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A new reduced integration solid-shell element based on EAS and ANS with hourglass stabilization. (English) Zbl 1352.74175

Summary: A novel reduced integration eight-node solid-shell finite element formulation with hourglass stabilization is proposed. The enhanced assumed strain method is adopted to eliminate the well-known volumetric and Poisson thickness locking phenomena with only one internal variable required. In order to alleviate the transverse shear and trapezoidal locking and correct rank deficiency simultaneously, the assumed natural strain method is implemented in conjunction with the Taylor expansion of the inverse Jacobian matrix. The projection of the hourglass strain-displacement matrix and reconstruction of its transverse shear components are further employed to avoid excessive hourglass stiffness. The proposed solid-shell element formulation successfully passes both the membrane and bending patch tests. Several typical examples are presented to demonstrate the excellent performance and extensive applicability of the proposed element.

MSC:

74K25 Shells
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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[1] Zienkiewicz, Reduced integration technique in general analysis of plates and shells, International Journal for Numerical Methods in Engineering 3 pp 275– (1971) · Zbl 0253.73048 · doi:10.1002/nme.1620030211
[2] Hughes, Reduced and selective integration techniques in the finite element analysis of plates, Nuclear Engineering and Design 46 pp 203– (1978) · doi:10.1016/0029-5493(78)90184-X
[3] Belytschko, Assumed strain stabilization of the eight node hexahedral element, Computer Methods in Applied Mechanics and Engineering 105 pp 225– (1993) · Zbl 0781.73061 · doi:10.1016/0045-7825(93)90124-G
[4] Simo, A class of mixed assumed strain methods and the method of incompatible modes, International Journal for Numerical Methods in Engineering 29 pp 1595– (1990) · Zbl 0724.73222 · doi:10.1002/nme.1620290802
[5] Sze, An explicit hybrid stabilized eighteen-node solid element for thin shell analysis, International Journal for Numerical Methods in Engineering 40 pp 1839– (1997) · doi:10.1002/(SICI)1097-0207(19970530)40:10<1839::AID-NME141>3.0.CO;2-O
[6] Xu, Three-dimensional finite element simulation of medium thick plate metal forming and springback, Finite Elements in Analysis and Design 51 pp 49– (2012) · doi:10.1016/j.finel.2011.10.008
[7] Sze, A hybrid stress ANS solid-shell element and its generalization for smart structure modelling, Part I-solid-shell element formulation, International Journal for Numerical Methods in Engineering 48 pp 545– (2000) · Zbl 0990.74073 · doi:10.1002/(SICI)1097-0207(20000610)48:4<545::AID-NME889>3.0.CO;2-6
[8] Sze, An eighteen-node hybrid-stress solid-shell element for homogenous and laminated structures, Finite Elements in Analysis and Design 38 pp 353– (2002) · Zbl 1051.74048 · doi:10.1016/S0168-874X(01)00089-0
[9] Parisch, A continuum-based shell theory for non-linear applications, International Journal for Numerical Methods in Engineering 38 pp 1855– (1995) · Zbl 0826.73041 · doi:10.1002/nme.1620381105
[10] Cardoso, One point quadrature shell element with through-thickness stretch, Computer Methods in Applied Mechanics and Engineering 194 pp 1161– (2005) · Zbl 1106.74056 · doi:10.1016/j.cma.2004.06.017
[11] Alves De Sousa, A new volumetric and shear locking-free 3D enhanced strain element, Engineering Computations 20 pp 896– (2003) · Zbl 1063.74537 · doi:10.1108/02644400310502036
[12] Alves De Sousa, 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 for Numerical Methods in Engineering 62 pp 952– · Zbl 1161.74487 · doi:10.1002/nme.1226
[13] Alves De Sousa, A new one-point quadrature enhanced assumed strain (EAS) solid-shell element with multiple integration points along thickness-part II: nonlinear applications, International Journal for Numerical Methods in Engineering 67 pp 160– (2006) · Zbl 1110.74840 · doi:10.1002/nme.1609
