海洋柔性立管防弯器结构非线性刚度拓扑优化  

NONLINEAR STIFFNESS TOPOLOGY OPTIMIZATION FOR THE BEND STIFFENER OF FLEXIBLE RISER

作　　者：范志瑞 杨志勋 许琦 苏琦 牛斌 赵国忠[1] Fan Zhirui;Yang Zhixun;Xu Qi;Su Qi;Niu Bin;Zhao Guozhong(State Key Laboratory of Structural Analysis for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian 116024,China;College of Mechanical and Electronic Engineering,Harbin Engineering University,Harbin 150001,China;School of Mechanical Engineering,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]大连理工大学工程力学系,工业装备结构分析国家重点实验室,大连116024 [2]哈尔滨工程大学机电工程学院,哈尔滨150001 [3]大连理工大学机械工程学院,大连116024

出　　处：《力学学报》2022年第4期929-938,I0002,共11页Chinese Journal of Theoretical and Applied Mechanics

基　　金：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);工业装备结构分析国家重点实验室开发基金(GZ20105)资助项目。

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.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 w

关 键 词：柔性立管 防弯器 非线性优化 拓扑优化 载荷方向 

分 类 号：TH122[机械工程—机械设计及理论]