A new approach to reduce membrane and transverse shear locking for one-point quadrature shell elements: linear formulation
2005; Wiley; Volume: 66; Issue: 2 Linguagem: Inglês
10.1002/nme.1548
ISSN1097-0207
AutoresRui P.R. Cardoso, Jeong Whan Yoon, Robertt Valente,
Tópico(s)Dynamics and Control of Mechanical Systems
ResumoInternational Journal for Numerical Methods in EngineeringVolume 66, Issue 2 p. 214-249 Research Article A new approach to reduce membrane and transverse shear locking for one-point quadrature shell elements: linear formulation Rui P. R. Cardoso, Corresponding Author Rui P. R. Cardoso [email protected] Department of Mechanical Engineering, University of Aveiro, 3810-193 Aveiro, PortugalDepartment of Mechanical Engineering, University of Aveiro, Campus Univ. Santiago, 3810-193 Aveiro, PortugalSearch for more papers by this authorJeong Whan Yoon, Jeong Whan Yoon [email protected] Department of Mechanical Engineering, University of Aveiro, 3810-193 Aveiro, Portugal Alloy Technology and Material Research Division, Alcoa Technical Center, 100 Technical Dr., PA 15069-0001, U.S.A.Search for more papers by this authorRobertt A. Fontes Valente, Robertt A. Fontes Valente [email protected] Department of Mechanical Engineering, University of Aveiro, 3810-193 Aveiro, PortugalSearch for more papers by this author Rui P. R. Cardoso, Corresponding Author Rui P. R. Cardoso [email protected] Department of Mechanical Engineering, University of Aveiro, 3810-193 Aveiro, PortugalDepartment of Mechanical Engineering, University of Aveiro, Campus Univ. Santiago, 3810-193 Aveiro, PortugalSearch for more papers by this authorJeong Whan Yoon, Jeong Whan Yoon [email protected] Department of Mechanical Engineering, University of Aveiro, 3810-193 Aveiro, Portugal Alloy Technology and Material Research Division, Alcoa Technical Center, 100 Technical Dr., PA 15069-0001, U.S.A.Search for more papers by this authorRobertt A. Fontes Valente, Robertt A. Fontes Valente [email protected] Department of Mechanical Engineering, University of Aveiro, 3810-193 Aveiro, PortugalSearch for more papers by this author First published: 14 November 2005 https://doi.org/10.1002/nme.1548Citations: 39AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract In the last decade, one-point quadrature shell elements attracted many academic and industrial researchers because of their computational performance, especially if applied for explicit finite element simulations. Nowadays, one-point quadrature finite element technology is not only applied for explicit codes, but also for implicit finite element simulations, essentially because of their efficiency in speed and memory usage as well as accuracy. In this work, one-point quadrature shell elements are combined with the enhanced assumed strain (EAS) method to develop a finite element formulation for shell analysis that is, simultaneously, computationally efficient and more accurate. The EAS method is formulated to alleviate locking pathologies existing in the stabilization matrices of one-point quadrature shell elements. An enhanced membrane field is first constructed based on the quadrilateral area coordinate method, to improve element's accuracy under in-plane loads. The finite element matrices were projected following the work of Wilson et al. (Numerical and Computer Methods in Structural Mechanics, Fenven ST et al. (eds). Academic Press: New York, 1973; 43–57) for the incompatible modes approach, but the present implementation led to more accurate results for distorted meshes because of the area coordinate method for quadrilateral interpolation. The EAS method is also used to include two more displacement vectors in the subspace basis of the mixed interpolation of tensorial components (MITC) formulation, thus increasing the dimension of the null space for the transverse shear strains. These two enhancing vectors are shown to be fundamental for the Morley skew plate example in particular, and in improving the element's transverse shear locking behaviour in general. Copyright © 2005 John Wiley & Sons, Ltd. REFERENCES 1 Belytschko T, Tsay CS. A stabilization procedure for the quadrilateral plate element with one-point quadrature. International Journal for Numerical Methods in Engineering 1983; 19: 405. 