基于有限质点法的分布协调式多尺度分析

COORDINATED DISTRIBUTING MULTI-SCALE ANALYSIS BASED ON FINITE PARTICLE METHOD

  • 摘要: 多尺度模型采用“整体宏观,局部精细”的方式来平衡结构数值模拟的计算精度与计算代价,能够在把握结构整体特征的同时获得结构局部信息。该文基于有限质点法点值描述与显式求解的特点,提出了一种考虑界面变形的分布协调式多尺度耦合方法。该文详述了分布协调式多尺度耦合的基本原理,给出了分布协调式多尺度耦合的有限质点法实现流程:计算界面处的作用力,依据力平衡关系将主质点上的界面作用力分配到从质点上,再依据位移协调关系和运动方程求解得到的从质点位移增量来求解主质点的运动。该文实现了梁-平面、梁-壳、梁-实体三种类型的多尺度连接,避免了耦合界面上的应力集中问题,通过算例对比验证了该方法在几何非线性与动力问题中的稳定性与可靠性,为结构多尺度精细化分析提供有效手段。

     

    Abstract: Multi-scale modeling is a common method to balance the accuracy and cost of numerical simulation of structures. This method enables designers to obtain both the whole characteristics and local information of structures simultaneously. Based on the Finite Particle Method, a coordinated distributing multi-scale coupling method aiming at deformable interface is proposed in this study. The paper derives the basic theory of coordinated distributing coupling and proposes a calculation process in the following steps. The calculated interface force is distributed to the slave particles according to the force balance relationship. The displacements of the slave particles are obtained through the motion equation. The motion of the master particle is calculated by applying the displacement coordination relationship. This method has realized the beam-plane, beam-shell and beam-solid coupling while avoiding stress concentration at the interface. Numerical tests have been conducted to validate its stability and reliability in dynamic nonlinear problems. The calculation results indicate that the method is effective for multi-scale fine analysis of structures.

     

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