基于Maple的非荷载因素下超静定结构解析求解

Analytical Solution of Statically Indeterminate Structure under Non-load Factors Based on Maple

文章利用结构内力与变形之间的关系,提出了将结构划分为若干杆单元,建立了温度变化下各杆单元的二阶弯矩微分方程和挠度微分方程,以及支座移动时的挠度四阶微分方程,积分得到弯矩和挠度的通解;再根据位移边界条件、结点变形协调条件、平衡条件确定积分常数;用Maple软件编制相应的计算机求解程序,实现了对非荷载因素下超静定结构解析解的计算机求解。计算实例表明,Maple求解程序编制程式化,可以快速获得弯矩、挠度等的精确解,值得在工程中推广应用。

Based on the relationship between internal force and deformation of the structure,this paper proposes to divide the structure into several bar elements,and establishes the second-order bending moment differential equation and deflection differential equation of each bar element under temperature change,as well as the fourth-order deflection differential equation when the support moves.The general solution of bending moment and deflection is obtained by integration.Then,the constant of integration is determined according to the displacement boundary condition,the node deformation compatibility condition and the equilibrium condition.The corresponding computer solution program is compiled by Maple software to solve the analytical solution of statically indeterminate structure under non-load factors.The calculation example shows that the Maple solution program can be programmed to quickly obtain the exact solutions of bending moment and deflection,which is worthy of popularization and application in engineering.