论文部分内容阅读
以高效模拟功能梯度材料(FGM)微观非均质性对整体热力学性能的影响为研究目的,通过随机形态描述函数(RMDF)法和体积分数的指数分布建立FGM二维微结构,在此基础上,发展了FGM热应力分析的耦合扩展多尺度有限元方法(CEMsFEM)。该方法基于扩展多尺度有限元方法(EMsFEM)的基本思想,对温度场和位移场构造数值基函数,以把微观非均质材料性质带到宏观响应中。同时为了考虑泊松效应导致的不同方向间的耦合作用,在位移场数值基函数中增加了耦合附加项。通过数值基函数建立宏微观单元信息的映射关系,在宏观尺度求解有效方程,节约计算量。为了更好地考虑微观载荷的影响,把结构的真实响应分解为宏观响应和微观扰动,进一步推导出修正的宏观载荷向量。通过不同体积分数分布的FGM在不同载荷工况下的热应力分析算例验证了本文中方法的正确性和有效性,最后讨论了微结构的尺寸效应对结构热力学响应的影响。
The purpose of this study was to simulate the effect of FGM heterogeneity on the overall thermodynamic performance efficiently. Based on the two-dimensional structure of FGM by means of the random shape description function (RMDF) method and exponential distribution of volume fraction, , A coupled extended multi-scale finite element method (CEMsFEM) for the thermal stress analysis of FGM has been developed. Based on the basic idea of extended multiscale finite element method (EMsFEM), this method constructs numerical basis functions for temperature and displacement fields to bring the properties of microscopic heterogeneous materials into the macroscopic response. At the same time, in order to consider the coupling effect between different directions caused by Poisson effect, coupled additional terms are added to the numerical basis function of displacement field. The mapping relationship between macro and micro cell information is established by numerical basis function, and the effective equation is solved on macroscopic scale to save the computational cost. In order to better consider the effect of microscopic load, the real response of the structure is decomposed into macroscopic response and microscopic disturbance, and the revised macro load vector is deduced further. The thermal stress analysis of FGM with different volume fraction distributions under different load conditions validates the correctness and effectiveness of the proposed method. Finally, the effect of the size effect of microstructures on the thermodynamic response of the structure is discussed.