High frequency modes meshfree analysis of Reissner–Mindlin plates

Timoshenk, 1959 Reissner, 1945, The effect of transverse shear deformation on the bending of elastic plates, J. Appl. Mech., 12, 69, 10.1115/1.4009435 Mindlin, 1951, Influence of rotary inertia and shear in flexural motions of isotropic, elastic plates, J. Appl. Mech., 18, 10.1115/1.4010217 Mindlin, 1956, Flexural vibrations of rectangular plates, J. Appl. Mech., 23, 430, 10.1115/1.4011349 Reddy, 2006 Young, 1950, Vibration of rectangular plates by the Ritz method, J. Appl. Mech., 17, 448, 10.1115/1.4010175 Yu, 2016, NURBS-based isogeometric analysis of buckling and free vibration problems for laminated composites plates with complicated cutouts using a new simple FSDT theory and level set method, Thin-Walled Struct., 101, 141, 10.1016/j.tws.2015.12.008 Roufaeil, 1980, Vibration of rectangular Mindlin plate by the finite strip method, Comput. Struct., 12, 833, 10.1016/0045-7949(80)90021-8 Kong, 1993, Application of the spline finite strip to the analysis of shear-deformable plates, Comput. Struct., 46, 985, 10.1016/0045-7949(93)90083-P Madasamy, 1994, Analysis of plated structures with rectangular cutouts and internal supports using the spline finite strip method, Comput. Struct., 52, 277, 10.1016/0045-7949(94)90280-1 Ng, 1995, Analysis of arbitrary Mindlin plates or bridge decks by spline finite strip method, Comput. Struct., 54, 111, 10.1016/0045-7949(94)00306-N Thompson, 2003, On optimal stabilized MITC4 plate bending elements for accurate frequency response analysis, Comput. Struct., 81, 995, 10.1016/S0045-7949(02)00405-4 Thompson, 2002, A stabilized MITC element for accurate wave response in Reissner-Mindlin plates, Comput. Struct., 80, 769, 10.1016/S0045-7949(02)00046-9 Lee, 2001, Free vibration analysis of plates and shells with a nine-node assumed natural degenerated shell element, J. Sound Vib., 241, 605, 10.1006/jsvi.2000.3313 Bui, 2016, On the high temperature mechanical behaviors analysis of heated functionally graded plates using FEM and a new third-order shear deformation plate theory, Compos. Part B: Eng., 92, 218, 10.1016/j.compositesb.2016.02.048 Zienkiewicz, 2002, Achievements and some unsolved problems of the finite element method, Int. J. Numer. Methods Eng., 47, 9, 10.1002/(SICI)1097-0207(20000110/30)47:1/3<9::AID-NME793>3.0.CO;2-P Wei, 2002, A novel approach for prediction and control of high frequency vibration, J. Sound Vib., 257, 207, 10.1006/jsvi.2002.5055 Zhao, 2002, Discrete singular convolution for the prediction of high frequency vibration of plates, Int. J. Solids Struct., 39, 65, 10.1016/S0020-7683(01)00183-4 Hou, 2005, DSC-Ritz method for the free vibration analysis of Mindlin plates, Int. J. Numer. Methods Eng., 62, 262, 10.1002/nme.1186 Lim, 2005, DSC-Ritz method for high-mode frequency analysis of thick shallow shells, Int. J. Numer. Methods Eng., 62, 205, 10.1002/nme.1179 Racz, 2012, Novel adaptive meshfree integration techniques in meshless method, Int. J. Numer. Methods Eng., 90, 1414, 10.1002/nme.4268 Belytschko, 1994, Element free Galerkin method, Int. J. Numer. Methods Eng., 37, 229, 10.1002/nme.1620370205 Tanaka, 2015, Analysis of cracked shear deformable plates by an effective meshfree plate formulation, Eng. Fract. Mech., 144, 142, 10.1016/j.engfracmech.2015.06.084 Bui, 2013, Meshfree Galerkin Kriging model for bending and buckling analysis of simply supported laminated composite plates, Int. J. Comput. Meth., 10, 1350011, 10.1142/S0219876213500114 Nguyen, 2014, Crack growth modeling in elastic solids by the extended meshfree Galerkin radial point interpolation method, Eng Anal Bound Elem, 44, 87, 