Abstract
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.
Highlights
1 Introduction It is well known that the presence of inclusions as well as of cracks in an elastic body can cause a high stress concentration
Problems for different models of elastic bodies containing rigid inclusions and cracks with both linear and nonlinear boundary conditions have been under active study; see [ – ]
The formula for the shape derivative of the energy functional is obtained for the equilibrium problem for an elastic body with a delaminated thin rigid inclusion [ ]
Summary
It is well known that the presence of inclusions as well as of cracks in an elastic body can cause a high stress concentration. Problems for different models of elastic bodies containing rigid inclusions and cracks with both linear and nonlinear boundary conditions have been under active study; see [ – ]. A framework for two-dimensional elasticity problems with nonlinear Signorini-type conditions on a part of boundary of a thin delaminated rigid inclusion is proposed in [ ]. The formula for the shape derivative of the energy functional is obtained for the equilibrium problem for an elastic body with a delaminated thin rigid inclusion [ ]. Due to the presence of a rigid inclusion in the plate, restrictions of the functions describing displacements χ to the domain ωt satisfy a special kind of relations. The variational formulation describing the equilibrium state for the elastic plate with the volume delaminated rigid inclusion can be formulated as follows: find ξt = (Ut, ut) ∈ Kt such that
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
