基于等参梯度单元的功能梯度材料结构分析  

Analysis of Functionally Graded Material Structures Based on Isoparametric Graded Element

作　　者：张龙[1] 邱荣凯[1] 程俊 刘秉斌[1] ZHANG Long;QIU Rongkai;CHENG Jun;LIU Bingbin(Facility Design and Instrumentation Institute,China Aerodynamics Research and Development Center,Mianyang 621000,China)

机构地区：[1]中国空气动力研究与发展中心设备设计及测试技术研究所,绵阳621000

出　　处：《南京航空航天大学学报》2021年第4期551-561,共11页Journal of Nanjing University of Aeronautics & Astronautics

基　　金：国家自然科学基金青年基金(51605476)资助项目;全军装备军内科研项目(JK20202A040525)资助项目。

摘　　要：为了解决功能梯度材料非均质特征引起的特殊力学行为的模拟仿真技术难题,本文基于有限元基本理论框架,将材料梯度引入形函数,对单元刚度矩阵进行改写,发展了平面四节点与八节点等参梯度单元,并采用高斯积分数值处理方法,基于ABAQUS平台开发了等参梯度单元UEL(User‑defined element)子程序,建立了功能梯度材料结构件的仿真分析方法。采用功能梯度材料正方形平板,研究网格密度对计算结果的影响,验证了平面四节点与八节点等参梯度单元的收敛性。将本文梯度单元与常规单元的计算精度进行了对比分析。当载荷条件较复杂时,常规单元计算的应力场出现阶跃,严重失真;而梯度单元得到的应力场光滑连续,可以采用较少数目的单元,即可得到比常规单元更为精确的计算结果。最后进行了功能梯度材料开孔结构和悬臂梁的计算分析,得到收敛解,需要采用的梯度单元数量远少于常规单元。研究表明,平面四节点与八节点梯度单元计算精度和效率均优于平面八节点常规单元,更优于平面四节点常规单元。Functionally graded materials are widely used in aerospace thermal structures.In order to solve the technical difficulty of simulating special mechanical behavior caused by the heterogeneous characteristics of functionally graded materials,based on the finite element method framework,the plane 4-node and 8-node isoparametric gradient elements are developed through reforming the element stiffness matrix of which the material gradient is introduced into the shape function.And the simulation technique for functionally graded material structure is established on the basis of the ABAQUS platform,where an isoparametric gradient element UEL(User-defined element)sub-routine is developed using Gaussian integral numerical method.First,a square plate of functionally graded material is used to study the influence of the mesh density on the simulated results,and the convergence of the plane 4-node and 8-node isoparametric gradient elements is verified.Then,a comparative analysis of simualtion accuracies of the gradient element and the conventional element is carried out.When subjected to complex load conditions,the stress field calculated by the conventional element appears to be stepped and achieves low fidelity,whereas the stress field obtained by the gradient element is smooth and continuous.The gradient element requires less number of element to obtain more accurate simulation results than the conventional element.In the end,the simulation of the functionally graded material perforated structure and cantilever is carried out.The number of gradient element required to obtain convergent results is far less than that of the conventional element.This work reveals that the simulation accuracy and efficiency of the plane 4-node and 8-node isoparametric gradient elements is higher than that of the plane 8-node conventional element,and even far higher than that of the plane 4-node conventional element.

关 键 词：功能梯度材料 等参梯度单元 结构分析 有限元 UEL 

分 类 号：V259[一般工业技术—材料科学与工程] O242.21[航空宇航科学与技术—航空宇航制造工程]