10.1016/j.enganabound.2014.04.021 Langley, 1998, A review of current analysis capabilities applicable to the high frequency vibration prediction of aerospace structures, Aeronaut. J., 102, 287, 10.1017/S0001924000065325 Beslin, 1997, A hierarchical functions set for predicting very high order plate bending modes with any boundary conditions, J. Sound Vib., 202, 633, 10.1006/jsvi.1996.0797 Babuska, 1981, The p-version of the finite element method, SIAM I Numer. Anal., 18, 515, 10.1137/0718033 Bui, 2011, A meshfree model without shear-locking for free vibration analysis of first-order shear deformable plates, Eng. Struct., 33, 3364, 10.1016/j.engstruct.2011.07.001 Bui, 2011, An efficient meshfree method for vibration analysis of laminated composite plates, Comput. Mech., 48, 175, 10.1007/s00466-011-0591-8 Bui, 2011, A moving Kriging interpolation-based meshfree method for free vibration analysis of Kirchhoff plates, Comput. Struct., 89, 380, 10.1016/j.compstruc.2010.11.006 Sayakoummane, 2007, A meshless analysis of shells based on moving Kriging interpolation, Int. J. Comput. Methods, 4, 543, 10.1142/S0219876207000935 Bui, 2009, A moving Kriging interpolation-based meshless method for numerical simulation of Kirchhoff plate problems, Int. J. Numer. Methods Eng., 77, 1371, 10.1002/nme.2462 Bui, 2011, An efficient meshfree method for analysis of two-dimensional piezoelectric structures, Smart Mater. Struct., 20, 065016, 10.1088/0964-1726/20/6/065016 Bui, 2011, A moving Kriging interpolation-based element free Galerkin method for structural dynamic analysis, Comput. Meth. Appl. Methods Eng., 200, 1354, 10.1016/j.cma.2010.12.017 Kanok-Nukulchai, 2001, On elimination of shear locking in the element-free Galerkin method, Int. J. Numer. Methods Eng., 52, 705, 10.1002/nme.223 Cho, 2008, Boundary locking induced by penalty enforcement of essential boundary conditions in mesh-free methods, Comput. Methods Appl. Mech. Eng., 131, 1167, 10.1016/j.cma.2007.09.020 Belyschko, 1995, A coupled finite element – element free Galerkin method, Comput. Mech., 17, 186, 10.1007/BF00364080 Krongauz, 1996, Enforcement of essential boundary conditions in meshless approximations using finite elements, Comput. Methods Appl. Mech. Eng., 131, 133, 10.1016/0045-7825(95)00954-X Fernandez-Mendez, 2004, Imposing essential boundary conditions in mesh-free methods, Comput. Methods Appl. Mech. Eng., 193, 1257, 10.1016/j.cma.2003.12.019 Hegen, 1996, Element-free Galerkin methods in combination with finite element approaches, Comput. Methods Appl. Mech. Eng., 135, 143, 10.1016/0045-7825(96)00994-2 Rabczuk, 2006, Coupling of mesh-free methods with finite elements: basic concepts and test results, Commun. Numer. Methods Eng., 22, 1031, 10.1002/cnm.871 Liew, 2004, Free vibration and buckling analyses of shear-deformable plates based on FSDT meshfree method, J. Sound Vib., 276, 997, 10.1016/j.jsv.2003.08.026 Tanaka, 2016, J-integral evaluation for 2D mixed-mode crack problems employing a meshfree stabilized conforming nodal integration method, Comput. Mech., 58, 185, 10.1007/s00466-016-1288-9 Abbassian, 1987, 40 Nguyen, 2016, Nonlinear dynamic and vibration analysis of piezoelectric eccentrically stiffened FGM plates in thermal environment, Int. J. Mech. Sci., 115–116, 711 Nguyen, 2016, Nonlinear thermo-mechanical dynamic analysis and vibration of higher order shear deformable piezoelectric functionally graded material sandwich plates resting on elastic foundations, J. Sandw. Struct. Mater., 1 Nguyen, 2016, Nonlinear dynamic response and vibration of imperfect shear deformable functionally graded plates subjected to blast and thermal loads, J. Mech. Adv. Mater. Struct.