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复合材料连续纤维方向及路径优化设计方法研究进展

李贵兴 陈园 叶林

李贵兴, 陈园, 叶林. 复合材料连续纤维方向及路径优化设计方法研究进展[J]. 复合材料学报, 2024, 42(0): 1-28.
引用本文: 李贵兴, 陈园, 叶林. 复合材料连续纤维方向及路径优化设计方法研究进展[J]. 复合材料学报, 2024, 42(0): 1-28.
LI Guixing, CHEN Yuan, YE Lin. Research progress on optimization design methods for continuous fiber direction and path of composites[J]. Acta Materiae Compositae Sinica.
Citation: LI Guixing, CHEN Yuan, YE Lin. Research progress on optimization design methods for continuous fiber direction and path of composites[J]. Acta Materiae Compositae Sinica.

复合材料连续纤维方向及路径优化设计方法研究进展

基金项目: 国家自然科学基金青年科学基金项目(12302177);深圳市自然科学基金面上项目(JCYJ20230807093602005);深圳市连续碳纤维复合材料智能制造重点实验室(ZDSYS20220527171404011);广东省普通高校重点领域专项 (高端装备制造) (2023ZDZX2025)
详细信息
    通讯作者:

    陈园,博士,助理教授,博士生导师,研究方向为复合材料力学 E-mail: chenyuan@sustech.edu.cn

    叶林,博士,教授,博士生导师,研究方向为先进复合材料与结构 E-mail: yelin@sustech.edu.cn

  • 中图分类号: TB332

Research progress on optimization design methods for continuous fiber direction and path of composites

Funds: National Natural Science Foundation of China (12302177); Shenzhen Science and Technology Program, China (JCYJ20230807093602005); Shenzhen Key Laboratory of Intelligent Manufacturing for Continuous Carbon Fibre Reinforced Composites (ZDSYS20220527171404011); Guangdong University Key-Area Special Program (2023ZDZX2025)
  • 摘要: 连续纤维增强复合材料因其优异的比刚度、比强度等特性,在航空航天、国防军工、医疗器件等高端装备领域得到了广泛的关注和应用。其中,纤维方向对连续纤维增强复合材料的力学性能有着重要影响,但是由于常规制造工艺的局限,纤维路径通常沿0°、45°、90°等规律一致的方向来设定,连续纤维增强复合材料的优势无法被充分利用。如今,3D打印技术促进了制造具有复杂曲线纤维路径复合材料的发展,其对应的纤维方向及路径优化设计方法正逐步引起国内外专家学者的重点关注。本文围绕纤维增强复合材料的纤维方向及路径优化设计方法,介绍了正交各向异性材料方向优化理论,回顾了纤维角度优化方法,总结了现有纤维路径规划算法,探讨了相关前沿问题并做出了未来展望。本文为高性能连续纤维增强复合材料的优化设计和制造提供了重要信息,有助于推动高性能连续纤维增强复合材料的快速发展和广泛应用。

     

  • 图  1  CFRC拓扑设计:(a)四点弯曲梁[40],(b) 具有负泊松比效应的超结构[41],(c) 三维悬臂梁结构[42],(d) 多载荷情况下的三维梁结构[42]

    Figure  1.  Topological design CFRC: (a) Four-point bending beam[40],(b) Meta-structures with negative Poisson’s ratio[41], (c) Three-dimension cantilever beam[42], (d) Three-dimension beam structure under multiple-loads[42]

    图  2  论文框架

    Figure  2.  Paper framework

    图  3  静态载荷作用下二维弹性正交各向异性结构[51]

    Figure  3.  Two-dimensional elastic orthotropic structure under static loading[51]

    图  4  BCP技术的说明[67]:(a) 4种候选材料;(b) 8种候选材料

    Figure  4.  Illustration of the BCP technique[67]: (a) Four candidate materials; (b) Eight candidate materials

    图  5  BIO策略中候选材料的选择过程[62]

    Figure  5.  Selection process of four candidate materials in BIO scheme[62]

    图  6  不同子区间数量情况下悬臂梁的优化结果[71]:(a) 1个子集;(b) 2个子集;(c) 3个子集

    Figure  6.  Optimization results of cantilever beams under different number of subintervals: (a) One subinterval; (b) Two subintervals; (c) Three subintervals

    图  7  不同条件下纤维取向结果的处理[72]

    Figure  7.  Treatment of the fiber orientation results under different conditions[72]

    图  8  (a) 双材料拓扑优化;(b) Michell梁设计域;(d) Michell梁优化结果[73]

    Figure  8.  (a) Bi-material topology optimization; (b) Michell beam design domain; (c) Optimized result of Michell beam[73]

