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

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.