F uid pressures on unanchored rigid rectangular tanks under action of uplifting acceleration
F uid pressures on unanchored rigid rectangular tanks under action of uplifting acceleration
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上升加速度作用下无锚固刚性矩形储罐的流体压力
DOI：
10.1115/1.4000546
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Y. Ando
中科院分区：
文献类型：
--
作者：
T. Taniguchi;Y. Ando
虽然人们一直认为平底圆柱壳储罐的上提运动会导致储罐的各种损坏，但其力学机理尚未完全了解。除了罐的上提位移外，罐的上提运动所伴随的流体压力可能在罐的损坏原因中起重要作用。对储罐上提运动引起的流体压力的准确估计对于保护储罐免受破坏性地震的影响是必不可少的。作为一系列研究的第一步，本研究从数学上推导了作用在旋转底边上的具有单位深度的刚性矩形储罐上的流体压力，该流体压力伴随角加速度。本文采用的矩形罐等效于刚性平底圆柱壳罐的中心垂直横截面的薄片。假定流体为理想流体，速度势为理想流体，由笛卡尔坐标系下的拉普拉斯方程给出连续性方程。伴随着壁面和底板运动的流体速度构成边界条件。由于该问题被设置为抛物型偏微分方程的Neumann问题，速度势求解与傅里叶余弦展开。速度势对时间的导数给出了罐内任意点的流体压力。用于评估伴随作用在罐的枢转底部边缘上的角加速度的流体压力的数学解由罐的尺寸变量的显式函数给出，但是具有傅立叶级数。所提出的数学解很好地收敛于傅里叶级数的几个第一项。通过显式有限元（FE）分析计算的流体压力值与建议的数学解吻合良好。为了设计者的方便，还提供了描绘由最大切向加速度归一化的流体压力的图表，所述最大切向加速度由角加速度和罐的对角线的乘积给出。因此，由傅立叶级数给出的数学解容易收敛，并且提供了对刚性矩形罐上的流体压力的精确评估，该流体压力伴随着作用在枢转底部边缘上的角加速度。流体压力分布的不规则性随着罐变高而增加。
Although uplift motion of flat-bottom cylindrical shell tanks has been considered to contribute toward various damages to the tanks, the mechanics were not fully understood. As well as uplift displacement of the tanks, fluid pressure accompanying the uplift motion of the tanks may play an important role in the cause of the damage. An accurate estimate of the fluid pressure induced by the uplift motion of the tanks is indispensable in protecting the tanks against destructive earthquakes. As a first step of a series of research, this study mathematically derives the fluid pressure on a rigid rectangular tank with a unit depth accompanying angular acceleration, which acts on a pivoting bottom edge. The rectangular tank employed herein is equivalent to a thin slice of the central vertical cross section of a rigid flat-bottom cylindrical shell tank. Assuming a perfect fluid and velocity potential, a continuity equation is given by the Laplace equation in Cartesian coordinates. The fluid velocities accompanying the motions of the walls and bottom plate constitute the boundary conditions. Since this problem is set as a parabolic partial differential equation of the Neumann problem, the velocity potential is solved with the Fourier-cosine expansion. The derivative of the velocity potential with respect to time gives the fluid pressure at an arbitrary point inside the tank. A mathematical solution for evaluating the fluid pressure accompanying the angular acceleration acting on the pivoting bottom edge of the tank is given by an explicit function of a dimensional variable of the tank, but with the Fourier series. The proposed mathematical solution well converges with a few first terms of the Fourier series. Values of the fluid pressure computed by the explicit finite element (FE) analysis well agrees with those by the proposed mathematical solution. For the designers’ convenience, diagrams that depict the fluid pressures normalized by the maximum tangential acceleration given by the product of the angular acceleration and diagonals of the tank are also presented. Consequently, the mathematical solution given by the Fourier series converges easily and provides accurate evaluation of the fluid pressures on a rigid rectangular tank accompanying the angular acceleration acting on the pivoting bottom edge. Irregularity in the fluid pressure distribution increases as the tank becomes taller.