考虑结构自重的基于NURBS插值的3D拓扑描述函数法

发布时间：2018-01-30 22:33

  本文关键词： 拓扑优化 拓扑描述函数 NURBS插值 等几何分析 自重载荷　出处：《力学学报》2016年06期 　论文类型：期刊论文

【摘要】：在许多如大坝、桥梁等大型土木工程结构中,结构的自重是初始设计阶段必须考虑的重要载荷之一,因此研究自重载荷作用下的结构拓扑优化设计问题具有十分重要的意义.针对考虑自重载荷作用的拓扑优化问题所面临的主要困难,总结了现有处理考虑自重载荷的拓扑优化问题的三类主要方法;提出一种基于非均匀有理B样条(non-uniform rational B-splines,NURBS)基函数插值的拓扑描述函数方法,基于此方法研究了考虑设计依赖自重载荷作用的2D/3D结构优化设计问题.在列式下,高阶NURBS基函数被同时用于三维NURBS实体片中的几何场、位移场及设计变量场插值,实现了几何模型、分析模型和优化模型的有效统一,确保了位移场及设计变量场的高阶连续性;详细推导了基于NURBS基函数插值的考虑自重载荷作用的三维结构拓扑优化模型及其灵敏度列式,并采用移动渐进线方法(method of moving asymptotes,MMA)进行了优化求解;多个算例验证了方法的有效性和稳定性,结果表明,优化迭代过程稳健,收敛快,能够有效地克服自重载荷作用下连续体结构拓扑优化中经常遇到的低密度区域材料的寄生效应及目标函数的非单调性等问题.
[Abstract]:In many large civil engineering structures such as dams and bridges, the weight of the structure is one of the important loads that must be considered in the initial design stage. Therefore, it is of great significance to study the structural topology optimization problem under the action of deadweight load. Three main methods to deal with topology optimization problems considering deadweight load are summarized. A topological description function method based on non-uniform rational B-splines (NURBS) basis function interpolation for nonuniform rational B-spline is proposed. Based on this method, the optimal design problem of 2D / 3D structure with design dependent on deadweight load is studied. High order NURBS basis function is used to interpolate geometric field, displacement field and design variable field in 3D NURBS solid chip at the same time, realizing the effective unification of geometric model, analytical model and optimization model. The high order continuity of displacement field and design variable field is ensured. Based on NURBS basis function interpolation, the topological optimization model and sensitivity formula of 3D structure considering deadweight load are derived in detail. The method of moving progressive line is used to solve the problem. The effectiveness and stability of the method are verified by several numerical examples. The results show that the iterative optimization process is robust and convergent. It can effectively overcome the parasitic effect of low density regional materials and the non-monotonicity of objective function in topology optimization of continuum structure under self-weight load.
【作者单位】： 大连理工大学汽车工程学院;大连理工大学工业装备结构分析国家重点实验室;
【基金】：国家自然科学基金(11272075,11302041) 中央高校基本科研业务费专项(DUT15RC(4)36)资助项目
【分类号】：O302
【正文快照】： 引言 e3二目速的i 酬 h material—penalization,SIMP)?和渐进结构优化方化结果和迭代过程的影响,而且对“没有材料就没有惯性”的理论最优解问题进行了阐述和研究.张阵胃[19]针对自重载荷作用下连续体结构拓扑优化+遇到的常见问题,提出了一种将_p插值模型与平均敏度过滤，

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