Equilibrium equations for 3D critical buckling of helical springs

In most cases,the research on the buckling of a helical spring is based on the column,the spring is equivalent to the column,and the torsion around the axial line is ignored.A three-dimensional(3D) helical spring model is considered in this paper.The equilibrium equations are established by introducing two coordinate systems,the Frenet and the principal axis coordinate systems,to describe the spatial deformation of the center line and the torsion of the cross section of the spring,respectively.By using a small deformation assumption,the variables of the deflection can be expanded into Taylor’s series,and the terms of high orders are ignored.Hence,the equations can be simplified to the functions of the twist angle and the arc length,which can be solved by a numerical method.The reaction loads of the spring caused by the axial load subjected to the center point are also discussed,giving the boundary conditions for the solution to the equilibrium equations.The present work is useful to the research on the behavior of the post-buckling of the compressed helical spring.     

螺旋弹簧临界屈曲失稳的平衡方程

目前,针对螺旋弹簧失稳现象的研究主要基于当量柱模型,将弹簧等效为柱模型,忽略其绕轴线的转动．该文建立了三维螺旋弹簧模型,通过曲线Frenet坐标系和主轴坐标系,建立了描述弹簧螺旋中心线的空间变形和截面扭转变形的平衡方程．采用小变形假设,通过对弹簧挠度变量采用Taylor级数展开,并忽略其高阶小量,平衡方程可以被简化为扭转角和弧长的函数,使获得方程的数值解成为可能．同时,讨论了作用于弹簧圆心位置的轴向力引起的弹簧约束端反作用力,为平衡方程的求解确定了边界载荷条件．该文的研究工作为进一步研究受压螺旋弹簧的后屈曲性奠定了基础．     

大型冷却塔的风致振动响应数值分析

风荷载是大型冷却塔建筑设计的主要荷载之一,通过风振时域分析可以全面地了解塔身的风振响应特性。本文探讨了采用线性滤波法中的自回归模型(auto-regressive,AR)模拟大型冷却塔风致振动响应的数值方法。首先根据AR模型,基于随机模拟方法,计算冷却塔表面不同高度的随机脉动风压。通过将随机脉动风压和平均风压作为冷却塔表面的外载,采用有限元分析软件计算某冷却塔的风致振动响应。结果表明,基于随机脉动风荷载模拟的数值计算方法,能正确反映冷却塔塔身的风振响应。该方法特别适用于冷却塔高度超出规范要求的情况下,评估冷却塔的风振响应。     

限制失稳模态方程及约束载荷计算

针对受压限制失稳结构,利用点接触、线接触屈曲模型,建立了杆在各种屈曲模态下的挠度曲线方程.通过求解曲线方程,可以得到发生限制失稳结构在各种屈曲模态下,与外部限制失稳构件之间的接触载荷大小,分析了受压结构与限制失稳构件之间的间隙对接触载荷的影响.通过对屈曲模态中各波形的形态进行调整,研究了同一屈曲模态,不同失稳波形下接触载荷的差异.