近场动力学与有限元的混合建模方法

综述了近场动力学与有限元混合建模方法的研究进展,阐明了各种混合建模方法的基本原理与特点,并重点介绍本课题组在近场动力学与有限元方法混合建模方面的研究工作。现有近场动力学与有限元混合建模方法包括位移协调约束、力耦合、混合函数方法以及子模型方法等,除子模型方法外,都可归结为并行式多尺度分析方法,其基本思想是将计算结构划分为近场动力学子域、有限元子域以及两者的交界区域(或重叠区域、或界面单元、或过渡区域)。子模型方法可归结为显-显分析方法,先采用显式有限元进行整体分析,后采用近场动力学方法对重点区域进行分析。混合建模方法需要着重提高交界区域的计算精度,并且消除虚假力和虚假应力波问题。提出了通过力耦合的近场动力学与有限元混合建模的隐式分析方法,该方法不再设置重叠区,通过杆单元连接近场动力学子域与有限元子域,其中界面上的有限元结点不仅与其所在单元的其他结点发生作用,还通过杆单元与以其为圆心、一定半径的圆域内的其他物质点相互作用。研究表明,本文提出的混合模型和求解方法既能有效解决裂纹扩展等不连续问题,又可提高计算效率,为工程结构破坏问题的计算分析提供一种有效方法。

Hybrid modeling methods of peridynamics and finite element method

Research progress of the hybrid modeling methods of peridynamics(PD)and the finite element method(FEM)is reviewed.All the basic principles and features of the existing hybrid modeling methods and the research work of our group on this topic are introduced.There are four types of existing hybrid modeling methods,including the displacement constraint method,force coupling method,morphing function method and submodeling method.Except submodeling method,the other ones belong to the concurrent multiscale analysis method,whose basic modeling idea is that the computational structure can be divided into peridynamic subregion,finite element subregions,and junction regions (or overlapping regions,or interface elements,or transition zones).The submodeling method can be regarded as an explicit and explicit analysis method.It is first solved by the FEM globally,then solved by PD locally.The computational accuracy of the junction and the ghost force need to be eliminated during the hybrid modeling.Through a comprehensive analysis,our group proposes a new approach to coupling the discretized PD and FEM based on the implicit scheme to take advantage of both methods.There is no longer an overlapping regions between PD subregions and FE subregions,therefore a truss element is introduced to bridge FE subregions and PD subregions.The FE nodes at the interface interact not only with other FE nodes of their connected elements,but also with PD points within the sphere of certain radius.As it has been proved to be effective and efficient in analyzing crack propagation problems,the proposed hybrid model is effective for failure analysis of engineering structures.