Accurate bending analysis of rectangular plates with two adjacent edges free and the others clamped or simply supported based on new symplectic approach

Timoshenko, 1959

Huang, 1952, Bending of a uniformly loaded rectangular plate with two adjacent edges clamped and the others either simply supported or free, J. Appl. Mech., 451, 10.1115/1.4010542

Leissa, 1963, Bending of a square plate with two adjacent edges free and the others clamped or simply supported, AIAA J., 1, 116, 10.2514/3.1480

Chang, 1981, Rectangular plates with two adjacent edges clamped and other two adjacent edges free, Acta Mech. Solida Sin., 4, 491

Holl, 1937, Cantilever plate with concentrated edge load, J. Appl. Mech., 4, 8, 10.1115/1.4008740

Barton, 1948, Finite difference equations for the analysis of thin rectangular plates with combinations of fixed and free edges, Defense Res. Lab, 175

MacNeal, 1951, The solution of elastic plate problems by electrical analogies, J. Appl. Mech., 59, 10.1115/1.4010221

Nash, 1952, Several approximate analyses of the bending of a rectangular cantilever plate by uniform normal pressure, J. Appl. Mech., 33, 10.1115/1.4010403

Zienkiewicz, 1964, The finite element method for analysis of elastic isotropic and orthotropic slabs, Proc. Inst. Civ. Eng., 28, 471, 10.1680/iicep.1964.10014

Shih, 1979, On the spline finite element method, J. Comput. Math., 1, 50

Cheung, 1976

Jaswon, 1968, An integral equation formulation of plate bending problems, J. Eng. Math., 2, 83, 10.1007/BF01534962

Civalek, 2007, Three-dimensional vibration, buckling and bending analyses of thick rectangular plates based on discrete singular convolution method, Int. J. Mech. Sci., 49, 752, 10.1016/j.ijmecsci.2006.10.002

Civalek, 2004, Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns, Eng. Struct., 26, 171, 10.1016/j.engstruct.2003.09.005

Malekzadeh, 2008, Large amplitude flexural vibration analysis of tapered plates with edges elastically restrained against rotation using DQM, Eng. Struct., 30, 2850, 10.1016/j.engstruct.2008.03.016

Malekzadeh, 2007, Large deformation analysis of orthotropic skew plates with nonlinear rotationally restrained edges using DQM, Compo. Struct., 80, 196, 10.1016/j.compstruct.2006.05.001

Malekzadeh, 2007, A DQ large deformation analysis of composite plates on nonlinear elastic foundations, Compo. Struct., 79, 251, 10.1016/j.compstruct.2006.01.004

Malekzadeh, 2007, A differential quadrature nonlinear free vibration analysis of laminated composite skew thin plates, Thin-Walled Struct., 45, 237, 10.1016/j.tws.2007.01.011

Han, 1999, Static analysis of Mindlin plates: the differential quadrature element method (DQEM), Comput. Methods Appl. Mech. Eng., 177, 51, 10.1016/S0045-7825(99)00371-0

Donning, 1998, Meshless methods for shear-deformable beams and plates, Comput. Methods Appl. Mech. Eng., 152, 47, 10.1016/S0045-7825(97)00181-3

Shen, 1995, Bending analysis of rectangular moderately thick plates using spline finite element method, Comput. Struct., 54, 1023, 10.1016/0045-7949(94)00401-N

Feng, 1985, On difference scheme and symplectic geometry, 42

Feng, 1986, Difference schemes for Hamiltonian formalism and symplectic geometry, J. Comput. Math., 4, 279

Feng, 1991, Hamilton algorithm for Hamiltonian dynamical systems, Progress Nat. Sci., 1, 105

Zhong, 1993, Physical interpretation of the symplectic orthogonality of the eigensolutions of a Hamiltonian or symplectic matrix, Comput. Mech. Struct. Eng., 49, 749, 10.1016/0045-7949(93)90077-Q

Zhong, 1993, Method of separation of variables and Hamiltonian system, Numer. Meth. Part. Differ. Eqn., 9, 63, 10.1002/num.1690090107

Zhong, 1995

Zhong, 1999, New solution system for plate bending, Comput. Mech. Struct. Eng., 31, 17, 10.1016/B978-008043008-9/50040-5

Lim, 2007, On new symplectic elasticity approach for exact bending solutions of rectangular thin plates with two opposite sides simply supported, Int. J. Solids Struct., 44, 5396, 10.1016/j.ijsolstr.2007.01.007

Yao, 2002

Yao, 2001, Hamiltonian system based Saint Venant solutions for multi-layered composite plane anisotropic plates, Int. J. Solids Struct., 38, 5807, 10.1016/S0020-7683(00)00371-1

Zhang, 2003, Hamiltonian principle based stress singularity analysis near crack corners of multi-material junctions, Int. J. Solids Struct., 40, 493, 10.1016/S0020-7683(02)00585-1

Leung, 2007, Closed form stress distribution in 2D elasticity for all boundary conditions, Appl. Math. Mech.-Engl. Edit., 28, 1629, 10.1007/s10483-007-1210-z

Leung, 2007, The boundary layer phenomena in two-dimensional transversely isotropic piezoelectric media by exact symplectic expansion, Int. J. Numer. Methods Eng., 69, 2381, 10.1002/nme.1855

Zhao, 2008, On numerical calculation in symplectic approach for elasticity problems, J. Zhejiang University-Sci. A, 9, 583, 10.1631/jzus.A0720124

Bao, 2005, Symplectic solution method for Mindlin middle thick plate, Acta Mech. Solida Sinica, 26, 102

Ju, 2008, Rectangular thick plate analysis based on Hamilton approach, Eng. Mech., 25, 1