetration condition;    variational inequality;    74G55;    49J40;    49J30;   

DOI  :  10.1186/s13661-015-0437-y

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We consider equilibrium problems for an inhomogeneous plate with a crack situated at the inclusion-matrix interface. The matrix of the plate is assumed to be elastic. The boundary condition on the crack curve are given in the form of inequalities and describes the mutual nonpenetration of the crack faces. We analyze the dependence of solutions on the size of rigid inclusion. The existence of the solution to the optimal control problem is proved. For that problem the cost functional characterizes the deviation of the displacement vector from a given function, while the size parameter of rigid inclusion is chosen as the control function.

【 授权许可】

CC BY