基于Arlequin方法的结构多尺度数值模拟

考察了Arlequin方法以及其在结构多尺度数值模拟中的应用.简要总结了国内外最新的可用于大型结构多尺度数值模拟的方法,并详细介绍了Arlequin方法的基本概念及其线弹性问题的连续和离散列式.探讨Arlequin方法中能量分配函数、耦合算子、H1算子中缩放参数等关键参数的选取方法.基于Matlab软件编制了相应的多尺度分析程序并对一维杆和二维平面梁进行了多尺度分析,分析结果验证了Arlequin多尺度分析的可行性并表明其在保证分析精度的同时可以提高计算效率.同时基于ABAQUS软件的二次开发功能对带V型切口的平板进行了应力分析,为进一步的大型结构多尺度模拟奠定了基础.

Multi-scale numerical simulation of structures based on Arlequin method

This work was concerned with the Arlequin theory and its application to numerical simulation of structures. Various available multi-scale simulation methods of large-scale structures were overviewed. The basic concept of the Arlequin method and its continuous and discrete formulations for linear elastic problems were introduced. The selection of key parameters such as the weight functions and coupling operators as well as the scaling parameter of H¹ coupling operator was suggested. The program based on Matlab software was developed and the multi scale analysis of a one dimensional rod and a two-dimensional beam was conducted. The numerical results verify the feasibility of the Arlequin multiscale analysis with the same precision and higher efficiency. The stress in a V-notched plate was also investigated by implementing the Arlequin method into ABAQUS software, indicating the potential in the multi-scale study of large-scale structures.