[14] Alves De Sousa, On the use of a reduced enhanced solid-shell (RESS) element for sheet forming simulations, International Journal of Plasticity 23 pp 490– · Zbl 1349.74314 · doi:10.1016/j.ijplas.2006.06.004
[15] Cardoso, Enhanced assumed strain (EAS) and assumed natural strain (ANS) methods for one-point quadrature solid-shell elements, International Journal for Numerical Methods in Engineering 75 pp 156– (2008) · Zbl 1195.74165 · doi:10.1002/nme.2250
[16] Hauptmann, Extension of the ’solid-shell’ concept for application to large elastic and large elastoplastic deformations, International Journal for Numerical Methods in Engineering 49 pp 1121– (2000) · Zbl 1048.74041 · doi:10.1002/1097-0207(20001130)49:9<1121::AID-NME130>3.0.CO;2-F
[17] Klinkel, A robust non-linear solid shell element based on a mixed variational formulation, Computer Methods in Applied Mechanics and Engineering 195 pp 179– (2006) · Zbl 1106.74058 · doi:10.1016/j.cma.2005.01.013
[18] Yunhua, Explanation and elimination of shear locking and membrane locking with field consistence approach, Computer Methods in Applied Mechanics and Engineering 162 pp 249– (1998) · Zbl 0949.74069 · doi:10.1016/S0045-7825(97)00346-0
[19] Koschnick, The discrete strain gap method and membrane locking, Computer Methods in Applied Mechanics and Engineering 194 pp 2444– (2005) · Zbl 1082.74053 · doi:10.1016/j.cma.2004.07.040
[20] Hauptmann, ’Solid-shell’ elements with linear and quadratic shape functions at large deformations with nearly incompressible materials, Computers & Structures 79 pp 1671– (2001) · doi:10.1016/S0045-7949(01)00103-1
[21] Mostafa, A solid-shell corotational element based on ANDES, ANS and EAS for geometrically nonlinear structural analysis, International Journal for Numerical Methods in Engineering 95 pp 145– · Zbl 1352.74414 · doi:10.1002/nme.4504
[22] Abed-Meraim, SHB8PS-a new adaptative, assumed-strain continuum mechanics shell element for impact analysis, Computers & Structures 80 pp 791– (2002) · doi:10.1016/S0045-7949(02)00047-0
[23] Schwarze, A reduced integration solid-shell finite element based on the EAS and the ANS concept-geometrically linear problems, International Journal for Numerical Methods in Engineering 80 pp 1322– (2009) · Zbl 1183.74315 · doi:10.1002/nme.2653
[24] Schwarze, A reduced integration solid-shell finite element based on the EAS and the ANS concept-large deformation problems, International Journal for Numerical Methods in Engineering 85 pp 289– (2011) · Zbl 1217.74135 · doi:10.1002/nme.2966
[25] Yang, A survey of recent shell finite elements, International Journal for Numerical Methods in Engineering 47 pp 101– (2000) · Zbl 0987.74001 · doi:10.1002/(SICI)1097-0207(20000110/30)47:1/3<101::AID-NME763>3.0.CO;2-C
[26] Schwarze, Sheet metal forming and springback simulation by means of a new reduced integration solid-shell finite element technology, Computer Methods in Applied Mechanics and Engineering 200 pp 454– · Zbl 1225.74107 · doi:10.1016/j.cma.2010.07.020
[27] Li, A stabilized underintegrated enhanced assumed strain solid-shell element for geometrically nonlinear plate/shell analysis, Finite Elements in Analysis and Design 47 pp 511– (2011) · doi:10.1016/j.finel.2011.01.001
[28] Dvorkin, A continuum mechanics based four-node shell element for general non-linear analysis, Engineering Computations 1 pp 77– (1984) · doi:10.1108/eb023562
[29] Petschek, Difference equations for two-dimensional elastic flow, Journal of Computational Physics 3 pp 307– (1968) · Zbl 0177.54202 · doi:10.1016/0021-9991(68)90024-7
[30] Key, A finite element procedure for the large deformation dynamic response of axisymmetric solids, Computer Methods in Applied Mechanics and Engineering 4 pp 195– (1974) · Zbl 0284.73047 · doi:10.1016/0045-7825(74)90034-6
[31] Kosloff, Treatment of hourglass patterns in low order finite element codes, International Journal for Numerical and Analytical Methods in Geomechanics 2 pp 57– (1978) · doi:10.1002/nag.1610020105