2 Belytschko T, Lin JI, Tsay CS. Explicit algorithms for the nonlinear dynamics of shells. Computer Methods in Applied Mechanics and Engineering 1984; 42: 225. 3 Hallquist JO, Benson PJ, Gougrean GL. Implementation of a modified Hughes–Liu shell into a fully vectorized explicit finite element code. In Finite Element Methods for Nonlinear Problems, P Bergan et al. (eds). Springer: Berlin, 1986; 283. 4 Belytschko T, Leviathan I. Physical stabilization of the 4-node shell element with one-point quadrature. Computer Methods in Applied Mechanics and Engineering 1994; 113: 321–350. 5 Cardoso RPR, Yoon JW, Grácio JJA, Barlat F, César de Sá JMA. Development of a one-point quadrature shell element for nonlinear applications with contact and anisotropy. Computer Methods in Applied Mechanics and Engineering 2002; 191: 5177–5206. 6 Cardoso RPR, Yoon JW. One point quadrature shell element with through-thickness stretch. Computer Methods in Applied Mechanics and Engineering 2005; 194: 1161–1199. 7 Cardoso RPR, Yoon JW. One point quadrature shell elements for sheet metal forming analysis. Archives of Computational Methods in Engineering 2005; 12: 3–66. 8 Dvorkin E, Bathe KJ. A continuum mechanics based four-node shell element for general nonlinear analysis. Engineering and Computations 1984; 1: 77–88. 9 Hughes TJR. Generalization of selective integration procedures to anisotropic and nonlinear media. International Journal for Numerical Methods in Engineering 1980; 15: 1413. 10 Zienkiewicz OC, Taylor RL, Too JM. Reduced integration technique in general analysis of plates and shells. International Journal for Numerical Methods in Engineering 1977; 3: 275. 11 Andelfinger U, Ramm E. EAS-elements for two-dimensional, three-dimensional, plate and shells and their equivalence to HR-elements. International Journal for Numerical Methods in Engineering 1993; 36: 1413–1449. 12 Wilson EL, Taylor RL, Doherty WP, Ghabussi T. Incompatible displacement models. In Numerical and Computer Methods in Structural Mechanics, ST Fenven et al. (eds). Academic Press: New York, 1973; 43–57. 13 Choi CK, Lee TY. Efficient remedy for membrane locking of 4-node flat shell elements by non-conforming modes. Computer Methods in Applied Mechanics and Engineering 2003; 192: 1961–1971. 14 Simo JC, Rifai MS. A class of mixed assumed strain methods and the method of incompatible modes. International Journal for Numerical Methods in Engineering 1990; 29: 1595–1638. 15 Simo JC, Armero F. Geometrically nonlinear enhanced strain mixed methods and the method of incompatible modes. International Journal for Numerical Methods in Engineering 1992; 33: 1413–1449. 16 Simo JC, Armero F, Taylor RL. Improved versions of assumed enhanced strain tri-linear elements for 3D-finite deformation problems. Computer Methods in Applied Mechanics and Engineering 1993; 110: 359–386. 17 Chen XM, Cen S, Long YQ, Yao ZH. Membrane elements insensitive to distortion using the quadrilateral area coordinate method. Computers and Structures 2004; 82: 35–54. 18 César de Sá JMA, Natal Jorge RM, Fontes Valente RA, Areias PMA. Development of shear locking-free shell elements using an enhanced assumed strain formulation. International Journal for Numerical Methods in Engineering 2002; 53: 1721–1750. 19 Fontes Valente RA. Developments on shell and solid-shell finite elements technology in nonlinear continuum mechanics. Ph.D. Dissertation, Faculty of Engineering of University of Porto (FEUP), Portugal, 2004 (http://sweet.ua.pt/∼f1933). 20 Bathe KJ. Finite Element Procedures ( 2nd edn). Prentice-Hall: Englewood Cliffs, NJ, 1996. 21 Belytschko T, Leviathan I. Projection schemes for one-point quadrature shell elements. Computer Methods in Applied Mechanics and Engineering 1994; 115: 277. 22 Long YQ, Li JX, Long ZF, Cen S. Area coordinates used in quadrilateral elements. Computational Mechanics 1999; 19: 533. 