    图  9  CFRC结构拓扑和纤维方向的协同优化框架[74]

    Figure  9.  The collaborative optimization framework for topological structure and fiber orientation of CFRC[74]

    图  10  不同的纤维打印路径:(a) 直线型[76];(b) Z字型[77];(c) 螺旋型[78];(d) 网格型[79];(e) 蜂窝型[80];(f) 轮廓型[81]

    Figure  10.  Different fiber printing paths: (a) Straight line[76]; (b) Zigzag[77];(c) Spiral[78]; (d) Grid[79]; (e) Honeycomb[80]; (f) Contour[81]

    图  11  线性变化的纤维角度以及对应的纤维路径[97,98]

    Figure  11.  Linear variation in fiber angles and corresponding fiber paths[97,98]

    图  12  (a) 主坐标系和辅助坐标系;(b)基于3阶多项式的变刚度平板[100,101]

    Figure  12.  (a) Main and auxiliary coordinate systems; (b) Variable-stiffness panel based on cubic polynomial function[100,101]

    图  13  基于LSF的纤维路径优化[106]$:(a) LSF;(b) LSF等值线;(c) 基于LSF等值线的纤维路径;(d) 纤维角度的定义

    Figure  13.  The optimization of fiber path based on LSF[106]$: (a) LSF, (b) Iso-contour of LSF; (c) The fiber path based on iso-contour of LSF;(d) Definition of fiber orientation

    图  14  (a) 顺序优化策略流程;(b) 协同优化策略流程[111]

    Figure  14.  (a) Flowcharts for sequential optimization scheme; (b) Flowcharts for simultaneous optimization scheme[111]

    图  15  基于LSF的连续纤维增强复合材料超结构设计:(a)(b) 复合材料超结构中基于LSF得到的连续纤维路径;(c)(d)复合材料超结构的3D打印纤维路径;(e) 复合材料超结构力学性能随调控参数的变化[41]

    Figure  15.  Design of continuous fiber reinforced meta-composites based on LSF: (a)(b) Continuous fiber path of meta-composite based on LSF; (c)(d) Actually printing path of meta-composite; (e) Variation of mechanical properties of meta-composite versus tailorable parameter[41]

    图  16  (a) MBB梁的设计域;(b) 初始纤维路径;优化得到的纤维路径 (c) $ \varepsilon =1 $,(d) $ \varepsilon =0.1 $[106]$

    Figure  16.  (a) The design domain of MBB beam; (b) Initial fiber paths; Optimized fiber paths with (c) $ \varepsilon =1 $ and (d) $ \varepsilon =0.1$[106]

    图  17  基于OM和LSM的拓扑优化过程[114]

    Figure  17.  Topology optimization based on offset and LSM[114]

    图  18  由于纤维方向突然变化造成的应力集中现象:(a) 纤维路径;(b) Von Misses应力分布[114]

    Figure  18.  Stress concentration phenomenon due to abrupt fiber orientation change: (a) Fiber path; (b) Von Misses stress distribution (units in GPa) [114]

    图  19  基于流线方法所设计的连续纤维路径:(a) 复合材料悬臂梁的平均载荷传递方向和连续纤维路径;(b) 复合材料悬臂梁的连续纤维打印路径;(c) 具有负泊松比效应的复合材料超结构;(d) 高弹性模量复合材料格栅结构的连续纤维打印路径[11,116]

    Figure  19.  Continuous fiber paths designed based on streamline methods: (a) The average load transmission orientation and continuous fiber paths of the cantilever beam; (b) The continuous fiber printing paths of the cantilever beam; (c) The meta-structures with negative Poisson’s ratio; (d) The composite grid structures of enhanced effective elastic modulus and their continuous fiber printing paths [11,116]

    图  20  (a) L型梁设计域;(b) 纤维路径分布;(c) 纤维含量分布;(d) Von Misses应力分布[117]

    Figure  20.  (a) Design domain of L-shaped beam; (b) Fiber paths distribution; (c) Fiber content distribution; (d) The Von Misses stress distribution[117]

    图  21  基于应力场的连续纤维打印路径规划算法:(a) 求解主应力矢量场;(b) 基于MST确定的主应力矢量场;(c) 识别主应力矢量紊乱的区域;(d) 移除混乱的主应力矢量;(e) 完整的主应力矢量场;(f) 连续纤维路径;(g) 最终的纤维打印路径[118]

    Figure  21.  Continuous fiber printing path planning algorithm based on stress field; (a) Solving the principal stress vector field; (b) Principal stress vectors field determined by MST; (c) Identify the region of disturbed principal stress vector; (d) Remove the principal stress vector from the disturbed area; (e) Full principal stress vector field; (f) Continuous fiber path; (g) Final fiber printing path[118]

