Investigation of the shapes of cuts in a plate in contact with a rigid stamp

Akmaral Abdigaliyeva, Venera Bigaliyeva, Sharaina Zholdassova, Daryn Shabdirov, Ainur Shagayeva

E3S Web of Conferences, 2021

Full text Open access: Gold Metadata (CSL-JSON)

DOI 10.1051/e3sconf/202128801026

Data confidence 70 medium

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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.