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利用汉克尔变换法,推演得到了文克勒地基、双参数地基、弹性半空间体地基上无限大薄板,赖斯纳、汉盖、克罗姆等中厚板,在任意竖向荷载作用下的统一解;并给出了竖向轴对称荷载条件下的无限大板挠度、弯矩、剪力系数、地基反力系数的计算公式;最后,对圆形均布荷载作用下的不同地基和板模型的板挠度和弯矩进行了对比分析。结果表明:半空间体地基板与文克勒地基板的荷载圆中点的弯矩参数十分相近,但其荷载圆中点挠度系数较后者大1/3~1/2;中厚板理论对地基板挠度有更好地拟合和解析,但对板弯矩等内力的计算精度无改善。
The Hankel transformation method was used to deduce the plate thicknesses of Winkler foundation, two-parameter foundation, infinite thin foundation on elastic half-space foundation, Reisner, Hanai, Crom and so on. Under any vertical load The formulas of the deflection, moment, shear force and foundation reaction coefficient under infinite axial load are given. Finally, The plate deflection and moment of plate model are compared and analyzed. The results show that the bending moment parameters at mid-point of the load-bearing half-space foundation and the Wenkele foundation are similar, but the mid-point deflection coefficient of the load circle is 1/3 ~ 1/2 larger than the latter. Plate theory The deflection of the ground plate is better fitted and resolved, but the calculation accuracy of internal forces such as plate bending moment is not improved.