    图  22  (a) LPP中的参数; (b) 带有孔洞MBB梁优化结果以及纤维路径;(c) 全局连续的纤维打印路径[119]

    Figure  22.  (a) The parameters in LPP; (b) Optimization results of MBB beam with a hole and corresponding fiber paths; (c) Global continuous fiber printing path[119]

    图  23  含有孔洞的复合材料平板优化设计:(a) 设计域和载荷;(b) 优化得到的纤维方向和纤维含量;(c) 根据材料汇编算法得到的纤维路径;(d) 用于可视化的3D打印样件[120]

    Figure  23.  Design optimization of a composite plate structure with a hole: (a) Design domain and loads; (b) Optimized fiber direction and fiber content; (c) Fiber path obtained by material compilation; (d) 3D printed sample for visualization[120]

    图  24  结构区域划分[121]

    Figure  24.  Structure region division[121]

    图  25  纤维点的分布[121]

    Figure  25.  Distribution of fiber points[121]

    图  26  纤维方向的光滑[121]

    Figure  26.  Fiber orientation smooth [121]

    图  27  通过A-A’ 截面中心的纤维路径数量被分为4部分[114]

    Figure  27.  The number of fiber paths passing through the central cross section A-A’ are divided in four sub-divisions[114]

    图  28  多尺度协同设计示意图[122]:(a) 协同优化结果;(b) 子结构内的纤维路径;(c) 纤维路径连接;(d) 纤维打印路径;(e) 打印过程

    Figure  28.  Schematic for multiscale concurrent design[122]: (a) Concurrent optimization result; (b) Fiber paths in sub-structures; (c) Fiber paths connection; (d) Fiber printing path; (e) Printing process

    图  29  具有全局连续性的打印策略[123]

    Figure  29.  Printing strategy with global continuity[123]

    表  1  基于应力方法得到的纤维极值角度

    Table  1.   Fiber extreme angle obtained from stress based method

    Cases Condition Extreme angle
    1 $ d > 0 $
    and
    4$ {d}^{2}\left[{({\sigma }_{1}-{\sigma }_{2})}^{2}+4{\sigma }_{12}^{2}\right] > {c}^{2}{\left({\sigma }_{1}+{\sigma }_{2}\right)}^{2} $
    $ {\theta }_{1}=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\left(\dfrac{2 b{\gamma }_{12}+\sqrt{4{b}^{2}\left[{({\varepsilon }_{1}-{\varepsilon }_{2})}^{2}+{\gamma }_{12}^{2}\right]-{a}^{2}{\left({\varepsilon }_{1}+{\varepsilon }_{2}\right)}^{2}}}{2 b\left({\varepsilon }_{1}-{\varepsilon }_{2}\right)-a({\varepsilon }_{1}+{\varepsilon }_{2})}\right) $
    $ {\theta }_{1}=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\left(\dfrac{2 b{\gamma }_{12}+\sqrt{4{b}^{2}\left[{({\varepsilon }_{1}-{\varepsilon }_{2})}^{2}+{\gamma }_{12}^{2}\right]-{a}^{2}{\left({\varepsilon }_{1}+{\varepsilon }_{2}\right)}^{2}}}{2 b\left({\varepsilon }_{1}-{\varepsilon }_{2}\right)-a({\varepsilon }_{1}+{\varepsilon }_{2})}\right) $
    2 $ d > 0 $
    and
    4$ {d}^{2}\left[{({\sigma }_{1}-{\sigma }_{2})}^{2}+4{\sigma }_{12}^{2}\right] < {c}^{2}{\left({\sigma }_{1}+{\sigma }_{2}\right)}^{2} $
    $ {\theta }_{1}={\theta }_{I} $
    $ {\theta }_{1}={\theta }_{II} $
    3 $ d < 0 $ $ {\theta }_{1}={\theta }_{I} $
    下载: 导出CSV

