基于精细积分法和传递矩阵法的变截面压杆临界力

Critical Loads of Variable Cross-Section Compressive Rods Based on Precise Integration Method and Transfer Matrix Method

摘要: 针对变截面压杆临界力提出了一种基于精细积分法和传递矩阵法的组合法。先将压杆离散为若干段，视每段压杆为等截面，采用材料力学理论、平衡原理及矩阵理论，导出了各段压杆的传递矩阵。然后利用相邻段间变形与内力关系，导出了整个变截面压杆的传递矩阵。最后，利用整个压杆两端约束条件，得到了求解变截面压杆临界力的特征方程。结果表明：本方法是一种易于编程、精度易于控制，也易于使用的方法。

Abstract: A combination method of critical load of variable cross-section compressive rods was put forward based on precise integration method and transfer matrix method. First of all, the rod was divided into many sections and every section was viewed as uniform cross-section; the transfer matrixes of all the compressive sections were deduced according to theory of material mechanics, equilibrium principle and theory of matrix. Then the transfer matrix of whole variable cross-section compressive rod was obtained by means of deformation and internal force relationships between adjacent sections. Finally, a characteristic equation to solve the critical load of the variable cross-section compressive rod was presented. Results show that the present method is an easy one to program, control precisely and use conveniently.