NONLINEAR STIFFNESS TOPOLOGY OPTIMIZATION FOR THE BEND STIFFENER OF FLEXIBLE RISER
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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.Abstract: The bend stiffener, as the key over-bending protection accessory, is of significant importance to improve the safety of the flexible riser used in deep water. At present, the size optimization method is mainly used in the structural design of the bend stiffener. However, compared with the topology optimization, the design freedom provided by this method is limited, and it lacks capacities in sufficiently improving the mechanical performance and finding the novel configurations of the bend stiffener. In the present study, under Dirichlet boundary conditions, a topology optimization method considering the material and geometric nonlinearity is developed to maximize the structural stiffness of the bend stiffener. The Helmholtz-PDE filter and Heaviside projection are introduced to eliminate the numerical issues caused by the checkerboard pattern and the gray element phenomenon, respectively. The symmetry operator is employed to enhance the load bearing capability under the reciprocating ocean wave load and improve the manufacturability of the bend stiffener. Making use of the adjoint method, a sensitivity analysis is performed to enable a gradient-based algorithm for solving the optimization problems. Simultaneously, a parallel computational framework based on PETSc library is also utilized to improve the efficiency of the structural analysis and optimization. In the numerical examples, with the constant material volume fraction, 2D and 3D optimizations for the bend stiffener are performed to improve the stiffness of the bend stiffener, respectively. Based on that, the load carrying capacity of the two optimization results under different load directions are compared. The numerical examples show that, compared to the 2D optimized result, the 3D optimization can significantly improve the stiffness of the bend stiffener in most loading directions. The present 3D nonlinear topology optimization method provides the new theorical model and implementation technology for the high-performance bend stiffener with the severe water environment in the deep ocean.
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Key words:
- flexible riser /
- bend stiffener /
- structural nonlinearity /
- topology optimization /
- load direction
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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${\boldsymbol{F}}$ 和${\boldsymbol{u}}$ 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 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 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 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
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