Surface parameterization complex geometry
- Authors: Yakupov S.N.1, Nizamova G.K.2
- Federal Research Center “Kazan Scientific Center of Russian Academy of Sciences”
- Peoples’ Friendship University of Russia (RUDN University)
- Issue: Vol 18, No 5 (2022)
- Pages: 467-474
- Section: Geometrical modeling of shell forms
- URL: https://journals.rudn.ru/structural-mechanics/article/view/33413
- DOI: https://doi.org/10.22363/1815-5235-2022-18-5-467-474
Among thin-walled structures, including building structures and constructions, shells of complex geometry are effective in their rigidity and strength characteristics, which are also distinguished by architectural harmony. For a wider application of shells of complex geometry, it is necessary to reliably assess their stress-strain state. In this case, an integral part of the calculation is the parametrization stage of the median surface of shells of complex geometry. There are shells of complex geometry of canonical and non-canonical forms. For shells of non-canonical shape, the median surface cannot be defined by analytical formulas. At the same time, difficulties arise at the stage of specifying (parameterizing) the shape of the median surface. The task becomes more complicated when the shell fragment has a complex contour and one or more surface points have fixed coordinates. For building structures, this is, for example, the presence of additional internal supports. Information about the spline version of the FEM is presented. Some well-known parametrization methods are noted. The approach of parametrization of a minimal surface of a complex shape bounded by four curved contours and a given (fixed) coordinate of one inner point of the surface is considered. An algorithm for constructing a spatial network, as well as determining coordinates, metric tensor components and Christoffel symbols necessary for solving parametrization problems in the spline version of the finite element method is described.
About the authors
Samat N. YakupovFederal Research Center “Kazan Scientific Center of Russian Academy of Sciences”
Author for correspondence.
ORCID iD: 0000-0003-0047-3679
PhD in Technical Sciences, senior researcher, Institute of Mechanics and Engineering2/31 Lobachevsky St, Kazan, 420111, Russian Federation
Guzial Kh. NizamovaPeoples’ Friendship University of Russia (RUDN University)
ORCID iD: 0000-0002-7193-9125
PhD in Technical Sciences, Associate Professor of the Department of Mechanical Engineering Technologies, Academy of Engineering6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation
- Yakupov N.M., Galimov Sh.K., Khismatullin N.I. From stone blocks to thin-walled structures. Kazan: SOS Publ.; 2001. (In Russ.)
- Krivoshapko S.N., Ivanov V.N. Encyclopedia of analytical surfaces. Springer; 2015.
- Aleynikov S.M. The method of boundary elements in contact problems for elastic spatially inhomogeneous bases. Moscow: DIA Publ.; 2000. (In Russ.)
- Alibeigloo A., Nouri V. Static analysis of functionally graded cylindrical shell with piezoelectric layers using differential quadrature method. Composite Structures. 2010;92(8):1775–1785.
- Gurkan I. The effect of using shell and solid models in structural stress analysis. Vibroengineering PROCEDIA. 2019;27:115–120. https://doi.org/10.21595/vp.2019.20977
- Peaters M., Santo G., Degroote J., Van Paepegem W. High-fidelity finite element models of composite wind turbine blades with shell and solid elements. Composite Structures. 2018;200:521–531. https://doi.org/10.1016/j.compstruct.2018.05.091
- Bognet B., Leygue A., Chinesta F. Separated representations of 3D elastic solutions in shell geometries. Advanced Modeling and Simulation in Engineering Sciences. 2014;1:4. https://doi.org/10.1186/2213-7467-1-4
- Cerracchio P., Gherlone M., Di Sciuva M., Tessler A. A novel approach for displacement and stress monitoring of sandwich structures based on the inverse finite element method. Composite Structures. 2015;127:69–76. https://doi.org/10.1016/j.compstruct.2015.02.081
- Gherlone M., Cerracchio P., Mattone M., Di Sciuva M., Tessler A. Shape sensing of 3D frame structures using an inverse finite element method. International Journal of Solids and Structure. 2012;49:3100–3112. https://doi.org/10.1016/j.ijsolstr.2012.06.009
- Kefal A., Tessler A., Oterkus E. An efficient inverse finite element method for shape and stress sensing of laminated composite and sandwich plates and shells. Hampton: NASA Langley Research Center; 2018.
- Magisano D., Liabg K., Garcea G., Leonetti L., Ruess M. An efficient mixed variational reduced order model formulation for nonlinear analyses of elastic shells. International Journal for Numerical Methods in Engineering. 2018;113(4):634–655. https://doi.org/10.1002/nme.5629
- Moazzez K., Googarchin H.S., Sharifi S.M.H. Natural frequency analysis of a cylindrical shell containing a variably oriented surface crack utilizing line-spring model. Thin-Shell Structures. 2018;125:63–75. https://doi.org/10.1016/j.tws.2018.01.009
- Yin T., Lam H.F. Dynamic analysis of finite-length circular cylindrical shells with a circumferential surface crack. Journal of Engineering Mechanics. 2013;139:1419–1434. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000587
- Nemish Yu.N. Three-dimensional boundary value problems of elasticity theory for non-canonical domains. Applied Mechanics. 1980;16(2):3–39. (In Russ.)
- Rekach V.G., Krivoshapko S.N. Calculation of shells of complex geometry. Moscow: RUDN Publ.; 1988. (In Russ.)
- Fung Y.C., Sechler E.E. (eds.) Thin-shell structures. Theory, experiment and design. California Institute of Technology, Prentice Hall; 1974.
- Vachitov M.B., Paymushin V.N., Yakupov N.M. On solution of the plane problem of reinforced panels of variable stiffness. Izvestiya Vysshikh Uchebnykh Zavedenii. Aviatsionnaya Tekhnika. 1978;2:9–16. (In Russ.)
- Yakupov N.M. On one method of calculating shells of complex geometry. Proceedings of the Seminar: Research on the Theory of Shells. 1984;17(II):4–17. (In Russ.)
- Kornishin M.S., Yakupov N.M. Spline variant of the finite element method for calculating shells of complex geometr. Applied Mechanics. 1987;23(3):38–44. (In Russ.)
- Kornishin M.S., Yakupov N.M. To the calculation of shells of complex geometry in cylindrical coordinates based on the spline version of the FEM. Applied Mechanics. 1989;25(8):53–60. (In Russ.)
- Yakupov N.M., Serazutdinov M.N. Calculation of elastic thin-walled structures of complex geometry. Kazan: IMM KSC RAS Publ.; 1993. (In Russ.)
- Yakupov N.M. Applied problems of mechanics of elastic thin-walled structures. Kazan: IMM KNC RAS, 1994. (In Russ.)
- Badriev I.B., Paimushin V.N. Refined models of contact interaction of a thin plate with positioned on both sides deformable foundations. Lobachevskii Journal of Mathematics. 2017;38(5):779–793.
- Yakupov S.N., Nurullin R.G., Yakupov N.M. Parametrization of structural elements of complex geometry. Structural Mechanics of Engineering Constructions and Buildings. 2017;(6):4–9. (In Russ.) https://doi.org/10.22363/1815-5235-2017-6-4-9
- Nizamov H.N., Sidorenko S.N., Yakupov N.M. Forecasting and prevention of corrosion destruction of structures. Moscow: RUDN Publ.; 2006. (In Russ.)