求解平面固体几何大变形问题的有限质点法

THE FINITE PARTICLE METHOD FOR SOLVING GEOMETRIC LARGE DEFORMATION OF PLANAR SOLIDS

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。

The finite particle method（FPM） is a new developed method for numerical calculation,which is based on the vector mechanics and physical thoughts.It models the analyzed domain by a set of particles instead of mathematical function and continuous bodies adopted in traditional method,and thus the motion of each particle is directly formulated by Newton’s second law.The formulations include a new description of kinematics called fictitious reverse motion to dissect rigid body and deformation displacement,and a set of deformation coordinates for each time increment to evaluate deformation and internal nodal forces.The explicit time integration is adopted to solve the equation of motion.Motions of all particles can describe the whole behavior.The fundamentals of PFM are presented first in this paper.Then,the formulations of the planar solid internal forces are derived.Finally,FPM is applied to the numerical calculations of geometric large deformations of planar solids.The results of numerical examples solved by self-designed program demonstrate that the presented method can achieve good accuracy and convergence.It also shows that FPM is quite effective and feasible for the analysis of planar solids undergoing large rotation and deflection.