Topology Optimization of Heat Transfer for Orthotropic Material Structure
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摘要: 基于变密度法建立了正交各向异性材料结构的稳态传热拓扑优化模型,完成了变截面梁和圆锯片的传热拓扑优化,散热弱度最大分别降低了68.78%和74.82%,同时减重39.03%和23.75%;重点研究了各向异性因子和材料方向角对各向异性材料结构最优拓扑构型及散热效果的影响。结果表明:散热效果均随各向异性因子增加而增强,当各向异性因子小于和大于1时,各向异性材料结构的散热性能分别劣于和优于各向同性材料结构。变截面梁的材料方向角及各向异性因子对其最优拓扑构型及散热效果影响很大;而对于几何形状及热载荷均对称的圆锯片,其材料方向角对最优拓扑构型及温度分布无影响。变截面梁的材料方向角建议在60°~75°之间取值,在各向异性材料结构传热拓扑优化中,合理选择各向异性因子和材料方向角可获得较优拓扑构型。Abstract: The steady heat transfer topology optimization model for orthotropic material structure is established based on the variable density method. The heat transfer topology optimization of variable section beam and circular saw blade is performed. The thermal compliance is reduced by 68.78% and 74.82%, and the weight reduction is of 39.03% and 23.75%. The effect of the orthotropic factors and off-angle on the optimal topology and heat dissipation of orthotropic material structure were emphasized. The results show that the heat dissipation increases with the increasing of orthotropic factors. The heat dissipation performance of composite materials is superior and inferior to isotropic material when the orthotropic factors is less than and greater than 1, respectively. The orthotropic factors and off-angle of the variable cross section beam have great influence on the optimal topology and heat dissipation, while for the circular saw blade with symmetrical geometry and thermal load, the off-angle has no effect on the optimal topology and temperature distribution. The off-angle of variable cross section beam is suggested to choose in the range of 60°~75°, and the better topology can be obtained by choosing orthotropic factors and off-angle reasonably in the structural optimization for heat transfer topology of orthotropic material.
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Key words:
- orthotropic material /
- heat transfer /
- topology optimization /
- orthotropic factors /
- off-angle
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表 1 各向异性因子对变截面梁散热弱度与最高温度值的影响
各向同性
(Rt=1)正交各向异性(θ=45°) Rt=1/16 Rt=1/8 Rt=1/4 Rt=4 Rt=8 Rt=16 散热弱度/105 11.663 44.991 29.181 20.529 8.140 5 7.317 6 6.773 1 最高温度/K 503.71 949.727 748.567 625.572 456.147 443.202 433.0 表 2 材料方向角对变截面梁散热弱度与最高温度值的影响
各向同性
(Rt=1)正交各向异性(Rt=8) θ=0 θ=15° θ=30° θ=45° θ=60° θ=75° 散热弱度/105 11.663 8.496 8 8.895 9 8.552 0 7.317 8 5.471 3 3.641 1 最高温度/K 503.71 459.579 465.562 456.189 443.202 420.672 400.298 表 3 各向异性因子对圆锯片散热弱度与最高温度值的影响
各向同性
(Rt=1)正交各向异性(θ=30°) Rt=1/16 Rt=1/8 Rt=1/4 Rt=4 Rt=8 Rt=16 散热弱度/103 38.305 131.17 98.745 69.529 17.382 12.343 9.645 8 最高温度/K 331.156 8 554.681 444.64 386.609 320.264 6 316.461 3 314.183 1 表 4 材料方向角对圆锯片散热弱度与最高温度值的影响
各向同性
(Rt=1)正交各向异性(Rt=8) θ=0° θ=15° θ=30° θ=45° θ=60° θ=75° 散热弱度/104 3.830 5 1.235 6 1.234 5 1.234 3 1.233 5 1.234 3 1.234 5 最高温度/K 331.156 8 316.467 9 316.464 7 316.461 3 316.459 3 316.461 2 316.464 6 -
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