正交各向异性材料结构热变形和热应力分析的无网格法计算模型及应用
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摘要
利用无网格伽辽金法(Element-free Galerkin,EFG)建立了正交各向异性材料结构热变形和热应力分析的计算模型,并推导了正交各向异性材料结构热弹性问题的EFG法离散控制方程。选择复合材料冷却栅管算例验证了计算模型和程序的正确性,利用该计算模型分析了具有不同材料方向角及热导率因子、热膨胀系数因子和主次泊松比因子的汽轮机叶轮,得到了其热变形总位移和Mises应力,讨论了材料方向角和上述正交各向异性材料因子对其热变形总位移和Mises应力的影响规律,给出了这些参数的合理取值范围,并选取一组参数与各向同性材料结构进行了热变形和热应力对比分析。结果表明,基于EFG法的热变形总位移和Mises应力的计算精度比有限元法高,材料方向角同时影响热变形总位移和Mises应力的大小和方向,而正交各向异性材料因子只影响热变形总位移和Mises应力的大小,不影响其方向。在复合材料结构设计过程中,合理选取材料方向角和正交各向异性材料因子可有效减小结构热变形和热应力。
A calculation model for thermal deformation and thermal stress of orthotropic material was established using Element-free Galerkin method(EFG)and the discreted governing equation for thermoelastic problem of orthotropic material based on EFG method was deduced.The reliability of present model and programs have been verified through a numerical example of composite cooling grid.The total thermal deformation displacement and Mises stress of orthotropic materials turbine impeller with different off-angles,thermal conductivity factors,thermal expansion coefficient factors and primary and secondary Poisson's ratio factors were analyzed using the calculation model.The effects of off-angle and the above orthotropic material factors on total thermal deformation displacement and Mises stress were discussed,and the reasonable ranges of these parameters were provided.A group of parameters were selected to analyze the thermal deformation and thermal stress of orthotropic material by using the proposed calculation model and compared with isotropic materials.The results show that the calculation accuracy of total thermal deformation displacement and Mises stress based on EFG method is higher than the finite element method.The off-angle affects both magnitude and direction of total thermal deformation displacement and Mises stress,while orthotropic factors only affect the magnitude of total thermal deformation displacement and the Mises stress without affecting direction.Reasonable selection of off-angle and orthotropic material factors can effectively reduce the thermal deformation and thermal stress during the design of composite materials.
A calculation model for thermal deformation and thermal stress of orthotropic material was established using Element-free Galerkin method(EFG)and the discreted governing equation for thermoelastic problem of orthotropic material based on EFG method was deduced.The reliability of present model and programs have been verified through a numerical example of composite cooling grid.The total thermal deformation displacement and Mises stress of orthotropic materials turbine impeller with different off-angles,thermal conductivity factors,thermal expansion coefficient factors and primary and secondary Poisson's ratio factors were analyzed using the calculation model.The effects of off-angle and the above orthotropic material factors on total thermal deformation displacement and Mises stress were discussed,and the reasonable ranges of these parameters were provided.A group of parameters were selected to analyze the thermal deformation and thermal stress of orthotropic material by using the proposed calculation model and compared with isotropic materials.The results show that the calculation accuracy of total thermal deformation displacement and Mises stress based on EFG method is higher than the finite element method.The off-angle affects both magnitude and direction of total thermal deformation displacement and Mises stress,while orthotropic factors only affect the magnitude of total thermal deformation displacement and the Mises stress without affecting direction.Reasonable selection of off-angle and orthotropic material factors can effectively reduce the thermal deformation and thermal stress during the design of composite materials.
引文
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[17]ZHANG J P,ZHOU G Q,GONG S G,et al.Steady heat transfer analysis of anisotropic structure based on ElementFree Galerkin method[J].International Journal of Thermal Sciences,2017,121:163-181.
[18]ZHANG J P,ZHOU G Q,GONG S G,et al.Transient heat transfer analysis of anisotropic material by using ElementFree Galerkin method[J].International Communications in Heat and Mass Transfer,2017,84:134-143.
[19]BELYTSCHKO T,LU Y Y,GU L.Element-free Galerkin methods[J].International Journal for Numerical Methods in Engineering,1994,37(2):229-256.
[20]WU S C,LIU G R,CUI X Y,et al.An edge-based smoothed point interpolation method(ES-PIM)for heat transfer analysis of rapid manufacturing system[J].International Journal of Heat and Mass Transfer,2010,53(9-10):1938-1950.
[2]BURLAYENKO V N,ALTENBACH H,SADOWSKI T,et al.Modelling functionally graded materials in heat transfer and thermal stress analysis by means of graded finite elements[J].Applied Mathematical Modelling,2017,45:422-438.
