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考虑剪切变形的影响,推导了圆形水池在轴对称荷载作用下的中厚壳有矩理论公式,其微分方程与Winkler地基上Timoshenko梁的微分方程一致,当圆形水池池壁剪切刚度取无穷大时,其可退化成相应薄壳理论公式。利用初参数法,推导了微分方程的解形式和建立了结构分析的传递矩阵法。分析了底部固结顶部自由、在分布荷载和径向荷载作用下阶梯形圆形水池横向挠度、转角、剪力、弯矩随池壁高度的变化,并与不考虑剪切变形影响的计算结果、Ansys结果进行了比较。计算结果表明:圆形水池考虑剪切变形影响的计算结果偏小、采用薄壳理论偏安全;剪切变形对弯矩、剪力影响比对环向力、径向位移影响大;所建立的圆形水池初参数解和转递矩阵法丰富了圆形水池和Winkler地基上Timoshenko梁的计算理论。
Considering the influence of shear deformation, the theoretical formula for the medium-thick shell with circular axis under axial symmetry load is deduced. The differential equation is consistent with the differential equation of Timoshenko beam on the Winkler foundation. When the shear stiffness of the circular pool wall Take infinity, which can degenerate into the corresponding shell theory formula. Using the method of initial parameters, the solution form of differential equation and the transfer matrix method of structural analysis are established. The variation of the transverse deflection, corner, shear force and bending moment of the circular trapezoidal circular pool with the height of the pool wall under the distributed load and the radial load was analyzed. The calculation results were also compared with those without considering the influence of the shear deformation Ansys results were compared. The calculation results show that the calculation results of the circular pool considering the influence of shear deformation are small and the shell theory is partial safety; the influence of shear deformation on the bending moment and shear force is greater than that of the circumferential force and radial displacement; The initial parameter solution and transfer matrix method of the circular pool enriched the computational theory of the Timoshenko beam on a circular pool and Winkler foundation.