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本文采用Reissner厚板理论,构造了一个假设二次应力场和一次位移函数的杂交法矩形单元;在此基础上,编制了可分析弹性半无限地基上四边自由矩形厚板的有限元计算程序。分析表明,它具有较好的单调性和较快的收敛速度;而且,由于考虑了横向剪切效应的影响,在板边或板角承受局部荷载和高集度荷载作用区域的解算结果比薄板理论解具有更好的精度。利用此程序,分析了板平面尺寸、板厚和荷载位置变化对板内应力的影响规律。
In this paper, Reissner slab theory is used to construct a hybrid rectangular cell which is assumed to be a quadratic stress field and a first-order displacement function. On this basis, a finite element program is developed to analyze four-sided free rectangular slab with elastic semi-infinite foundation. The analysis shows that it has a better monotonicity and faster convergence rate. Moreover, considering the effect of transverse shearing effect, the results of solving the problem of local load and high degree of concentrated load on the edge of slab or slab Sheet theory solution has better accuracy. Using this program, the influence of plate plane size, plate thickness and load position on internal stress was analyzed.