基于非局部理论, 分析了双层完好粘接板在双轴受压和温度场耦合作用下屈曲的尺度效应和非局部效应. 通过理论计算对经典弹性理论和非局部理论的计算结果进行了比较分析. 结果表明: 在非局部理论下, 由于系统内部结构之间的相互作用, 系统的屈曲临界力有所降低, 并且当屈曲波数越大时, 内部结构相互作用域进一步收缩, 使得有效弯曲刚度减小, 所以非局部参数对屈曲力的影响更为显著; 在外载荷和温度耦合作用下, 温度升高会导致屈曲临界力减小, 温度降低会导致屈曲临界力增大. 还对3 种不同温度场进行了讨论, 分析了在3 种温度场下温度变化对外载荷的影响, 以及与系统尺寸大小的关系.
The scale effect on buckling of bonding materials under biaxial compression coupled with temperature changes is studied. A developed nonlocal plate theory is applied to study the buckling behavior of the nonlocal multiple-plate model. The Navier’s approach is used to obtain exact solutions for buckling loads under simply supported boundary conditions. The effects of the scale coefficient, wave number, thickness ratio, elastic modular ratio and temperature changes on the buckling loads are investigated. It is shown that the critical buckling force may be overestimated with the classical continuum theory. The nonlocal effect is proved to be more prominent for higher buckling modes. In addition, three kinds of temperature changes are taken into account. The influence of temperature
changes on the buckling loads and the relationship with the system size are analyzed.
[1] Chen X, Hutchinson J W. Herringbone buckling patterns of compressed thin films on compliant substrates [J]. Journal of Applied Mechanics, 2004, 71(5): 597-603.
[2] Huang R. Kinetic wrinkling of an elastic film on a viscoelastic substrate [J]. Journal of the Mechanics and Physics of Solids, 2005, 53(1): 63-89.
[3] Huang R, Suo Z. Instability of a compressed elastic film on a viscous layer [J]. International Journal of Solids and Structures, 2002, 39(7): 1791-1802.
[4] Huang R, Suo Z. Wrinkling of a compressed elastic film on a viscous layer [J]. Journal of Applied Physics, 2002, 91(3): 1135-1142.
[5] Li B, Huang S Q, Feng X Q. Buckling and postbuckling of a compressed thin film bonded on a soft elastic layer: a three-dimensional analysis [J]. Arch Appl Mech, 2010, 80(2): 175-188.
[6] Eringen A C. Nonlocal polar elastic continua [J]. International Journal of Engineering Science, 1972, 10(1): 1-16.
[7] Eringen A C. On differential-equations of nonlocal elasticity and solutions of screw dislocation and surface-waves [J]. Journal of Applied Physics, 1983, 54(9): 4703-4710.
[8] Eringen A C. Nonlocal contimuum field theories [M]. New York: Springer, 2001.
[9] Shen H S. Nonlocal plate model for nonlinear analysis of thin films on elastic foundations in thermal environments [J]. Composite Structures, 2011, 93(3): 1143-1152.
[10] Pijaudier S M G, Bazant Z P. Nonlocal damage theory [J]. Journal of Engineering Mechanics, 1987, 113(10): 1512-1533.
[11] Bazant Z P. Nonlocal damage theory based on micro-mechanics of crack interactions [J]. Journal of Engineering Mechanics, 1994, 120(1): 593-617.
[12] Pradhan S C. Buckling of single layer graphene sheet based on nonlocal elasticity and higher order shear deformation theory [J]. Phys Lett A, 2009, 373(45): 4182-4188.
[13] Pradhan S C, Murmu T. Small scale effect on the buckling of single-layered graphene sheets under bi-axial compression via nonlocal continuum mechanics [J]. Computational Material Science, 2009, 47(1): 268-274.
[14] Pradhan S C, Murmu T. Small scale effect on the buckling analysis of single-layered graphene sheet embedded in an elastic medium based on nonlocal plate theory [J]. Physica E, 2010, 42(5): 1293-1301.
[15] Wang Q, Liew K M. Application of nonlocal continuum mechanics to static analysis of microand nano-structures [J]. Physics Letters A, 2007, 363(3): 236-242.
