基于有限质点法的结构屈曲行为分析

BUCKLING ANALYSIS OF STRUCTURES BY THE FINITE PARTICLE METHOD

有限质点法是一种新颖的结构分析方法,它以向量力学和数值计算为基础,将结构离散为质点群,采用牛顿第二定律描述这些质点的运动。该方法中引入移动基础架构求解结构单元内力。采用显示时间积分求解运动方程,避免了迭代求解非线性方程组。该文采用有限质点法分析结构的屈曲行为。以空间杆单元为例推导了有限质点法计算公式。利用自编程序,对空间杆系结构的屈曲行为进行了模拟。在不经过任何特殊处理的情况下,该方法不仅可以越过屈曲极值点,而且能够跟踪结构屈曲后的行为。此外,该方法无需分级加载即可模拟结构的屈曲行为,结构荷载可以在计算分析的初始步全部加在结构上,更符合实际情况。通过算例验证表明有限质点法在结构屈曲行为模拟中的适用性和真实性。

The finite particle method （FPM） is a new structural analysis method which is based on the Vector Mechanics and numerical calculations. In this method, the analyzed domain is discretized into finite particles, whose motion follows Newton＇s second law. The convected material frame is introduced to calculate the internal force of the structural element. To avoid iteration in solving nonlinear motion equations, the explicit time integration is adopted. This paper presents a buckling analysis of structures using FPM. Taking the three dimensional bar element as an example, the formulations of the FPM are derived in the paper. Structural buckling behaviors are simulated with the program based on the FPM algorithm. This method can reach the critical load and track post-buckling behaviors of structures without any special considerations. In addition, there is no need to apply structural loads gradually. All loads can be applied to the structures at the initial step of the analysis, which accords with the practical situation. Several numerical examples are presented to demonstrate the capabilities and accuracy of this method in the buckling analysis of structures.