An alternative alpha finite element method with discrete shear gap technique for analysis of isotropic Mindlin–Reissner plates
Tài liệu tham khảo
Zienkiewicz, 1988, A robust triangular plate bending element of the Reissner–Mindlin type, International Journal for Numerical Methods in Engineering, 26, 1169, 10.1002/nme.1620260511
Ayad, 1998, A new hybrid-mixed variational approach for Reissner–Mindlin plate, International Journal for Numerical Methods in Engineering, 42, 1149, 10.1002/(SICI)1097-0207(19980815)42:7<1149::AID-NME391>3.0.CO;2-2
Lovadina, 1998, Analysis of a mixed finite element method for the Reissner–Mindlin plate problems, Computer Methods in Applied Mechanics and Engineering, 163, 71, 10.1016/S0045-7825(98)00003-6
Taylor, 1993, Linked interpolation for Reissner–Mindlin plate element: part II-A simple triangle, International Journal for Numerical Methods in Engineering, 36, 3043, 10.1002/nme.1620361803
Simo, 1990, A class of mixed assumed strain methods and the method of incompatible modes, International Journal for Numerical Methods in Engineering, 29, 1595, 10.1002/nme.1620290802
César de Sá, 1999, New enhanced strain elements for incompatible problems, International Journal for Numerical Methods in Engineering, 44, 229, 10.1002/(SICI)1097-0207(19990120)44:2<229::AID-NME503>3.0.CO;2-I
César de Sá, 2002, Development of shear locking-free shell elements using an enhanced assumed strain formulation, International Journal for Numerical Methods in Engineering, 53, 1721, 10.1002/nme.360
Cardoso, 2008, 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, 156, 10.1002/nme.2250
Bletzinger, 2000, A unified approach for shear-locking free triangular and rectangular shell finite elements, International Journal for Numerical Methods in Engineering, 75, 321
Liu, 2007, A smoothed finite element method for mechanics problems, Computational Mechanics, 39, 859, 10.1007/s00466-006-0075-4
Dai, 2007, An n-sided polygonal smoothed finite element method (nSFEM) for solid mechanics, Finite Elements in Analysis and Design, 43, 847, 10.1016/j.finel.2007.05.009
Dai, 2007, Free and forced vibration analysis using the smoothed finite element method (SFEM), Journal of Sound and Vibration, 301, 803, 10.1016/j.jsv.2006.10.035
H. Nguyen-Xuan, T. Nguyen-Thoi, A stabilized smoothed finite element method for free vibration analysis of Mindlin–Reissner plates, Communications in Numerical Methods in Engineering, doi: 10.1002/cnm.1137, in press.
Rabczuk, 2007, A three dimensional meshfree method for static and dynamic multiple crack nucleation/propagation with crack path continuity, Computational Mechanics, 40, 473, 10.1007/s00466-006-0122-1
Nguyen-Xuan, 2008, A smoothed finite element method for plate analysis, Computer Methods in Applied Mechanics and Engineering, 197, 1184, 10.1016/j.cma.2007.10.008
Nguyen-Thanh, 2008, A smoothed finite element method for shell analysis, Computer Methods in Applied Mechanics and Engineering, 198, 165, 10.1016/j.cma.2008.05.029
Rabczuk, 2007, A meshfree thin shell method for non-linear dynamic fracture, International Journal for Numerical Methods in Engineering, 72, 524, 10.1002/nme.2013
Rabczuk, 2006, A meshfree thin shell for arbitrary evolving cracks based on an external enrichment, Computer Modeling in Engineering and Sciences, 16, 115
Bordas, 2008, Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment, Engineering Fracture Mechanics, 75, 943, 10.1016/j.engfracmech.2007.05.010
Bordas, 2010, Strain smoothing in FEM and XFEM, Computers and Structures, 88, 1419, 10.1016/j.compstruc.2008.07.006
Rabczuk, 2005, Adaptivity for structured meshfree particle methods in 2D and 3D, International Journal for Numerical Methods in Engineering, 63, 1559, 10.1002/nme.1326
Rabczuk, 2006, Application of meshfree particle methods to static fracture of reinforced concrete structures, International Journal of Fracture, 137, 19, 10.1007/s10704-005-3075-z
Rabczuk, 2007, A simplified meshfree method for shear bands with cohesive surfaces, International Journal for Numerical Methods in Engineering, 69, 993, 10.1002/nme.1797
Rabczuk, 2004, Stable particle methods based on Lagrangian kernels, Computer Methods in Applied Mechanics and Engineering, 193, 1035, 10.1016/j.cma.2003.12.005
Rabczuk, 2009, Simulations of instability in dynamic fracture by the cracking particles method, Engineering Fracture Mechanics, 76, 730, 10.1016/j.engfracmech.2008.06.002
Liu, 2008, A generalized gradient smoothing technique and the smoothed bilinear form for Galerkin formulation of a wide class of computational methods, International Journal Computation Methods, 2, 199, 10.1142/S0219876208001510
Liu, 2009, A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems, Computational Structural, 87, 14, 10.1016/j.compstruc.2008.09.003
