PSI - Issue 59

Available online at www.sciencedirect.com Available online at www.sciencedirect.com ScienceDirect Structural Integrity Procedia 00 (2023) 000 – 000

www.elsevier.com/locate/procedia

ScienceDirect

Procedia Structural Integrity 59 (2024) 494–501 Structural Integrity Procedia 00 (2023) 000 – 000

www.elsevier.com/locate/procedia

2452-3216 © 2024 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of DMDP 2023 Organizers 10.1016/j.prostr.2024.04.070 2452-3216 © 2024 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of DMDP 2023 Organizers 2452-3216 © 2024 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of DMDP 2023 Organizers © 2024 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of DMDP 2023 Organizers Abstract The formulation and solution of the problem were carried out using linearized relations of the nonlinear elasticity theory. The predeformed plate was modeled by a prestressed layer. A rigid axisymmetric indenter, which is in contact with the plate, has a complex shape: it is consisting of a part of a plane and a paraboloid. The problem was reduced to the solution of a system of dual integral equations, which is carried out by representing the sought functions in the form of a partial series sum by Bessel functions with unknown coefficients. In order to determine these coefficients, finite systems of linear algebraic equations were constructed. In the article was analyzed the influence of the indenter shape, the plate thickness and its initial deformations on the magnitude and characteristics of contact stresses and vertical displacements on the plate surface. The analysis was carried out for the case of compressible (Bartenev – Khazanovich potential) and incompressible (harmonic-type potential) solids. Keywords: predeformed plate, prestressed layer, contact stresses, vertical displacements, complex shape indenter, dual integral equations 1. Introduction One of the most important stages of structural elements and machine parts design is calculation of its strength. In order to minimize calculation errors, you need to take into account the maximum number of factors that affect the contact interaction of bodies. Therefore, the presence of initial stresses and strains in contacting bodies should be taken into account. In the general case, solving problems of this type requires a nonlinear elasticity theory. However, for sufficiently high levels of initial deformations, linearized statements can be used. In particular, the linearized formulation was used by Lapusta et al (2008) to build a three-dimensional finite-element model aimed at studying microstrains in joints strengthened with isotropic and anisotropic fibers, by Mahesh et al (2021) to build a Abstract The formulation and solution of the problem were carried out using linearized relations of the nonlinear elasticity theory. The predeformed plate was modeled by a prestressed layer. A rigid axisymmetric indenter, which is in contact with the plate, has a complex shape: it is consisting of a part of a plane and a paraboloid. The problem was reduced to the solution of a system of dual integral equations, which is carried out by representing the sought functions in the form of a partial series sum by Bessel functions with unknown coefficients. In order to determine these coefficients, finite systems of linear algebraic equations were constructed. In the article was analyzed the influence of the indenter shape, the plate thickness and its initial deformations on the magnitude and characteristics of contact stresses and vertical displacements on the plate surface. The analysis was carried out for the case of compressible (Bartenev – Khazanovich potential) and incompressible (harmonic-type potential) solids. Keywords: predeformed plate, prestressed layer, contact stresses, vertical displacements, complex shape indenter, dual integral equations 1. Introduction One of the most important stages of structural elements and machine parts design is calculation of its strength. In order to minimize calculation errors, you need to take into account the maximum number of factors that affect the contact interaction of bodies. Therefore, the presence of initial stresses and strains in contacting bodies should be taken into account. In the general case, solving problems of this type requires a nonlinear elasticity theory. However, for sufficiently high levels of initial deformations, linearized statements can be used. In particular, the linearized formulation was used by Lapusta et al (2008) to build a three-dimensional finite-element model aimed at studying microstrains in joints strengthened with isotropic and anisotropic fibers, by Mahesh et al (2021) to build a VII International Conference “In -service Damage of Materials: Diagnostics and Prediction ” (DMDP 2023) Strength analysis of a predeformed plate in contact with a complex shape indenter Hryhorii Habrusiev*, Iryna Habrusieva, Borys Shelestovskyi Ternopil Ivan Puluj National Technical University, Ternopil, Ukraine VII International Conference “In -service Damage of Materials: Diagnostics and Prediction ” (DMDP 2023) Strength analysis of a predeformed plate in contact with a complex shape indenter Hryhorii Habrusiev*, Iryna Habrusieva, Borys Shelestovskyi Ternopil Ivan Puluj National Technical University, Ternopil, Ukraine * Corresponding author. Tel.: +38-093-471-45-25 E-mail address: habrusiev@gmail.com * Corresponding author. Tel.: +38-093-471-45-25 E-mail address: habrusiev@gmail.com