# The use of IT technologies in the mechanics of deformable bodies.

### Abstract

The article is devoted to the research of two problems of contact interaction of prestressed bodies, namely: 1) the pressure of an elastic cylinder die upon an elastic layer and foundation with initial (residual) stresses; 2) contact interaction of elastic layer with initial stresses and prestressed coaxial cylinders with using the IT technologies. The authors developed a computer program and algorithm of numerical calculation components deflected mode of contacting bodies with initial stresses. In general, the research was carried out for the theory of great initial (ultimate) and two variants of the theory of small initial deformations within the framework of linearized theory of elasticity with the elastic potential having arbitrary structure. It is assumed that elastic potentials are two continuously differentiated functions of algebraic invariants of the Green tensor deformation (the initial states of the layer, of the cylindrical punch and of the foundation remains uniform and equal). Was used method of solving the dual integral equations. These equations are reduced to Fredholm integral equation of the second kind. Solution of integral equations was found by a method of successive approximations. The problem was reduced to solving an infinite system of algebraic equations. The system was solved by numerical methods (by reduction) and software tools. Key words: IT technologies, linearized theory of elasticity, initial (residual) stress, Fredholm integral equations, the method of consecutive approximations.### References

1. Guz' A.N., Babich S.Ju., Rudnickij V.B. Kontaktnoe vzaimodejstvie uprugih tel s nachal'nymi (osta-tochnymi) naprjazhenijami, Razvitie idej L.A. Galina v mehanike, M., Izhevsk, Institut komp'juternyh issledo-vanij, 2013, 480 p.

2. Guz' A.N., Rudnickij V.B. Osnovy teorii kontaktnogo vzaimodejstvija uprugih tel s nachal'nymi (ostatochnymi) naprjazhenijami, Hmel'nic'kij, vyd. PP Mel'nik, 2006, 710 p.

3. Maksymchuk D.M. Rozvyazannya kontaktnoyi zadachi dlya poperedn'o napruzhenoho sharu ta dvokh spivvisnykh pruzhnykh shtampiv z pochatkovymy (zalyshkovymy) napruzhennyamy, Dopovidi Natsion-al'noyi Akademiyi nauk Ukrayiny: Naukovo-teoretychnyy zhurnal, 2015, Vol. 4, P. 49 – 55.

4. Vasilikis D., Karamanos S. Discussion: Mechanics of Confined Thin-Walled Cylinders Subjected to External Pressure, Appl. Mech. Reviews, Vol. 66, No 1, 2014, P. 312 – 321.

5. Gao X.-L., Mao J.C.L. Solution of the Contact Problem of a Rigid Conical Frustum Indenting a Transversely Isotropic Elastic Half-Space, Appl. Mech., Vol. 81, No 4, 2014, P. 107 – 119.

6. Yarets'ka N.O., Vplyv pochatkovykh (zalyshkovykh) napruzhen' na kontaktnu vzayemodiyu pruzhnoho tsylindrychnoho shtampu ta pruzhnoho sharu, Dopovidi NAN Ukrayiny, Vol. 1, 2014, P. 57 – 62.

7. Yaretskaya N.A. Three-Dimensional Contact Problem for an Elastic Layer and a Cylindrical Punch with Prestresses, International Applied Mechanics, Vol. 50, No 4, July 2014, P. 378 – 388.

8. Іaretska N.A., Rudnitsky V.B. Research of contact interaction of prestressed stamps, layer and foun-dation without friction, Visnyk Ternopil’s’koho nacional’noho texnichnoho universytetu. Naukovyj zhurnal, Vol. 83. No 3, 2016, pp.28–37.

2. Guz' A.N., Rudnickij V.B. Osnovy teorii kontaktnogo vzaimodejstvija uprugih tel s nachal'nymi (ostatochnymi) naprjazhenijami, Hmel'nic'kij, vyd. PP Mel'nik, 2006, 710 p.

3. Maksymchuk D.M. Rozvyazannya kontaktnoyi zadachi dlya poperedn'o napruzhenoho sharu ta dvokh spivvisnykh pruzhnykh shtampiv z pochatkovymy (zalyshkovymy) napruzhennyamy, Dopovidi Natsion-al'noyi Akademiyi nauk Ukrayiny: Naukovo-teoretychnyy zhurnal, 2015, Vol. 4, P. 49 – 55.

4. Vasilikis D., Karamanos S. Discussion: Mechanics of Confined Thin-Walled Cylinders Subjected to External Pressure, Appl. Mech. Reviews, Vol. 66, No 1, 2014, P. 312 – 321.

5. Gao X.-L., Mao J.C.L. Solution of the Contact Problem of a Rigid Conical Frustum Indenting a Transversely Isotropic Elastic Half-Space, Appl. Mech., Vol. 81, No 4, 2014, P. 107 – 119.

6. Yarets'ka N.O., Vplyv pochatkovykh (zalyshkovykh) napruzhen' na kontaktnu vzayemodiyu pruzhnoho tsylindrychnoho shtampu ta pruzhnoho sharu, Dopovidi NAN Ukrayiny, Vol. 1, 2014, P. 57 – 62.

7. Yaretskaya N.A. Three-Dimensional Contact Problem for an Elastic Layer and a Cylindrical Punch with Prestresses, International Applied Mechanics, Vol. 50, No 4, July 2014, P. 378 – 388.

8. Іaretska N.A., Rudnitsky V.B. Research of contact interaction of prestressed stamps, layer and foun-dation without friction, Visnyk Ternopil’s’koho nacional’noho texnichnoho universytetu. Naukovyj zhurnal, Vol. 83. No 3, 2016, pp.28–37.

Published

2017-06-20

How to Cite

*Problems of Tribology*,

*84*(2), 22-30. Retrieved from https://tribology.khnu.km.ua/index.php/ProbTrib/article/view/593

Issue

Section

Articles