基于有限质点法的多尺度精细化分析

MULTI-SCALE FINE ANALYSIS BASED ON THE FINITE PARTICLE METHOD

多尺度作为一种精细化分析的建模手段,能有效平衡结构分析中的计算效率和精度。有限质点法是一种能准确分析结构非线性行为的方法,在多种复杂行为分析中得到应用。该文利用有限质点法以质点为基本元素和显式积分的特点,基于梁、壳等低维单元的平截面假定,将多尺度连接处的质点分为主质点和从质点,集成从质点的质量、质量惯性矩阵、力、力矩等物理量至主质点,求解主质点运动方程后,由位移约束条件求得从质点位移,从而实现不同维度单元的多尺度连接。算例表明该多尺度方法对梁-壳、梁-固体及壳-固体的连接是有效的,在几何非线性及动力问题中具有良好的精度及稳定性,适合于结构复杂行为分析。

As a modeling method of fine analysis, multi-scale modeling can effectively balance efficiency and accuracy of structural analysis. Finite Particle Method（FPM） is a numerical method for analyzing nonlinear behavior of structures accurately, and it is applied to cases of various complex behaviors. In FPM, particles are basic units and explicit integration is adopted. The multi-scale modeling method proposed in this paper is based on these FPM＇s characteristics and the plane section assumption of beam and shell elements. The particles in the connection section are divided into master and slave particles. The mass, mass inertia matrix, force and moment of slave particles are assembled into master particles. After the motion equations of master particles are solved, slave particles＇ displacements are acquired from displacement constraint conditions, thus the connection of elements with different dimensions is implemented. The results of numerical examples demonstrate that this multi-scale modeling method is effective for beam-shell, beam-solid and shell-solid connections and achieves good accuracy and stability for geometric nonlinear and dynamic problems. This method is suitable for the analysis of complex behaviors of structures.