Abstract
A mathematical model of a contact interaction between a plate and rigid stamp is derived taking into account physical and design details. The plate is considered to have a crack, that changes its form. The problem of the contact is evaluated based on the theory of variational inequalities. The shape of the stamp is assumed to be perpendicular to the plate surface and the Poisson’s ratio is between 0 and 0.5. Analytical formulation of the study consists of transformation equation, boundary conditions and integral equation. The result is used in maximization and minimization problems for choosing extremal shape of the vertical break in the plate.
Highlights
Dynamic contact problems of the theory of elasticity and plasticity have a wide range of applications
A variational approach to solving contact problems is based on the formulation of the boundary conditions of contact interaction in the form of variational inequalities with one-sided constraints
The section shape is described by an equation yy = εεεε(xx), xx ∈, containing a parameter εε
Summary
Dynamic contact problems of the theory of elasticity and plasticity have a wide range of applications. It is associated with the study of impact and penetration of obstacles, explosive and hydroexplosive stamping and mechanical processing of materials. It is found that for the contact problems with unknown contact area, a variational approach is effective [1,2,3,4]. A variational approach to solving contact problems is based on the formulation of the boundary conditions of contact interaction in the form of variational inequalities with one-sided constraints. The properties of the solution to the problem of contact of a plate without cuts with a rigid stamp were studied in [13]. The paper substantiates the fundamental possibility of finding extreme forms of sections
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.
