Co-rotational formulation of a solid-shell element utilizing the ans and eas methods

• Autorzy: Polat C.

Warianty tytułu

PL

Współrotacyjny opis bryłowo-powłokowego elementu skończonego oparty na metodzie założonych (ANS) i poszerzonych (EAS) odkształceń

• Języki publikacji: EN

Abstrakty

EN

An efficient eight-node solid-shell element is demonstrated. The Assumed Natural Strain (ANS) and the Enhanced Assumed Strain (EAS) methods are used to alleviate the locking problems. A co-rotational formulation is adopted in the description, thus geometric nonlinearity is taken into account by rotation of the local coordinate system. Several benchmark problems are examined to demonstrate the efficiency of the element.

PL

W pracy zaprezentowano opis ośmiowęzłowego bryłowo-powłokowego elementu skończonego. W celu osłabienia tzw. efektu blokady zastosowano metody założonych (ANS) i poszerzonych (EAS) odkształceń. Do opisu elementu zaadoptowano sformułowanie współrotacyjne, co pozwoliło na uwzględnienie nieliniowości poprzez obrót lokalnego układu współrzędnych. Przedstawiono także kilka zagadnień sprawdzających (zadań progowych) dla demonstracji efektywności tak zdefiniowanego elementu skończonego.

Słowa kluczowe

EN

solid-shell element; co-rotational formulation; ANS-EAS method

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2010
• Tom: Vol. 48 nr 3
• Strony: 771--788
• Opis fizyczny: Bibliogr. 35 poz., rys.

Twórcy

autor

Polat C.

• Faculty of Engineering, Department of Civil Engineering, Firat University, Elazig, Turkey,

