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海洋柔性立管防弯器结构非线性刚度拓扑优化

范志瑞 杨志勋 许琦 苏琦 牛斌 赵国忠

范志瑞, 杨志勋, 许琦, 苏琦, 牛斌, 赵国忠. 海洋柔性立管防弯器结构非线性刚度拓扑优化. 力学学报, 2022, 54(4): 929-938 doi: 10.6052/0459-1879-21-589
引用本文: 范志瑞, 杨志勋, 许琦, 苏琦, 牛斌, 赵国忠. 海洋柔性立管防弯器结构非线性刚度拓扑优化. 力学学报, 2022, 54(4): 929-938 doi: 10.6052/0459-1879-21-589
Fan Zhirui, Yang Zhixun, Xu Qi, Su Qi, Niu Bin, Zhao Guozhong. Nonlinear stiffness topology optimization for the bend stiffener of flexible riser. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(4): 929-938 doi: 10.6052/0459-1879-21-589
Citation: Fan Zhirui, Yang Zhixun, Xu Qi, Su Qi, Niu Bin, Zhao Guozhong. Nonlinear stiffness topology optimization for the bend stiffener of flexible riser. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(4): 929-938 doi: 10.6052/0459-1879-21-589

海洋柔性立管防弯器结构非线性刚度拓扑优化

doi: 10.6052/0459-1879-21-589
基金项目: 国家自然科学基金(U1906233, 52001088, 11732004和51975087), 山东省重点研发计划(2019 JZZY010801), 黑龙江省自然科学基金(LH2021 E050)和工业装备结构分析国家重点实验室开发基金(GZ20105)资助项目
详细信息
    作者简介:

    杨志勋, 副教授, 主要研究方向: 海洋工程柔性管缆结构多尺度分析及实验验证. E-mail: yangzhixun@hrbeu.edu.cn

  • 中图分类号: TH122

NONLINEAR STIFFNESS TOPOLOGY OPTIMIZATION FOR THE BEND STIFFENER OF FLEXIBLE RISER

  • 摘要: 防弯器是海洋柔性立管过弯保护的关键附件, 对提高立管的结构安全性具有重要意义. 目前, 防弯器结构设计主要采用尺寸优化方法. 然而, 与拓扑优化方法相比, 该方法能提供的设计空间有限, 其在提高防弯器的力学性能, 以及探索防弯器创新构型方面具有很大不足. 本文在Dirichlet边界条件下, 以最大化弯曲刚度为目标, 对同时考虑材料和几何非线性的防弯器结构拓扑优化方法进行研究. 通过引入Helmholtz-PDE过滤和Heaviside惩罚, 以克服优化中出现的棋盘格现象和灰度单元等数值不稳定性问题. 与此同时, 研究引入了对称算子, 以提高往复性载荷作用下防弯器结构的承载能力和可制造性, 并且采用伴随法对优化问题的灵敏度进行了推导. 此外, 为了提高结构分析和优化的效率, 研究还基于PETSc库建立了并行程序框架. 数值算例中, 在材料体分比相同的情况下, 对防弯器结构分别进行了2D和3D非线性拓扑优化, 并对两种优化结果的承载能力进行了对比. 数值算例结果表明, 相比于防弯器2D拓扑优化结果, 在大部分波浪载荷方向下, 3D拓扑优化所给出的防弯器设计方案具有更为优越的结构性能. 本文所建立的3D非线性拓扑优化技术, 为深水恶劣海况下的高性能防弯器结构设计提供了新的理论模型和实现技术.

     

  • 图  1  柔性立管与防弯器结构示意图

    Figure  1.  Schematic diagram about the flexible riser and bend stiffener

    图  2  切线刚度${{\boldsymbol{K}}_{\tan }}$与割线刚度${{\boldsymbol{K}}_{\cot }}$的定义, 其中${\boldsymbol{F}}$${\boldsymbol{u}}$分别为结构的载荷和位移

    Figure  2.  The definition of tangent stiffness ${{\boldsymbol{K}}_{\tan }}$ and secant stiffness ${{\boldsymbol{K}}_{\cot }}$, where ${\boldsymbol{F}}$ and ${\boldsymbol{u}}$ are the force and displacement of a structure, respectively

    图  3  海洋柔性立管、防弯器力学模型及边界条件

    Figure  3.  The mechanical model and boundary conditions of ocean flexible riser and the bend stiffener

    图  4  式(1)所定义目标函数的力学含义

    Figure  4.  Nature of the objective defined by Eq. (1)

    图  5  应变能与式(1)所定义目标函数的不同

    Figure  5.  The Difference between the strain energy and the objective defined by Eq. (1)

    图  6  切线刚度与式(1)所定义目标函数的不同

    Figure  6.  The difference between the tangent stiffness and the objective defined by Eq. (1)

    图  7  Dirichlet边界条件结构分析示意图

    Figure  7.  Illustration of Dirichlet boundary conditions

    图  8  Heaviside函数的性质

    Figure  8.  The characteristic of Heaviside function

    图  9  算例1中悬臂梁结构的设计域及边界条件

    Figure  9.  Geometry of the admissible domain and boundary conditions about the cantilever beam considered in example 1

    图  10  算例1中防弯器2D拓扑优化结果

    Figure  10.  The 2D optimized result of bend stiffener in example 1

    图  11  算例1中旋转操作后所得防弯器优化结果剖面图

    Figure  11.  Sectional view about the optimized results of bend stiffener in example 1 obtained by using rotation operation

    图  12  算例2中所采用的结构有限元模型

    Figure  12.  The FEM model used in example 2

    图  13  算例2中防弯器3D拓扑优化结果

    Figure  13.  The 3D optimized result of bend stiffener in example 2

    图  14  算例2中对称操作后所得优化结果

    Figure  14.  The optimized results obtained by symmetry operation in example 2

    图  15  不同载荷方向($\theta $)下, 算例1和算例2优化结果的刚度对比

    Figure  15.  Stiffness comparison between the optimized results of example 1 and 2 with different loading directions ($\theta $)

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出版历程
  • 收稿日期:  2021-11-11
  • 录用日期:  2021-12-16
  • 网络出版日期:  2021-12-17
  • 刊出日期:  2022-04-18

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