[32] Wing, Finite element stabilization matrices-a unification approach, Computer Methods in Applied Mechanics and Engineering 53 pp 13– (1985) · Zbl 0553.73065 · doi:10.1016/0045-7825(85)90074-X
[33] Abed-Meraim, An improved assumed strain solid-shell element formulation with physical stabilization for geometric non-linear applications and elastic-plastic stability analysis, International Journal for Numerical Methods in Engineering 80 pp 1640– (2009) · Zbl 1183.74254 · doi:10.1002/nme.2676
[34] Reese, A large deformation solid-shell concept based on reduced integration with hourglass stabilization, International Journal for Numerical Methods in Engineering 69 pp 1671– (2007) · Zbl 1194.74469 · doi:10.1002/nme.1827
[35] Flanagan, A uniform strain hexahedron and quadrilateral with orthogonal hourglass control, International Journal for Numerical Methods in Engineering 17 pp 679– (1981) · Zbl 0478.73049 · doi:10.1002/nme.1620170504
[36] Ovsson, Shear locking reduction in eight-noded tri-linear solid finite elements, Computers & Structures 84 pp 476– (2006) · doi:10.1016/j.compstruc.2005.09.014
[37] Simo, Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems, Computer Methods in Applied Mechanics and Engineering 110 pp 359– (1993) · Zbl 0846.73068 · doi:10.1016/0045-7825(93)90215-J
[38] Wilson, Incompatible Displacement Models. Numerical and Computer Mehtods in Structural Mechanics (1973)
[39] Taylor, A non-conforming element for stress analysis, International Journal for Numerical Methods in Engineering 10 pp 1211– (1976) · Zbl 0338.73041 · doi:10.1002/nme.1620100602
[40] Norachan, A co-rotational 8-node degenerated thin-walled element with assumed natural strain and enhanced assumed strain, Finite Elements in Analysis and Design 50 pp 70– (2012) · doi:10.1016/j.finel.2011.08.023
[41] Harnau, About linear and quadratic ” Solid-Shell” elements at large deformations, Computers & Structures 80 pp 805– (2002) · doi:10.1016/S0045-7949(02)00048-2
[42] Edem, Physically stabilised displacement-based ANS solid-shell element, Finite Elements in Analysis and Design 74 pp 30– (2013) · Zbl 1368.74036 · doi:10.1016/j.finel.2013.05.009
[43] Tan, Efficient and accurate multilayer solid-shell element: Non-linear materials at finite strain, International Journal for Numerical Methods in Engineering 63 pp 2124– (2005) · Zbl 1134.74414 · doi:10.1002/nme.1360
[44] Vu-Quoc, Optimal solid shells for non-linear analyses of multilayer composites. I. Statics, Computer Methods in Applied Mechanics and Engineering 192 pp 975– (2003) · Zbl 1091.74524 · doi:10.1016/S0045-7825(02)00435-8
[45] Reese, A model-adaptive hanging node concept based on a new non-linear solid-shell formulation, Computer Methods in Applied Mechanics and Engineering 197 pp 61– (2007) · Zbl 1169.74629 · doi:10.1016/j.cma.2007.07.007
[46] Puso, A highly efficient enhanced assumed strain physically stabilized hexahedral element, International Journal for Numerical Methods in Engineering 49 pp 1029– (2000) · Zbl 0994.74075 · doi:10.1002/1097-0207(20001120)49:8<1029::AID-NME990>3.0.CO;2-3
[47] Prathap G Finite Element Analysis as Computation Online book by Dr Gangan Prathap http://www.cmmacs.ernet.in/cmmacs/Personnel/gpframe1.html
[48] Bazeley GP Cheung YK Irons BM Zienkiewicz OC Triangular elements in plate bending-conforming and nonconforming solutions Ohio, US 1966 547 576
[49] Macneal, A proposed standard set of problems to test finite element accuracy, Finite Elements in Analysis and Design 1 pp 3– (1985) · doi:10.1016/0168-874X(85)90003-4
[50] Belytschko, Physical stabilization of the 4-node shell element with one point quadrature, Computer Methods in Applied Mechanics and Engineering 113 pp 321– (1994) · Zbl 0846.73058 · doi:10.1016/0045-7825(94)90052-3
[51] Simo, On a stress resultant geometrically exact shell model. Part II: The linear theory; computational aspects, Computer Methods in Applied Mechanics and Engineering 73 pp 53– (1989) · Zbl 0724.73138 · doi:10.1016/0045-7825(89)90098-4
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