剪切可变形多孔梯度梁屈曲的解析解

Analytical Buckling Solutions of Shear Deformable Porous Gradient Beams

多孔梯度梁具有优异的力学性能,受到研究者的广泛关注.然而,同时考虑轴线可伸长和剪切可变形效应的多孔梁屈曲问题尚未得到充分重视.基于屈曲控制方程和泰勒级数展开方法,推导出四种典型边界约束条件下多孔梁屈曲临界载荷的解析表达式.然后,定义轴线可伸长和剪切可变形作用的影响系数,并分别考虑影响系数,孔隙率和孔隙分布对屈曲临界载荷的影响.结果表明,影响系数会降低梁的屈曲临界载荷;孔隙率越大,临界屈曲载荷越小.此外,合理设计孔隙分布有助于提高多孔梁的稳定性.

Porous gradient beams have excellent mechanical properties and have attracted wide attention from researchers.However,the buckling problem of porous beams considering both axial elongation and shear deformability has not been given sufficient attention.Based on the buckling governing equation and Taylor series expansion method,the analytical expressions of the critical buckling loads of the porous beams under four typical boundary constraints are derived.Then,the influence coefficients of axial elongation and shear deformability are defined,and the effects of the influence coefficient,porosity and pore distribution on the critical buckling load are investigated,respectively.The results show that the influence coefficient can reduce the critical buckling load of the beam.The larger the porosity,the smaller the critical buckling load.In addition,a reasonable design of pore distribution is helpful in improving the stability of porous beams.