MODERN APPROACHES TO SOLVING THE CONTACT PROBLEM OF PRESSING A DOUBLESTAMP STAMP INTO AN ELASTIC HALF-SPACE
DOI:
https://doi.org/10.20998/2079-0023.2021.01.12Abstract
The work is devoted to solving indentation problems into an elastic half-space of a cylindrical punch with a flat base by the vertical force. The force is aimed through the center of the base. The cross-section of the stamp is a doubly connected area bounded by two concentric lines. A concise review of methods for solving problems of analyzing the contact interaction of cylindrical dies with an elastic half-space is given. The solution of the problem in the form of decomposition by a small parameter is used when the equation of the edge curves depends on the same small parameter. To achieve it, in each approximation, the problem of indentation of a stamp with a doubly connected contact area in the form of a non-circular ring is reduced to a similar problem of indentation of a stamp with a contact area in the form of a circular ring. The software in the Java language has been developed for processing the analytical solution according to the obtained calculation formulas. With the help of the ANSYS software package, a finite element model of the contact interaction of an absolutely rigid stamp with an elastic half-space has been created. Numerical modeling was carried out using a licensed version of the program, free of charge. Several problems have been solved for square rings of different widths. The distribution of pressure under the stamp over different sections and the deepening of the stamp have been obtained. The pressure distribution graphs are plotted. When considering several test problems to assess the adequacy of the finite element model, the numerical results are compared with the results obtained analytically. The resulting model can analyze and predict loads, wear, and fracture of the contact area. The research prospects can include the solution of several problems of analysis of the stress-strain state of the interaction of dies of a complex shape with an elastic half-space, as well as groups of stamps of a complex shape, and the analysis of behavior models depending on the properties and characteristics of an elastic half-space.
Keywords: contact problem, stamp, stress-strain state, modeling, JAVA language, finite element analysis, ANSYS software package.
References
Spitsa O. G. Chislennyj analiz kontaktnogo vzaimodejstviya shtampa i mnogoslojnogo uprugogo poluprostranstva [Numerical analysis of the contact interaction of the stamp and the multilayer elastic halfspace]. Vіsnik Zaporіz’kogo nacіonal’nogo unіversitetu [Bulletin of Zaporizhzhya National University]. Zaporizhia, "ZNU" Publ., 2015, no 3, pp. 249–255.
Bosakov S. Two Contact Problems for Circular Die Pressing-In in Elastic Half Space. Science and Technique. 2018, vol. 17, no. 6, pp. 458–464.
Pushchin R. V., Pykhalov A. A. Analiz napryazhenij zamkovoj chasti rabochih lopatok aviacionnyh dvigatelej s konechno-elementnym resheniem kontaktnoj zadachi teorii uprugosti [Stress analysis of the locking part of the blades of aircraft engines with a finite-element solution of the contact problem of the theory of elasticity]. Trudy MAI. 2020, no. 110, pp. 14–21. doi: 10.34759/trd-2020-110-11.
Andrievsky V. P., Maksymyuk Yu. V., Mytsiuk S. V., Piskunov S. O. Doslіdzhennya evolyucії napruzheno-deformovanogo stanu і viznachennya rozrahunkovogo resursu masivnih elementіv vіsesimetrichnih konstrukcіj іz vikoristannyam unіversal’nogo skіnchennogo elementu [Investigation of the evolution of the stressstrain state and determination of the calculated resource of massive elements of axisymmetric structures using a universal finite element]. Vestnik Nats. tekhn. un-ta "KhPI": sb. nauch. tr. Temat. vyp.: Sistemnyy analiz, upravlenie i informatsionnye tekhnologii [Bulletin of the National Technical University "KhPI": a collection of scientific papers. Thematic issue: System analysis, management, and information technology]. Kharkov, NTU "KhPI" Publ., 2018, no. 22 (1298), pp. 66–72.
Mikhailova E., Tarlakovskii D., Fedotenkov G. Transient contact problem for spherical shell and elastic half-space. Shell Structures: Theory and Applications. 2017, vol. 4, pp. 301–304. doi: 10.1201/9781315166605-67.
Igumnov L. A., Markov I. P. Modelirovanie dinamiki trekhmernyh linejnyh elektrouprugih tel s otverstiyami s pomoshch’yu metoda granichnyh elementov [Modeling the dynamics of three-dimensional linear electroelastic bodies with holes using the method of boundary elements]. Problems of strength and ductility. 2017, vol. 79, no. 3, pp. 348–356. doi: 10.32326/1814-9146-2017-79-3-348-356.
