Multi-grid finite elements in calculations of multilayer oval cylindrical shells

Автор: Pustovoi N. V., Grishanov A. N., Matveev А. D.

Журнал: Siberian Aerospace Journal @vestnik-sibsau-en

Рубрика: Informatics, computer technology and management

Статья в выпуске: 2 vol.20, 2019 года.

Бесплатный доступ

The method of finite elements (FEM) is actively used in calculations of composite shell constructions (rotation shells, circle and oval cylindrical shells), which are widely used in space-rocket and aviation equipment. To calculate multi-layer oval cylindrical shells three-dimensional curvilinear Lagrange multi-grid finite elements (MGFE) are suggested. When building a k-grid finite element (FE), k nested grids are used. The fine grid is generated by the basic split of MGFE that takes into account its complex heterogeneous structure and shape. On k-1 large grids the move functions used for decreasing MGFE dimension are determined. The stress-strain state in MGFE is described by the elasticity theory three-dimensional task equations (without introduction of additional hypotheses) in local Cartesian coordinates systems. The procedure of building shell-type Lagrange MGFE with the use of Lagrange polynomials presented in curvilinear coordinate systems is demonstrated. With the size reduction of discrete models MGFE have constant thickness equal to the thickness of the shell. The Lagrange polynomials nodes coincide in thickness with the MGFE large grid nodes and are located on the shared borders of different module layers. The use of such MGFE generates approximate solutions sequences that uniformly and quickly converge to precise solutions. The main advantages of MGFE are as follows: they form discrete models with the dimension 102–106 times smaller than the basic models dimension and they generate small error solutions. Examples of calculations are given for four- and three-layer oval shells of various thickness and shape under both uniform and local loading with the use of 3-grid FE. Comparative analysis of the obtained solutions with the solutions built with the help of the software package ANSYS shows high efficiency of the suggested MGFE in calculations of multi-grid oval shells.

Еще

Elasticity, composite, oval cylindrical shell, multi-grid finite elements, Lagrange polynomials, convergence of the solution sequence, software package ANSYS

Короткий адрес: https://sciup.org/148321675

IDR: 148321675   |   DOI: 10.31772/2587-6066-2019-20-2-174-182

Список литературы Multi-grid finite elements in calculations of multilayer oval cylindrical shells

  • Noor A. K., Burton W. S. Assessment of computational models for multilayered composite shells. Applied Mechanics Reviews. 1990, Vol. 43, P. 67–97.
  • Reddy J. N. Mechanics of laminated composite plates and shells: theory and analysis. 2004, CRC Press, 858 p.
  • Zienkiewicz O. C., Taylor R. L., Zhu J. Z. The finite element method: its basis and fundamentals. Oxford: Elsevier Butterworth-Heinemann, 2013, 715 p.
  • Norrie D. H., de Vries G. Vvedenie v metod konechnykh elementov [An introduction to finite element analysis]. Moscow, Mir Publ., 1981, 304 p.
  • Golovanov A. I., Tyuleneva O. I., Shigabutdinov A. F. Metod konechnykh elementov v statike i dinamike tonkostennykh konstruktsiy [Finite element method in statics and dynamics of thin-wall constructions]. Moscow, Fizmatlit Publ., 2006, 392 p.
  • Bate K., Wilson E. Chislennye metody analiza i metod konechnykh elementov [Numerical methods in finite element analysis]. Moscow, Stroyizdat Publ., 1982, 448 p.
  • Obraztsov I. F., Savelyev L. M., Khazanov Kh. S. Metod konechnykh elementov v zadachakh stroitelnoy mekhaniki letatelnykh apparatov [Finite element method in aircraft structural mechanics problems]. Moscow, Vysshaya shkola Publ., 1985, 392 p.
  • Sekulovich M. Metod konechnyh ehlementov [Finite element method]. Moscow, Stroyizdat Publ., 1993, 664 p.
  • Matveev A. D., Grishanov A. N. [Single and double grid curvilinear elements of three-dimensional cylindrical plates and shells]. Izvestiya AltGU. 2014, No. 1/1, P. 84–94 (In Russ.).
  • Matveev A. D., Grishanov A. N. [Multi-grid Lagrange curvilinear elements in three-dimensional analysis of composite cylindrical plates and shells]. Vestnik KrasGAU. 2015, No. 1, P. 75–85 (In Russ.).
  • Matveev A. D., Grishanov A. N. [Threedimensional composite multigrid finite elements of shell type]. Izvestiya AltGU. 2017, No. 4, P. 120–125 (In Russ.).
  • Kulikov G. M. Plotnikova C. V. [Solution of the problem of statics for an elastic shell in a spatial statement]. Doklady RAN. 2011, Vol. 439, No. 5, P. 613–616 (In Russ.).
  • Kulikov G. M. Plotnikova C. V. [Solution of three-dimensional problems for thick elastic shells based on the method of reference surfaces]. Mekhanika tverdogo tela. 2014, No. 4, P. 54–64 (In Russ.).
  • Kulikov G. M., Plotnikova S. V. On the use of a new concept of sampling surfaces in shell theory. Advanced Structured Materials. 2011, Vol. 15, P. 715–726.
  • Kulikov G. M., Plotnikova S. V. [Calculation of composite constructions under tracking load using geometrically accurate shell element]. Mekhanika kompozitnykh materialov. 2009, Vol. 45, No. 6, P. 789–804 (In Russ.).
  • Zheleznov L. P., Kabanov V. V., Boyko D. V. [Nonlinear deformation and stability of oval cylindric shells under pure bending and internal pressure]. Prikladnaya mekhanika i tekhnicheskaya fizika. 2006, Vol. 47, No. 3, P. 119–125 (In Russ.).
Еще
Статья научная