Liu, 2009, A novel Galerkin-like weakform and a superconvergent alpha finite element method (SαFEM) for mechanics problems using triangular meshes, Journal of Computational Physics, 228, 4055, 10.1016/j.jcp.2009.02.017
Liu, 2008, A novel alpha finite element method (α FEM) for exact solution to mechanics problems using triangular and tetrahedral elements, Computer Methods in Applied Mechanics and Engineering, 197, 3883, 10.1016/j.cma.2008.03.011
Nguyen-Thanh, 2010, An alternative alpha finite element method (Aαfem) free and forced vibration analysis of solids using triangular meshes, Journal of Computational and Applied Mathematics, 223, 2112, 10.1016/j.cam.2009.08.117
Liew, 2004, Free vibration and buckling analyses of shear-deformable plates based on FSDT meshfree method, Journal of Sound and Vibration, 276, 997, 10.1016/j.jsv.2003.08.026
Liu, 2008, A superconvergent point interpolation method (SC-PIM) with piecewise linear strain field using triangular mesh, International Journal for Numerical Methods in Engineering, 77, 1439, 10.1002/nme.2464
Zienkiewicz, 2000
Belytschko, 1986, Efficient implementation of quadrilaterals with high coarse-mesh accuracy, Computer Methods in Applied Mechanics and Engineering, 54, 279, 10.1016/0045-7825(86)90107-6
Belytschko, 1983, Assumed strain stabilization of the 4-node quadrilateral with 1-point quadrature for nonlinear problems, Computer Methods in Applied Mechanics and Engineering, 88, 311, 10.1016/0045-7825(91)90093-L
Fredriksson, 2004, Fast and accurate 4-node quadrilateral, International Journal for Numerical Methods in Engineering, 61, 1809, 10.1002/nme.1133
Piltner, 2000, Triangular finite elements with rotational degrees of freedom and enhanced strain modes, Computers and Structures, 75, 361, 10.1016/S0045-7949(99)00095-4
Pian, 2006
Bathe, 1985, A four-node plate bending element based on Mindlin–Reissner plate theory and a mixed interpolation, International Journal for Numerical Methods in Engineering, 21, 367, 10.1002/nme.1620210213
Tessler, 1985, A three-node Mindlin plate element with improved transverse shear, Computer Methods in Applied Mechanics and Engineering, 50, 71, 10.1016/0045-7825(85)90114-8
Nguyen-Xuan, 2010, An edge-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates, Computer Methods in Applied Mechanics and Engineering, 199, 471, 10.1016/j.cma.2009.09.001
Zienkiewicz, 1993, Linked interpolation for Reissner–Mindlin plate elements: part I-a simple quadrilateral, International Journal for Numerical Methods in Engineering, 36, 3043, 10.1002/nme.1620361802
Katili, 1993, A new discrete Kirchhoff–Mindlin element based on Mindlin–Reissner plate theory and assumed shear strain fields—part II: an extended DKQ element for thick-plate bending analysis, International Journal for Numerical Methods in Engineering, 36, 1885, 10.1002/nme.1620361107
Lee, 2004, Free vibration analysis of plates by using a four-node finite element formulated with assumed natural transverse shear strain, Journal of Sound and Vibration, 278, 657, 10.1016/j.jsv.2003.10.018
Lee, 2001, Free-vibration analysis of plates and shells with a nine-node assumed natural degenerated shell element, Journal of Sound and Vibration, 241, 605, 10.1006/jsvi.2000.3313
Liew, 2004, Buckling of rectangular Mindlin plates subjected to partial in-plane edge loads using the radial point interpolation method, International Journal of Solids and Structures, 41, 1677, 10.1016/j.ijsolstr.2003.10.022
Karunasena, 1996, Free vibration of cantilevered arbitrary triangular Mindlin plates, Mechanical Sciences, 38, 431, 10.1016/0020-7403(95)00060-7
Nagashima, 1999, Node-by-node meshless approach and its applications to structural analyses, International Journal for Numerical Methods in Engineering, 46, 341, 10.1002/(SICI)1097-0207(19990930)46:3<341::AID-NME678>3.0.CO;2-T
Morley, 1963
Cen, 2006, Application of the quadrilateral area co-ordinate method: a new element for Mindlin–Reissner plate, International Journal for Numerical Methods in Engineering, 66, 1, 10.1002/nme.1533
Abbassian, 1987
A.W. Leissa, Vibration of plates, NASA, SP-160, Washington DC, 1969.
McGee, 1992, Vibrations of cantilevered skewed trapezodial and triangular plates with corner stress singularities, Mechanical Sciences, 34, 63, 10.1016/0020-7403(92)90054-K
Timoshenko, 1970
Tham, 1990, Buckling analysis of arbitrary shaped plates by spline finite strip method, Computers and Structures, 36, 729, 10.1016/0045-7949(90)90087-I
Kitipornchai, 1993, Buckling of thick skew plates, International Journal for Numerical Methods in Engineering, 36, 1299, 10.1002/nme.1620360804
Azhari, 2000, On the use of bubble functions in the local buckling analysis of plate structures by the spline finite strip method, International Journal for Numerical Methods in Engineering, 48, 583, 10.1002/(SICI)1097-0207(20000610)48:4<583::AID-NME898>3.0.CO;2-A