Selective and reduced numerical integrations for NURBS-based isogeometric analysis
Tài liệu tham khảo
I.C. Taig, Structural Analysis by the Matrix Displacement Method, Technical Report, English Electric Aviation Report No. So17, 1961.
Irons, 1966, Engineering applications of numerical integration in stiffness method, J. Am. Inst. Aeronaut. Astronaut., 14, 2035, 10.2514/3.3836
Strang, 1973
Cottrell, 2009
Hughes, 2010, Efficient quadrature for NURBS-based isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 199, 301, 10.1016/j.cma.2008.12.004
Schillinger, 2014, Reduced Bezier element quadrature rules for quadratic and cubic splines in isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 10.1016/j.cma.2014.04.008
Auricchio, 2012, A simple algorithm for obtaining nearly optimal quadrature rules for NURBS-based isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 249–252, 15, 10.1016/j.cma.2012.04.014
Hughes, 2005, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194, 4135, 10.1016/j.cma.2004.10.008
Cottrell, 2007, Studies of refinement and continuity in isogeometric structural analysis, Comput. Methods Appl. Mech. Engrg., 196, 4160, 10.1016/j.cma.2007.04.007
Hughes, 2000
Cools, 1993, Monomial cubature rules since “Stroud”: a compilation, J. Comput. Appl. Math., 48, 309, 10.1016/0377-0427(93)90027-9
Cools, 1999, Monomial cubature rules since “Stroud”: a compilation — part 2, J. Comput. Appl. Math., 112, 21, 10.1016/S0377-0427(99)00229-0
Bouclier, 2012, Locking free isogeometric formulations of curved thick beams, Comput. Methods Appl. Mech. Engrg., 245–246, 144, 10.1016/j.cma.2012.06.008
Adam, 2014, Improved numerical integration for locking treatment in isogeometric structural elements. Part I: beams, Comput. Methods Appl. Mech. Engrg., 279, 1, 10.1016/j.cma.2014.06.023
Adam, 2015, Improved numerical integration for locking treatment in isogeometric structural elements. Part II: plates and shells, Comput. Methods Appl. Mech. Engrg., 284, 106, 10.1016/j.cma.2014.07.020
Zienkiewicz, 1974, Reduced integration technique in general analysis of plates and shells, Int J. Numer. Methods Eng., 3, 275, 10.1002/nme.1620030211
Malkus, 1978, Mixed finite element methods-reduced and selective integration techniques: a unification of concepts, Comput. Methods Appl. Mech. Engrg., 15, 63, 10.1016/0045-7825(78)90005-1
Hughes, 1980, Generalization of selective integration procedures to anisotropic and nonlinear media, Int. J. Numer. Methods Engrg., 15, 1413, 10.1002/nme.1620150914
Stolarski, 1982, Membrane locking and reduced integration for curved element, J. Appl. Mech., 49, 172, 10.1115/1.3161961
Prathap, 1982, Reduced integration and the shear-flexible beam element, Internat. J. Numer. Methods Engrg., 18, 172, 10.1002/nme.1620180205
Elguedj, 2008, B̄ and F̄ projection methods for nearly incompressible linear and non-linear elasticity and plasticity using high-order NURBS elements, Comput. Methods Appl. Mech. Engrg., 197, 2732, 10.1016/j.cma.2008.01.012
Timoshenko, 1970
Kasper, 2000, A mixed-enhanced strain method. Part I: geometrycally linear problems, Comput. Struct., 75, 237, 10.1016/S0045-7949(99)00134-0
Kasper, 2000, A mixed-enhanced strain method. Part II: geometrycally linear problems, Comput. Struct., 75, 252, 10.1016/S0045-7949(99)00134-0
Simo, 1990, A class of mixed assumed strain methods and the method of incompatible modes, Int. J. Numer. Methods Engrg., 29, 1595, 10.1002/nme.1620290802
Simo, 1992, Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes, Int. J. Numer. Methods Engrg., 33, 1413, 10.1002/nme.1620330705
Hughes, 1997, Equivalence of finite elements for nearly incompressible elasticity, Trans. ASME, J. Appl. Mech., 44, 181, 10.1115/1.3423994
Hughes, 1977, A simple and efficient finite element for plate bending, Int. J. Numer. Methods Engrg., 11, 1529, 10.1002/nme.1620111005
Stolarski, 1983, Shear and membrane locking in curved C0 elements, Comput. Methods Appl. Mech. Engrg., 41, 279, 10.1016/0045-7825(83)90010-5
Bicanic, 1979, Spurious modes in two-dimensional isoparametric elements, Comput. Methods Appl. Mech. Engrg., 14, 1545
Belytschko, 1984, Hourglass control in linear and nonlinear problems, Comput. Methods Appl. Mech. Engrg., 43, 251, 10.1016/0045-7825(84)90067-7
Reese, 2000, A stabilization technique to avoid hourglassing in finite elasticity, Int. J. Numer. Methods Engrg., 48, 79, 10.1002/(SICI)1097-0207(20000510)48:1<79::AID-NME869>3.0.CO;2-D
Wriggers, 2008
MATLAB, Version 7.10.0 (R2010a), The MathWorks Inc., Natick, Massachusetts, 2010.
Belytschko, 1985, Stress projection for membrane and shear locking in shell finite elements, Comput. Methods Appl. Mech. Engrg., 51, 221, 10.1016/0045-7825(85)90035-0
MacNeal, 1985, A proposed standard set of problems to test finite element accuracy, Finite Elem. Anal. Des., 1, 3, 10.1016/0168-874X(85)90003-4
Bouclier, 2013, Efficient isogeometric NURBS-based solid-shell elements: mixed formulation and B̄-method, Comput. Methods Appl. Mech. Engrg., 267, 86, 10.1016/j.cma.2013.08.002
