具有弹性约束和初挠度的弹性压杆力与位移关系分析

Analysis of the Relationship Between Force and Displacement of an Elastic Strut with Elastic Restraint and Initial Deflection

实际桁架中的受压杆件可以视为具有弹性约束和初挠度的压杆,对桁架结构的承载能力起决定性作用。以具有弹性约束和初挠度的弹性压杆作为研究对象,应用大挠度弯曲变形理论研究其失稳后的力学行为即压杆轴向压力与位移的关系。建立了压杆的力学模型和数学模型,采用龙格-库塔(Range-Kutta)法求出其数值解。计算结果表明:压杆失稳后轴向压力与位移之间呈非线性关系;在轴向压力一定的情况下,弹性压杆的杆端位移量随初挠度的增大而增大,且压杆的初始位移量在轴向压力越小时影响越显著;轴向压力一定时,支承刚度越大弹性压杆的轴向位移也就越小;轴向位移一定时,支座的支承刚度越大所需的轴向压力也就越大;支承刚度和初挠度共同作用时,支承刚度可以在一定程度上抵消初挠度对弹性压杆力与位移关系的影响。因此,考虑受压杆件的支承刚度约束和初挠度对研究桁架结构破坏过程的计算机模拟是十分必要的。

The compression member in the actual truss can be regarded as the compression member with elastic constraint and initial deflection,which plays a critical role in the bearing capacity of the truss structure.In this paper,the elastic compression bar with elastic constraints and initial deflection is taken as the research object,and the mechanical behavior of the buckling bar is studied by employing the theory of bending deformation with large deflection,ie.the relation between axial pressure and displacement of the compression bar.The mechanical model and mathematical model of the compression bar are established,and the numerical solution is obtained by runge-Kutta method.The calculation results show that;The relation between axial pressure and displacement is nonlinear.When the axial pressure is constant,the rod end displacement increases with the initial deflection,and the influence of the initial displacement is more significant when the axial pressure(F>F;) is small.When the axial pressure is constant,the greater the supporting stiffness is,the smaller the axial displacement of the elastic compression bar is.When the axial displacement is constant,the greater the bearing stiffness is,the greater the axial pressure will be.When the supporting stiffness and the initial deflection act together,the supporting stiffness can offset the influence of the initial deflection on the relationship between the force and displacement of the elastic compression bar to a certain extent.Therefore,it is necessary to study the failure process of truss structure by computer simulation considering the support stiffness constraint and initial deflection of the truss.