双向弹簧夹层假定的弹性地基上双层板的解

Solutions of Double-Layer Plates With Two-Way Spring Interlayers on Elastic Foundations

建立了轴对称条件下,层间有双向弹簧夹层的弹性地基上双层板力学模型,应用Hankel(汉克尔)变换法推演得到了任意轴对称荷载作用下的Winkler(文克勒)地基、双参数地基和弹性半空间体地基上无限大双层板的一般解析解,给出了双层板的挠度、弯矩、剪力,以及层间反力和位移的计算公式.进而,利用该力学模型的解,分析了层间条件对双层板挠度、弯矩的影响规律,计算了上、下层板的中性轴位置,讨论了层间双向弹簧系数的取值方法.结果表明:1)随着层间竖向弹簧参数增大,上层板挠度和弯曲应力减小,下层板挠度和弯曲应力增大;随着层间水平摩阻参数增大,上、下层板的挠度和弯矩均减小;2)当双层板的剪切和压缩效应系数分别取2/3,3/5时,双层板的剪切和压缩效应可较好地被考虑;3)上、下层板的中性轴位置是变化的,它随着距荷载圆中心点的距离增大而向上、下层板各自中面趋近.

Under axisymmetric conditions, a mechanics model for double-layer plates with two-way spring interlayers on elastic foundations was built. The Hankel transform method was used to derive the general analytical solutions of the infinite double-layer plates respectively on the Winkler foundation, the two-parameter foundation and the elastic half-space foundation under arbitrary axisymmetric load. Then the calculating formulae for the deflection, bending mo- ment, shearing force and the interlayer reaction force and displacement were given. The analytical solutions were applied to study the effects of the interlayer conditions on the deflection and bending moment of the double-layer plates, calculate the positions of neutral axes of the upper and lower plates, and discuss the specific values of the interlayer spring coefficients. The re- sults show that, 1 ） with the increase of the vertical spring coefficient, the deflection and ben- ding stress of the upper plate decrease, while those of the lower plate increase; on the other hand, with the increase of the horizontal friction parameter, those of both the upper and lower plates decrease; 2） when the shearing coefficient and compressibility of the double-layer plates are given values of 2/3 and 3/5 respectively, the effects of shearing and compression could be well considered; 3） the neutral axes＇ positions of the upper and lower plates are changeable, but respectively approach the center planes of the upper and lower plates with the increase of the distance from the load center.