23 Long ZF, Long YQ, Li JX, Cen S, Long YQ. Some basic formulae for area coordinates used in quadrilateral elements. Computational Mechanics 1999; 19: 841. 24 Huang HC. Static and Dynamic Analyses of Plates and Shells—Theory, Software and Applications. Springer: Berlin, Heidelberg, New York, 1989. 25 César de Sá JMA, Natal Jorge RM. New enhanced strain elements for incompressible problems. International Journal for Numerical Methods in Engineering 1999; 44: 229–248. 26 Fontes Valente RA, Parente MPL, Natal Jorge RM, César de Sá JMA, Grácio JJ. Enhanced transverse shear strain shell formulation applied to large elasto-plastic deformation problems. International Journal for Numerical Methods in Engineering 2005; 62: 1360–1398. 27 Taylor RL, Beresford PJ, Wilson EL. A non-conforming element for stress analysis. International Journal for Numerical Methods in Engineering 1976; 10: 1211–1219. 28 Simo JC, Fox DD, Rifai MS. On a stress resultant geometrically exact shell model. Part I: formulation and optimal parametrization. Computer Methods in Applied Mechanics and Engineering 1989; 72: 267–304. 29 Simo JC, Fox DD, Rifai MS. On a stress resultant geometrically exact shell model. Part II: the linear theory-computational aspects. Computer Methods in Applied Mechanics and Engineering 1989; 73: 53–92. 30 Kemp BL, Cho C, Lee SW. A four-node solid shell element formulation with assumed strain. International Journal for Numerical Methods in Engineering 1998; 43: 909–924. 31 Cardoso RPR. Development of one-point quadrature shell elements with anisotropic material models for sheet metal forming analysis. Ph.D. Dissertation, Department of Mechanical Engineering, University of Aveiro (UA), Portugal, 2002 (http://rcardoso.home.sapo.pt). 32 Fontes Valente RA, Natal Jorge RM, Cardoso RPR, César de Sá JMA, Grácio JJ. On the use of an enhanced transverse shear strain shell element for problems involving large rotations. Computational Mechanics 2003; 30: 286–296. 33 ABAQUS. Theory Manual, Version 6.3. Hibbitt, Karlsson & Sorensen, Inc.: Rhode-Island, U.S.A., 2002. 34 MacNeal RH, Harder RL. A proposed standard set of problems to test finite element accuracy. Finite Elements in Analysis and Design 1985; 1: 1–20. 35 Ibrahimbegović A, Taylor RL, Wilson EL. A robust quadrilateral membrane finite element with drilling degrees of freedom. International Journal for Numerical Methods in Engineering 1990; 30: 445–457. 36 Slavković R, Miroslav Z, Kojić M. Enhanced 8-node three-dimensional solid and 4-node shell elements with incompatible generalized displacements. Communications in Numerical Methods in Engineering 1994; 10: 699–709. 37 Kasper EP, Taylor RL. A mixed-enhanced strain method. Part I: geometrically linear problems. Computers and Structures 2000; 75: 237–250. 38 MacNeal RH. Finite Elements: Their Design and Performance. Marcel Dekker: New York, 1994. 39 Bucalem ML, Bathe KJ. Higher-order MITC general shell elements. International Journal for Numerical Methods in Engineering 1993; 36: 3729–3754. 40 Parisch H. An investigation of a finite rotation four node assumed strain shell element. International Journal for Numerical Methods in Engineering 1991; 31: 127–150. 41 Groenwold AA, Slander N. An efficient 4-node 24 DOF thick shell finite element with 5-point quadrature. Engineering and Computations 1995; 12: 723–747. 42 Morley LSD. Skew Plates and Structures. Pergamon Press: London, 1963. 43 Yunhua L, Eriksson A. An alternative assumed strain method. Computer Methods in Applied Mechanics and Engineering 1999; 178: 23–37. 44 ABAQUS. Benchmarks Manual, Version 6.3. Hibbitt, Karlsson & Sorensen, Inc.: Rhode-Island, U.S.A., 2002. 45 Knight NF. The Raasch challenge for shell elements. AIAA Journal 1997; 35: 375–381. 46 Massin P, al Mikdad M. Nine-node and seven-node thick shell elements with large displacements and rotations. Computers and Structures 2002; 80: 835–847. 47 Batoz JL, Dhatt G. Modélisation des Structures par Éléments Finis, Volume 3—Coques. Hermés: Paris, 1992. Citing Literature Volume66, Issue29 April 2006Pages 214-249 ReferencesRelatedInformation
Referência(s)