    表  2  基于应变方法得到的纤维极值角度

    Table  2.   Fiber extreme angle obtained from strain based method

    Cases Condition Extreme angle
    1 $ b < 0 $
    and
    4$ {b}^{2}\left[{({\varepsilon }_{1}-{\varepsilon }_{2})}^{2}+4{\varepsilon }_{12}^{2}\right] > {a}^{2}{\left({\varepsilon }_{1}+{\varepsilon }_{2}\right)}^{2} $
    $ {\theta }_{1}=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\left(\dfrac{2 b{\gamma }_{12}+\sqrt{4{b}^{2}\left[{({\varepsilon }_{1}-{\varepsilon }_{2})}^{2}+{\gamma }_{12}^{2}\right]-{a}^{2}{\left({\varepsilon }_{1}+{\varepsilon }_{2}\right)}^{2}}}{2 b\left({\varepsilon }_{1}-{\varepsilon }_{2}\right)-a({\varepsilon }_{1}+{\varepsilon }_{2})}\right) $
    $ {\theta }_{1}=\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{t}\mathrm{a}\mathrm{n}\left(\dfrac{2 b{\gamma }_{12}-\sqrt{4{b}^{2}\left[{({\varepsilon }_{1}-{\varepsilon }_{2})}^{2}+{\gamma }_{12}^{2}\right]-{a}^{2}{\left({\varepsilon }_{1}+{\varepsilon }_{2}\right)}^{2}}}{2 b\left({\varepsilon }_{1}-{\varepsilon }_{2}\right)-a({\varepsilon }_{1}+{\varepsilon }_{2})}\right) $
    2 $ b < 0 $
    and
    4$ {b}^{2}\left[{({\varepsilon }_{1}-{\varepsilon }_{2})}^{2}+4{\varepsilon }_{12}^{2}\right] > {a}^{2}{\left({\varepsilon }_{1}+{\varepsilon }_{2}\right)}^{2} $
    $ {\theta }_{1}={\theta }_{I} $
    下载: 导出CSV

    表  3  不同情况下的极值角度[55]

    Table  3.   The extreme angle under different circumstance.

    Extreme angle $ {\theta }_{e} $ Relatively “low” shear stiffness $ {\alpha }_{3} > 0 $ Relatively “high” shear stiffness $ {\alpha }_{3} < 0 $
    $ \gamma < -1 $ $ -1 < \gamma < 1 $ $ \gamma > 1 $ $ \gamma < -1 $ $ -1 < \gamma < 1 $ $ \gamma > 1 $
    $ {0}^\circ $ Global min Global max Global max Global max Local min Globa min
    $ {90}^\circ $ Global max Local max Global min Global min Global min Global max
    $ \mathrm{cos}\left(2{\theta }_{e}\right)=-\gamma $ Global min Global max
    下载: 导出CSV

    表  4  DFOO 算法以及一个离散单元所需设计变量个数

    Table  4.   DFOO algorithms and the number of required design variables for a discrete element.

    Method The number of design variables required
    Discrete material optimization (DMO)[59] $ {n}_{e} $
    Shape function with penalization (SFP) [60] $ {n}_{e}/2 $
    Bi-value coding parameterization (BCP) [61] $ \left\lceil {{log}_{2}{n}_{e}} \right\rceil $
    Bipartite interpolation optimization (BIO) [62] $\left\lceil {{log}_{2}{n}_{e}} \right\rceil $
    Normal distribution fiber optimization (NDFO)[63] 1
    下载: 导出CSV

    表  5  若干种处理CFOO问题的方法及其优缺点

    Table  5.   Several approaches to CFOO and their advantages and disadvantages

    Method Advantage Disadvantage Reference
    Shepard interpolation for fiber angle The continuity of fiber angle is guaranteed The optimization result depends on the
    initial design;
    Ends at local optimal solution
    [69]
    Gradient descent method Superior convergence properties Poor continuity of fiber angles [70]
    Discrete-continuous
    parameterization
    The solution space is complete;
    It reduces the risk of local optimal
    Difficulty in determining the number of subintervals [71]
    Principal stress orientation interpolated continuous fiber angle Reduce the phenomenon of local fiber
    discontinuity;
    Higher convergence efficiency
    Optimization results depend on the
    direction of principal stress
    [72]
    Full-scale topology
    optimization
    The difficulty of optimization is low;
    Can generate continuous fiber paths
    High computational cost [73]
    Deep neural network models Reduces the number of optimization iterations and decreases computational costs Post-processing step required;
    Problem-dependent
    [74]
    下载: 导出CSV

    表  6  三类连续纤维路径优化设计方法

    Table  6.   Three types of continuous fiber path optimization design methods

    Method Optimized variables The representation of fiber paths Advantage Disadvantage
    Based on continuous and differentiable functions Functional
    coefficients
    Function trajectory Convenient for adding
    manufacturing
    constraints
    Low design freedom;
    Optimization results depend on the selection of fiber representation functions
    Based on level set function Level set function
    or expansion
    coefficient
    Iso-contours of level set function Fiber paths without gaps and overlaps Fiber path may occur sharp corners
    Based on stress vector fields Stream function Streamline More robust and
    Straightforward
    Post-processing step required
    下载: 导出CSV
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