正交各向异性材料热弹性问题的三维无网格法计算模型及应用  

Three-dimensional meshless computational model and its application for thermoelastic problem of orthotropic material structure

作　　者：张建平[1] 刘庭显 王树森 龚曙光[1] 胡慧瑶 Zhang Jianping;Liu Tingxian;Wang Shusen;Gong Shuguang;Hu Huiyao(School of Mechanical Engineering,Xiangtan University,411105,Xiangtan,China)

机构地区：[1]湘潭大学机械工程学院,湘潭411105

出　　处：《应用力学学报》2021年第1期1-10,共10页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(51975503,51875493);湖南省自然科学基金(2020JJ4582);湖南省普通高校青年骨干教师培养经费资助项目(湘教通[2020]43号)。

摘　　要：建立了正交各向异性材料热弹性问题的三维无网格伽辽金(Element Free Galerkin, EFG)法计算模型。利用该计算模型对三维复合材料汽轮机叶轮和轴承座进行了热弹性分析,对比了材料方向角及热导率因子、热膨胀系数因子和拉压弹性模量因子不同组合情况下轴承座的最大热变形总位移和当量应力值,讨论了材料方向角及上述正交各向异性因子对热变形和当量应力的影响规律,并与各向同性材料进行了对比。结果表明:三维EFG模型的热变形总位移和当量应力相对误差范数分别比有限元法小0.1215%和0.1359%;材料方向角同时影响热变形的大小和方向,但对当量应力方向影响不大;正交各向异性材料因子主要影响热变形和当量应力的大小。在考虑热-机械载荷作用下的三维复合材料零件结构设计中,当以刚度或强度为主要需求时,材料方向角、热导率因子、热膨胀系数因子、拉压弹性模量因子分别在(45°~60°,8:1:4~10:1:5,(1/6):(1/5):1~(1/5):(1/4):1,(7/5):1:(9/5)~(3/2):1:2)或(0°~10°,(1/10):1:(1/5)~(1/8):1:(1/4),(1/5):1:(1/6)~(1/4):1:(1/5),1:(1/5):(1/10)~1:(1/4):(1/8))范围内取值能有效降低轴承座等结构的热变形和当量应力。The calculation model of thermoelastic problem for orthotropic material structure is established by using the three-dimensional Element Free Galerkin method. The thermoelastic analysis of three-dimensional composite turbine impeller and bearing seat are carried out by using the proposed model. The maximum thermal deformation total displacement and equivalent stress of bearing seat under different combinations of off-angle, thermal conductivity factor, thermal expansion coefficient and elastic modulus factors in tension and compression are compared. The effects of off-angle and the above orthotropic material factors on the thermal deformation total displacement and equivalent stress of bearing seat are discussed, and the thermoelastic properties are compared with those of isotropic materials structure. The results show that the relative error norm of the thermal deformation total displacement and equivalent stress of the three-dimensional EFG model is 0.1215% and 0.1359% less than that of the finite element method, respectively. The off-angle affects both magnitude and direction of thermal deformation total displacement, but it has little effect on the equivalent stress direction;and the orthotropic material factors mainly affect the magnitude of thermal deformation total displacement and equivalent stress. In the structural design of three-dimensional composite parts under thermal-mechanical loads, when the rigidity or strength is the main requirement, the off-angle, thermal conductivity factor, thermal expansion coefficient and elastic modulus factors are respectively in the range of 45°~ 60°, 8 :1: 4 ~ 10 :1: 5,(1 6) :(1 5) :1 ~(1 5) :(1 4) :1,(7 5) :1:(9 5) ~(3/2) :1: 2 and 0°~ 10°,(1 10) :1:(1 5) ~(1 8) :1:(1 4),(1 5) :1:(1 6) ~(1 4) :1:(1 5), 1:(1 5) :(1 10) ~ 1:(1 4) :(1 8), which can effectively reduce the thermal deformation and equivalent stress of bearing seat and other structures.

关 键 词：正交各向异性材料 三维无网格伽辽金法 热弹性分析 材料方向角 拉压弹性模量因子 

分 类 号：TB330.1[一般工业技术—材料科学与工程] TH114[机械工程—机械设计及理论]