[3]杨东生,张盛,张洪武.基于耦合扩展多尺度有限元方法的功能梯度材料热应力分析[J].复合材料学报,2015,32(4):1107-1117.YANG Dongsheng,ZHANG Sheng,ZHANG Hongwu,et al.Thermal stress analysis of functionally graded material based on coupling extended multiscale finite element method[J].Acta Materiae Compositae Sinica,2015,32(4):1107-1117(in Chinese).
[4]KIM K M,PARK J S,DONG H L,et al.Analysis of conjugated heat transfer,stress and failure in a gas turbine blade with circular cooling passages[J].Engineering Failure Analysis,2011,18(4):1212-1222.
[5]HEMATIYAN M R,MOHAMMADI M,MARIN L,et al.Boundary element analysis of uncoupled transient thermoelastic problems with time and space-dependent heat sources[J].Applied Mathematics and Computation,2011,218(5):1862-1882.
[6]GIUNTA G,DE PIETRO G,NASSER H,et al.A thermal stress finite element analysis of beam structures by hierarchical modelling[J].Composites Part B:Engineering,2016,95(11):179-195.
[7]BRESSAN J D,MARTINS M M,VAZ JR M.Stress evolution and thermal shock computation using the finite volume method[J].Journal of Thermal Stresses,2010,33(6):533-558.
[8]MOHAMMADI M,HEMATIYAN M R,ALIABADI M H.Boundary element analysis of thermo-elastic problems with non-uniform heat sources[J].Journal of Strain Analysis for Engineering Design,2010,1(8):1-23.
[9]SHANG Y,OUYANG W G.4-node unsymmetric quadrilateral membrane element with drilling DOFs insensitive to severe mesh-distortion[J].International Journal for Numerical Methods in Engineering,2017,113(20):1589-1606.
[10]王峰,周宜红,郑保敬,等.基于滑动Kriging插值的MLPG法求解结构非耦合热应力问题[J].应用数学和力学,2016,37(11):1217-1227.WANG Feng,ZHOU Yihong,ZHENG Baojing,et al.Ameshless local Petrov-Galerkin method based on the moving kriging interpolation for structural uncoupled thermal stress analysis[J].Applied Mathematics and Mechanics,2016,37(11):1217-1227(in Chinese).
[11]刘宜军,鲁欢,张桂勇,等.采用单元基光滑点插值法的高温管道热应力分析[J].浙江大学学报:工学版,2016,50(11):2113-2119.LIU Yijun,LU Huan,ZHANG Guiyong,et al.Thermal stress analysis of high temperature pipe using cell-based smoothed point interpolation method(CS-PIM)[J].Journal of Zhejiang University:Engineering Science,2016,50(11):2113-2119(in Chinese).
[12]SLADEK J,SLASWK V,ZHANG C H,et al.Meshless local Petro-Galerkin method for linear coupled thermoelastic analysis[J].Computer Modeling in Engineering&Sciences,2006,16(1):57-68.
[13]JABERZADEH E,AZHARI M,BOROOMAND B.Thermal buckling of functionally graded skew and trapezoidal plates with different boundary conditions using the elementfree Galerkin method[J].European Journal of Mechanics A:Solids,2013,42:18-26.
[14]HOSTOS J C,BENCOMO A D,PUCHI CABRERA E S.Simple iterative procedure for the thermal-mechanical analysis of continuous casting processes,using the element-free Galerkin method[J].Journal of Thermal Stresses,2017,41(2):160-181.
[15]PATHAK H,SINGH A,SINGH I V.Simulation of 3-Dthermo-elastic fracture problems using coupled FE-EFGapproach[J].Procedia Materials Science,2014,6:1927-1935.
[16]BOBARU F,MUKHERJEE S.Meshless approach to shape optimization of linear thermoelastic solids[J].International Journal for Numerical Methods in Engineering,2002,53(4):765-796.
[17]ZHANG J P,ZHOU G Q,GONG S G,et al.Steady heat transfer analysis of anisotropic structure based on ElementFree Galerkin method[J].International Journal of Thermal Sciences,2017,121:163-181.
[18]ZHANG J P,ZHOU G Q,GONG S G,et al.Transient heat transfer analysis of anisotropic material by using ElementFree Galerkin method[J].International Communications in Heat and Mass Transfer,2017,84:134-143.
[19]BELYTSCHKO T,LU Y Y,GU L.Element-free Galerkin methods[J].International Journal for Numerical Methods in Engineering,1994,37(2):229-256.
[20]WU S C,LIU G R,CUI X Y,et al.An edge-based smoothed point interpolation method(ES-PIM)for heat transfer analysis of rapid manufacturing system[J].International Journal of Heat and Mass Transfer,2010,53(9-10):1938-1950.