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有限质点法是基于向量式力学提出的一种新兴的数值计算方法。它采用物理计算模式,将分析域定义成一组质点的集合,并根据牛顿第二定律描述质点的运动,从而取代了传统数值方法中数学连续体的概念。该方法通过虚拟逆向运动分离刚体位移和变形位移,并采用变形坐标的形式来计算内力,再利用显式时间积分逐步求解质点运动方程。分析中可以通过描述各质点的轨迹来追踪整体的运动行为。该文阐述了有限质点法的基本概念和原理,推导了平面固体的内力求解公式,并将其应用于平面固体几何大变形问题的数值计算,通过自编程序对实例计算的结果表明,该方法有良好的精度和收敛性,对于求解平面固体的大位移、大转动问题是有效的、可行的。
Finite point method is based on vectorial mechanics proposed a new numerical method. It uses the physical computing model to define the analytic domain as a set of particles and to describe the particle motion according to Newton’s second law, thus replacing the concept of mathematical continuum in traditional numerical methods. The method separates rigid body displacement and deformation displacement through virtual reverse motion, calculates internal forces in the form of deformation coordinates, and then uses explicit time integral to solve the particle equation of motion step by step. In the analysis, the overall motion behavior can be tracked by describing the trajectory of each particle. In this paper, the basic concept and principle of finite element method are expounded. The internal force formula of plane solid is deduced and applied to the numerical calculation of large solid geometric deformation problem. The result of self-programmed program shows that this method With good accuracy and convergence, it is effective and feasible to solve the problem of large displacement and large rotation of planar solid.