The trapezoidal finite element in absolute coordinates for dynamic modeling of automotive tire and air spring bellows. Part 1: equations of motion

• Autorzy: Pogorelov Dmitry , Rodikov Alexander

Identyfikatory

DOI

10.21307/tp-2021-030

• Języki publikacji: EN

Abstrakty

EN

Equations of motion of a finite element in absolute coordinates including mass matrix, generalized inertia and internal forces are derived. A trapezoidal element for dynamic models of flexible shells in the shape of surface of revolution is considered. The element can be used for modeling dynamics of automotive tire and air spring bellows and some other flexible elements of transport systems undergoing large elastic deflections.

Słowa kluczowe

EN

absolute nodal coordinates; finite elements; dynamic tire model

PL

bezwzględne współrzędne węzłowe; elementy skończone; model dynamiczny opony

• Wydawca: Wydawnictwo Politechniki Śląskiej
• Czasopismo: Transport Problems
• Rocznik: 2021
• Tom: T. 16, z. 2
• Strony: 141--152
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Pogorelov Dmitry

• Bryansk State Technical University, Laboratory of Computational Mechanics, bulv. 50 let Oktyabrya 7, Bryansk, 241035, Russia

autor

Rodikov Alexander

• Bryansk State Technical University, Laboratory of Computational Mechanics, bulv. 50 let Oktyabrya 7, Bryansk, 241035, Russia

Bibliografia

• 1. Bampton, M. & Craig, R. Coupling of Substructures for Dynamic Analyses. AIAA Journal. 1968. Vol. 6. No. 7. P. 1313-1319.
• 2. Shabana, A.A. Flexible multibody dynamics: review of past and recent developments. Multibody System Dynamics. 1997. Vol. 1. P. 189-222.
• 3. Dmitrochenko, O.N. & Pogorelov, D.Yu. Generalization of plate finite elements for absolute nodal coordinate formulation. Multibody System Dynamics. 2003. Vol. 10. P. 17-43.
• 4. Schwab, A.L. & Gerstmayr, J. & Meijaard, J.P. Comparison of three-dimensional flexible thin plate elements for multibody dynamic analysis: finite element formulation and absolute nodal coordinate formulation. In: Proceedings of the ASME 2007 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference. Las Vegas, Nevada, USA. 2007. DETC2007-34754.
• 5. Vetyukov, Yu. Finite element modeling of Kirchhoff-Love shells as smooth material surfaces. Zeitschrift für Angewandte Mathematik und Mechanik. 2014. Vol. 94. No. 1-2. P. 150-163.
• 6. Ebel, H. & Matikainen, M.K. & Hurskainen, V.·& at al. Higher-order beam elements based on the absolute nodal coordinate formulation for three-dimensional elasticity. Nonlinear Dynamics. 2017. No. 88. P.1075-1091.
• 7. Simeon, B. DAEs and PDEs in elastic multibody systems. Numerical Algorithms. 1998. Vol. 19. P. 235-246.
• 8. Wempner, G. Finite elements, finite rotations and small strains of flexible shells. International Journal of Solids and Structures. 1969. Vol. 5. P. 117-153.
• 9. Belytschko, T. & Schwer, L. Large displacement transient analysis of space frames. International Journal for Numerical Methods in Engineering. 1977. Vol. 11. P. 65-84.
• 10. Felippa, C.A. & Haugen, B. A unified formulation of small-strain corotational finite elements: I. Theory. Computer Methods in Applied Mechanics and Engineering. 2005. Vol. 194. P. 2285-2335.
• 11. Yang, J & Xia, P. Finite element corotational formulation for geometric nonlinear analysis of thin shells with large rotation and small strain. Science China Technological Sciences. 2012. Vol. 55. P. 3142-3152.
• 12. Низаметдинов, Ф.Р. & Сорокин, Ф.Д. Особенности применения вектора Эйлера для описания больших поворотов при моделировании элементов конструкций летательных аппаратов на примере стержневого конечного элемента. Труды МАИ. 2018. No. 102. 27 p. [In Russian: Euler vector application specifics for large rotations while flying vehicles structural elements modeling on the example of a beam finite element].
• 13. Погорелов, Д.Ю. & Родиков, А.Н. Уравнения движения упругого тела в абсолютных узловых координатах и их применение для моделирования динамики шины. In: Proceedings of XII All-Russian congress on fundamental problems of theoretical and applied mechanics. Ufa: Bashkir State University. 2019. Vol. 1. P. 493-495. [In Russian: Equations of motion of flexible body in absolute coordinates with application to tire dynamics].
• 14. Pogorelov, D. & Dmitrochenko, O. & Mikheev, G. & et al. Flexible multibody approaches for dynamical simulation of beam structures in drilling. In: Proceedings of the ASME 2014 10th Int. Conf. on Multibody Systems, Nonlinear Dynamics, and Control. Buffalo, New York, USA. 2014. DETC2014-35113.
• 15. Zienkiewicz, O.C. & Taylor, R.L. The Finite Element Method. Volume 2: Solid Mechanics. Butterworth-Heinemann. 2000. 459 p.
• 16. Постнов, В.А. & Хархурим, И.Я. Метод конечных элементов в расчетах судовых конструкций. Ленинград: Судостроение. 1974. 344 с. [In Russian: Finite element method in computation of ship structures].
• 17. Zienkiewicz, O.C. The finite element method in engineering science. London: McGraw-Hill. 1971. 521 p.
• 18. Григолюк, Э.И. & Куликов, Г.М. Многослойные армированные оболочки: Расчет пневматических шин. Москва: Машиностроение. 1988. 288 с. [In Russian: Multilayer reinforced shells: calculation of pneumatic tires].
• 19. Pelc, J. Large displacements in tire inflation problem. Engineering Transactions. 1992. Vol. 40. No. 1. P. 102-113.