圆形均布荷载作用下弹性地基上结合式双层板中性面分析

弹性地基上结合式双层板问题分析的关键在于中性面的求解,但目前对于两层板泊松比不同时的情况仍没有理想的理论公式和求解方法.文中根据薄板假设,推导了该问题的中性面方程,并提出一种数值法来求解此方程,得到了中性面曲线,发现它不仅与双层板的力学参数有关,还同荷载属性相关,如集中荷载、圆形均布荷载半径等,但它们对中性面位置的影响很小.双层板的泊松比对中性面的不稳定区域有较大的影响,两者越接近,则不稳定区域越小.

Neutral Plane Analysis of Bonded Two Layered Slab on the Elastic Foundation Subjected to Circular Uniformly-Distributed Load

Determination of neutral plane position is the key to the analysis of bonded two layered slab on an elastic foundation,however,there are no theoretical formulas and solving methods for it when the Poisson's ratios of two slabs are different.Based on the Kirchhoff's hypotheses,the equation of neutral plane is deduced in this paper and numerical method is employed to solve the equation and the curve of neutral plane is drawn.The analysis shows that the position of neutral plane is related to the load property especially the mechanical parameter,such as concentrated load,radius of circular uniformly distributed load,etc.but their effects is very little.The Poisson's ratios of two slabs have great effect on the unstable region of neutral plane,which will reduce as the two values of Poisson's ratios become closer.