Zhao J., Vollebregt E. A., Oosterlee C. W. Extending the BEM for Elastic Contact Problems Beyond the Half-Space Approach. Mathematical Modeling and Analysis. 2016, vol. 21, no. 1, pp. 119– 141. doi: 10.3846 / 13926292.2016.1138418.
Yulong L., Arutiunian A., Kuznetsova E., Fedotenkov G. Method for solving plane unsteady contact problems for rigid stamp and elastic half-space with a cavity of arbitrary geometry and location. INCAS BULLETIN. 2020, vol. 12, pp. 99–113. doi: 10.13111/2066- 8201.2020.12.S.9.
Schanz M., Ye W., Xiao J. Comparison of the convolution quadrature method and enhanced inverse FFT with application in elastodynamic boundary element method. Computational Mechanics. 2016, vol. 57, pp. 523–536. doi: 10.1007/s00466-015-1237-z.
Guz A. N., Rudnitsky V. B. Osnovy teorii kontaktnogo vzaimodejstviya uprugih tel s nachal’nymi (ostatochnymi) napryazheniyami [Fundamentals of the theory of contact interaction of elastic bodies with initial (residual) stresses]. Khmelnytsky, Melnik Publ., 2006. 710 p.
Babich. S. Contact Problem for Two Identical Strips Reinforced by Periodically Arranged Fasteners with Initial Stresses. International Applied Mechanics. 2019, vol. 55, no. 6, pp. 629–635.
Yaretskaya N. A. Contact Problem for the Rigid Ring Stamp and the Half-Space with Initial (Residual) Stresses. International Applied Mechanics. 2018, vol. 54, no. 5, pp. 539–543.
Rvachev V. L., Protsenko V. S. Kontaktnыe zadachy teoryy upruhosty dlia neklassycheskykh oblastei [Contact problems of elasticity theory for non-classical domains]. Kyiv, Nauk. Dumka Publ., 1977. 235p.
Roitman A. B., Shishkanova S. F. The solution of the annular punch problem with the aid of recursion relations. Soviet Applied Mechanics. 1973, no. 9(7), pp. 725–729.
Shyshkanova S. F. Indentation of an elliptical die with a rounded edge into an elastic half-space. Mechanics of solids. 1987, no. 22(3), pp. 74–77.
Shyshkanova G. A., Zaуtseva T. A., Frydman A. D. The analysis of manufacturing errors effect on contact stresses distribution under the ring parts deformed asymmetrically. Metallurgical and Mining Industry. 2015, no. 7, pp. 352–357.
Zaitseva T. A., Shishkanova G. A. Rozv’yazannya prostorovih kontaktnih zadach dlya neklasichnih bagatozv’yaznih oblastej [Solving spatial contact problems for nonclassical multiconnected domains]. Dnipro, DNU Publ., 2011. 192 p.
Moaz H. Finite Element Analysis is A Powerful Approach To Predictive Manufacturing Parameters. Journal of the University of Babylon for Pure and Applied Sciences. 2017, no. 26(1), pp. 229–238.
Zaytseva T. A., Shmelov I. I. Vikoristannya metodu skіnchennih elementіv dlya modelyuvannya kontaktnih zadach v paketі Ansys [Using the finite element method for modeling contact problems in the Ansys package]. Trudy mezhdunar. konferentsii "Matematichne ta programne zabezpechennya іntelektual’nih sistem (MPZІS-2020)" (18–20 listopada, 2020, Dnipro) [Proc. of the Int. Conf. " Mathematical support and software for intelligent systems (MSSIS2020)"]. Dnipro, DNU Publ., 2020, pp. 114–115.
Gulakov S. V., Shcherbakov S. V. Primenenie programmnoj sistemy konechno-elementnogo analiza ANSYS dlya komp’yuternogo modelirovaniya napryazhennogo sostoyaniya cilindricheskih izdelij pri vozdejstvii lokal’nym istochnikom nagreva [Application of the ANSYS finite element analysis software system for computer modeling of the stress state of cylindrical products under the influence of a local heat source]. Vіsnik Priazovs’kogo Derzhavnogo Tekhnіchnogo Unіversitetu. Ser.: Tekhnіchnі nauki [Bulletin of the Azov State Technical University. Thematic issue: Technical Sciences]. 2015, vol. 2, no. 30, pp. 21–26.
Ansys Free Student Software Downloads. Available at: https://www.ansys.com/academic/free-student-products (accessed 30.02.2021).
Downloads
Published
How to Cite
Issue
Section
License
LicenseAuthors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
