充液矩形贮箱弹性箱底板应力与变形分析

基于相容拉格朗日-欧拉法,通过对流场与弹性固体间流固耦合作用的分析,得到了矩形贮箱弹性底板流固耦合系统的自由振动微分方程。将伯努利方程与外加激励条件、速度势函数耦合到自由振动方程中,采用迦辽金积分法,给出了矩形贮箱在流体作用下的应力与变形的解析解。讨论了弹性底板的抗弯刚度、结构尺寸、底板材料参数及流体深度等因素对底板应力与变形的影响。研究结果表明:在液体晃动非线性激励作用下,贮箱底板的应力和变形随着液体深度、板长的增大而增大,随着板厚的减小而增大,且成非线性变化关系;底板的变形及应力与底板的材料常数相关,其中板厚的变化对其变形和应力影响要比板长及液体深度的影响显著得多。本文结果可为工程实际中矩形贮箱的设计提供参考。

Deformation and stress analysis of rectangular tank elastic bottom

Based on united Lagrangian-Eulerian method,the differential equation of rectangular tank elastic bottom free vibration is presented by the fluid-solid interaction theory.Then Bernoulli’s equations,and the potential function are coupled into the vibration equation,thus the theoretical solutions of deformation and stress of tank bottom are given by using Galerkin integral method.The effects of rigidity,geometric shape,materials parameters of elastic bottom and height of fluid on the deformation and stress of bottom are analyzed.It is indicated that the deformation and stress of tank bottom increase with height of fluid,bottom’s length being increased and bottom’s thickness being decreased by nonlinear external excitation of fluid.And the degree of influence is not linearly.The deformation and stress of bottom are related to the bottom materials parameters.The bottom thickness has a much greater impact on deformation and stress than the length of bottom and height of fluid does.The research results may provide a reference for rectangular tank design in engineering practice.