剪切变形对厚壁圆形贮液池的影响

将池壁厚度较大的圆形贮液池当作中厚壳圆筒,考虑剪切变形的影响,建立贮液池结构分析的中厚壳理论,其微分方程与Winkler地基上Timoshenko梁的微分方程一致,当贮液池池壁剪切刚度取无穷大时,其可退化成相应薄壳理论,是一个通用模型.利用初参数法,推导微分方程的解和有限元列式,分析底部固结、顶部自由圆形贮液池在三角形分布荷载和池顶弯矩作用下,其环向力系数、弯矩系数随池壁厚度、高度的变化,并与不考虑剪切变形影响的计算结果进行比较.数值计算结果表明:在圆形贮液池中考虑剪切变形影响的挠度等计算结果偏小;壁厚越大,计算结果越小;剪切变形对环向力和径向位移的影响比对弯矩和剪力的影响大,其影响程度与贮液池结构、边界条件及作用荷载形式有关.

Shear deformation influence on cylindrical liquid-storage tank with thick wall

Treating cylindrical liquid-storage tank with relatively thick wall as thick shell cylinder, and considering the shear deformation effect, analysis theory of thick shell was established, whose differential equation was the same as the interactive equation of Timoshenko beam on Winkler foundation. When the shear stiffness of tank wall tended to infinite, thick shell theory was degenerated into thin shell theory. So the thick shell theory was a general model. Using initial parameter method, solutions to differential equation were derived and finite element formulation was established. The solutions to the cylindrical liquid-storage tank under triangular distributing load and top moment were analyzed. To demonstrate the shear deflection effect, loop force and moment coefficients were presented to describe the change with the tank height and thickness. Results of thin shell and thick shell theories were compared. The results show that shear deformation leads to small results of deflection and so on. The thicker the tank walls, the less the computing results. Shear deformation affects loop force and radial displacement more than the moment and shear force, which depends on the structures, boundary conditions and loads.