Bibliografia

• 1. Andelfinger U., Ramm E., 1993, EAS-elements for two-dimensional, three-dimensional, plate and shell structures and their equivalence to HR-elements, International Journal for Numerical Methods in Engineering, 36, 1311-1337
• 2. Argyris J.H., Bahner H., Doltsnis J., et al., 1979, Finite element method – the natural approach, Computer Methods in Applied Mechanics and Engineering, 17/18, l-106
• 3. Bathe K.J., Dvorkin E.N., 1986, A formulation of general shell elements – The use of mixed interpolation of tensorial components, International Journal for Numerical Methods in Engineering, 22, 697-722
• 4. Belytschko T., Glaum L.W., 1979, Application of higher order corotational stretch theories to nonlinear finite element analysis, Computers and Structures, 10, 175-182
• 5. Bucalem M.L., Bathe K.J., 1993, Higher-orderMITC general shell elements, International Journal for Numerical Methods in Engineering, 36, 3729-3754
• 6. Chroscielewski J., Makowski J., Stumpf H., 1992, Genuinely resultant shell finite elements accounting for geometric and material non-linearity, International Journal for Numerical Methods in Engineering, 35, 6394
• 7. Crisfield M.A.,Moita G.F., 1996, A co-rotational formulation for 2-D continua including incompatible modes, International Journal of Numerical Methods in Engineering, 39, 2619-2633
• 8. Felippa C.A., Haugen B., 2005, A unified formulation of small strain corotational finite elements: I. Theory, Computer Methods in Applied Mechanics and Engineering, 194, 2285-2335
• 9. Feng Y.T., Peric D., Owen D.R.J., 1995, Determination of travel directions in path-following methods, Mathematical and Computer Modelling, 21, 43-59
• 10. Feng Y.T., Peric D., Owen D.R.J., 1996, A new criterion for determination of initial loading parameter in arc-length methods, Computers and Structures, 58, 479-485
• 11. Fontes Valente R.A., 2004, Developments on Shell and Solid-Shell Finite Elements Technology in Nonlinear Continuum Mechanics, Ph.D. Thesis, University of Porto, Portugal
• 12. Harnau M., Schweizerhof K., 2002, About linear and quadratic ”solid-shell” elements at large deformations, Computers and Structures, 80, 805-817
• 13. Hauptmann R., Schweizerhof K., 1998, A systematic development of ”solid-shell” element formulations for linear and non-linear analyses employing only displacement degrees of freedom, International Journal for Numerical Methods in Engineering, 42, 49-69
• 14. Hauptmann R., Scheizerhof K., Doll S., 2000, Extension of the ”solid-shell” concept for application to large elastic and large elastoplastic deformations, International Journal for Numerical Methods in Engineering, 49, 1121-1141
• 15. Hughes T.J.R., Cohen M., Haroun M., 1978, Reduced and selective integration techniques in the finite element analysis of plates, Nuclear Engineering and Design, 46, 203-222
• 16. Hughes T.J.R., Taylor R.L., Kanoknukulchai W., 1977, A simple and efficient finite element for plate bending, International Journal for Numerical Methods in Engineering, 11, 1529-1543
• 17. Ibrahimbegovic A., Frey F., 1994, Stress resultant geometrically nonlinear shell theory with drilling rotations – Part II: Computational aspects, Computer Methods in Applied Mechanics and Engineering, 118, 285-308
• 18. Klinkel S., Wagner W., 1997, A geometrical non-linear brick element, International Journal for Numerical Methods in Engineering, 40, 4529-4545
• 19. Kreja I., Schmidt R., Reddy J.N., 1997. Finite elements based on a first-order shear deformation moderate rotation shell theory with applications to the analysis of composite structures, International Journal of Non-Linear Mechanics, 32, 11231142
• 20. Miehe C., 1998, Theoretical and computational model for isotropic elastoplastic stress analysis in shells at large strains, Computer Methods in Applied Mechanics and Engineering, 155, 193-233
• 21. Moita G.F., Crisfield M.A., 1996, A finite element formulation for 3-D continua using the co-rotational technique, International Journal of Numerical Methods in Engineering, 39, 3775-3792
• 22. Panasz P., Wisniewski K., 2008, Nine-node shell elements with 6 dofs/node based on two-level approximations. Part I Theory and linear tests, Finite Elements in Analysis and Design, 44, 784796
• 23. Sansour C., Bednarczyk H., 1995, The Cosserat surface as a shell model, theory and finite-element formulation, Computer Methods in Applied Mechanics and Engineering, 120, 132
• 24. Simo J.C., Rifai M.S., 1990, A class of mixed assumed strain methods and the method of incompatible modes, International Journal for Numerical Methods in Engineering, 29, 1595-1638
• 25. Sousa R.J.A., Cardoso R.P.R., Fontes Valente R.A., Yoon Y.W., Gracio J.J., Natal Jorge R.M., 2004, A new one-point quadrature Enhanced Assumed Strain (EAS) solid-shell element with multiple integration points along thickness. Part I – Geometrically linear applications, International Journal of Numerical Methods in Engineering, 62, 952-977
• 26. Sousa R.J.A., Cardoso R.P.R., Fontes Valente R.A., Yoon Y.W., Gracio J.J., Natal Jorge R.M., 2006. A new one-point quadrature Enhanced Assumed Strain solid-shell element with multiple integration points along thickness. Part II - Nonlinear applications, International Journal of Numerical Methods in Engineering, 67, 160-188
• 27. Sze K.Y., Liu X.H., Lo S.H., 2004, Popular benchmark problems for geometric nonlinear analysis of shells, Finite Elements in Analysis and Design, 40, 1551-1569
• 28. Sze K.Y., Yao L.Q., 2000, A hybrid stress ANS solid-shell element and its generalization for smart structure modelling. Part I: Solid-shell element formulation, International Journal of Numerical Methods in Engineering, 48, 545-564
• 29. Sze K.Y., Yao L.Q., Yi S., 2000, A hybrid stress ANS solid-shell element and its generalization for smart structure modelling. Part II: Smart structure modelling, International Journal of Numerical Methods in Engineering, 48, 565-582
• 30. Tan X.G., Vu-Quoc L., 2005, Optimal solid shell element for large deformable composite structures with piezoelectric layers and active vibration control, International Journal of Numerical Methods in Engineering, 64, 1981-2013
• 31. Urthaler Y., Reddy J.N., 2005, A corotational finite element formulation for the analysis of planar beams, Communications in Numerical Methods In Engineering, 21, 553-570
• 32. Vu-Quoc L., Tan X.G., 2003, Optimal solid shells for non-linear analyses of multilayer composites. I Statics, Computer Methods in Applied Mechanics and Engineering, 192, 975-1016
• 33. Wempner G., 1969, Finite elements, finite rotations and small strains of flexible shells, The International Journal of Solids and Structures, 5, 117-153
• 34. Witkowski W., 2009, 4-Node combined shell element with semi-EAS-ANS strain interpolations in 6-parameter shell theories with drilling degrees of freedom, Computational Mechanics, 43, 307319
• 35. Zienkiewicz O.C., Taylor R.L., Too J.M., 1971, Reduced integration techniques in finite element method, International Journal for Numerical Methods in Engineering, 3, 275-290 788 C.