Discrete systems behave as nonlocal structural elements: Bending, buckling and vibration analysis
Tóm tắt
Từ khóa
Tài liệu tham khảo
Andrianov, 2006, On an elastic dissipation model as continuous approximation for discrete media, Math. Probl. Eng., 27373, 1, 10.1155/MPE/2006/27373
Andrianov, 2010, Improved continuous models for discrete media, Math. Probl. Eng., 986242, 1, 10.1155/2010/986242
Challamel, 2008, The small length scale effect for a non-local cantilever beam: a paradox solved, Nanotechnology, 19, 345703, 10.1088/0957-4484/19/34/345703
Challamel, 2009, A dispersive wave equation using non-local elasticity, C. R. Mécanique, 337, 591, 10.1016/j.crme.2009.06.028
Challamel, 2013, Variational formulation of gradient or/and nonlocal higher-order shear elasticity beams, Compos. Struct., 105, 351, 10.1016/j.compstruct.2013.05.026
Challamel, 2013, Analytical length scale calibration of nonlocal continuum from a microstructured buckling model, Z. Angew. Math. Mech., 10.1002/zamm.201200130
Challamel, 2013, Nonlocal equivalent continua for buckling and vibration analyses of microstructured beams, J. Nanomech. Micromech., ASCE, 10.1061/(ASCE)NM.2153-5477.0000062
Charlotte, 2012, Lattice dynamics from a continuum viewpoint, J. Mech. Phys. Sol., 60, 1508, 10.1016/j.jmps.2012.03.004
Domokos, 1993, Qualitative convergence in the discrete approximation of the Euler problem, Mech. Struct. Mach., 21, 529, 10.1080/08905459308905200
Duan, 2013, Development of analytical vibration solutions for microstructured beam model to calibrate length scale coefficient in nonlocal Timoshenko beams, J. Appl. Phys., 114, 1
Elaydi, 2005
Elishakoff, 1998
Elishakoff, 2012
El Naschie, 1990
Eringen, 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Appl. Phys., 54, 4703, 10.1063/1.332803
Galef, 1968, Bending frequencies of compressed beams, J. Acoust. Soc. America, 44, 643, 10.1121/1.1911144
Hencky H., Habilitationschrift, D. Sc. Thesis, Technical University of Darmstadt, Germany 1920.
Kunin, 1982
Lazar, 2006, On a theory of nonlocal elasticity of bi-Helmholtz type and some applications, Int. J. Sol. Struct., 43, 1404, 10.1016/j.ijsolstr.2005.04.027
Massonnet, 1940, Les relations entre les modes normaux de vibration et la stabilité des systèmes élastiques, Bull. du CERES Liège, 183
Milton, 2007, On modifications of Newton’s second law and linear continuum elastodynamics, Proc. R. Soc. A., 463, 855, 10.1098/rspa.2006.1795
Mindlin, 1964, Micro-structure in linear elasticity, Arch. Rat. Mech. Anal., 16, 51, 10.1007/BF00248490
Noor, 1988, Continuum modeling for repetitive lattice structures, Appl. Mech. Rev., 41, 285, 10.1115/1.3151907
Ostoja-Starzewski, 2002, Lattice models in micromechanics, Appl. Mech. Rev., 55, 35, 10.1115/1.1432990
Peddieson, 2003, Application of nonlocal continuum models to nanotechnology, Int. J. Eng. Sci., 41, 305, 10.1016/S0020-7225(02)00210-0
Polyzos, 2012, Derivation of Mindlin's first and second strain gradient elastic theory via simple lattice and continuum models, Int. J. Sol. Struct., 49, 470, 10.1016/j.ijsolstr.2011.10.021
Reddy, 2008, Nonlocal continuum theories of beams for the analysis of carbon nanotubes, J. Appl. Phys., 103
Salvadori, 1951, Numerical computation of buckling loads by finite differences, Trans. ASCE, 116, 590
Santoro, 2006, Accuracy of the finite difference method in stochastic setting, J. Sound Vibrat., 291, 275, 10.1016/j.jsv.2005.06.038
Seide, 1975, Accuracy of some numerical methods for column buckling, J. Eng. Mech., 101, 549
Silverman, 1951, Discussion on the paper of “Salvadori M.G., Numerical computation of buckling loads by finite differences, Trans. ASCE, 116, 590
Tarnai, 1995, The Southwell and the Dunkerley theorems, 141
Wang, 2006, Buckling analysis of micro- and nano-rods/tubes based on nonlocal Timoshenko beam theory, J. Phys. D: Appl. Phys., 39, 3904, 10.1088/0022-3727/39/17/029
Wang, 2008, Beam bending solutions based on nonlocal Timoshenko beam theory, J. Eng. Mech., 134, 475, 10.1061/(ASCE)0733-9399(2008)134:6(475)
Wang, 2009, Postbuckling of nano rods/tubes based on nonlocal beam theory, Int. J. Appl. Mech., 1, 259, 10.1142/S1758825109000150
Wang, 2013, Calibration of Eringen’s small length scale coefficient for initially stressed vibrating nonlocal Euler beams based on microstructured beam model, J. Phys. D: Appl. Phys., 46, 345501, 10.1088/0022-3727/46/34/345501
Wang, 1951, Discussion on the paper of “Salvadori M.G., Numerical computation of buckling loads by finite differences”, Trans. ASCE, 116, 629
Wang, 1953
Wattis, 2000, Quasi-continuum approximations to lattice equations arising from the discrete non-linear telegraph equation, J. Phys. A: Math. Gen., 33, 5925, 10.1088/0305-4470/33/33/311
Xu, 2013, Stability analysis of nonlocal elastic columns with initial imperfection, Math. Probl. Eng., 341232
Zhang, 2010, Bending, buckling and vibration of hybrid nonlocal beams, J. Eng. Mech., 136, 562, 10.1061/(ASCE)EM.1943-7889.0000107
Zhang, 2013, Eringen's small length scale coefficient for buckling of nonlocal Timoshenko beam based on a microstructured beam model, J. Appl. Phys., 114, 1