Symplectic method for the influence of surface effect on thermal buckling of graded porous nanobeams - LI Qinglu; NIU Xiaojie; ZHANG Jinghua (Xibei Gongye Daxue Xuebao)
The influences of surface effect on the thermal buckling behavior of graded porous nano-beams were analyzed. Based on the Grutin-Murdoch surface elasticity theory and Euler beam theory, the thermal buckling of graded porous nano-beams was studied by using Hamilton system. In the symplectic space, the buckling problem of gradient porous beams was reduced to the zero eigenvalue problem of the system, and the critical buckling temperature and buckling mode of nano-beams correspond to the symplectic eigenvalue and eigensolution of the Hamiltonian system. It is assumed that the performance of gradient porous materials varies continuously throughout the thickness, and two cosine forms of uneven distribution of porosity along its thickness are considered. By using bifurcation conditions and normalization methods, the critical buckling temperature rise for buckling modes and nano-beams was analytically determined. Finally, the influence of surface effects on the thermal buckling of gradient porous nano-beams was presented in the form of a chart. The results indicate that graded porous nano-beams have significant surface effects. Considering surface effects, the critical thermal load and critical buckling temperature of porous nano-beams will be increased. At the same time, appropriate porosity coefficients and pore distribution can effectively improve the mechanical properties of porous nano-beams.