基于类格栅连续体模型的板结构拓扑优化研究.pdf

华侨大学硕士学位论文基于类格栅连续体模型的板结构拓扑优化研究姓名：乔惠云申请学位级别：硕士专业：结构工程指导教师：周克民20090501华侨大学硕士学位论文 2原创性声明 本人声明兹呈交的学位论文是本人在导师指导下完成的研究成果论文写作中不包含其他人已经发表或撰写过的研究内容，如参考他人或集体的科研成果，均在论文中以明确的方式说明本人依法享有和承担由此论文所产生的权利和责任 学位论文作者签名： 日期： 学位论文版权使用授权声明 本人同意授权华侨大学有权保留并向国家机关或机构送交学位论文和磁盘，允许学位论文被查阅和借阅 论文作者签名： 指导教师签名： 签 名 日 期： 签 名 日 期： 华侨大学硕士学位论文 3摘 要 结构拓扑优化是目前结构优化研究领域的热点之一与尺寸优化和形状优化相比，结构拓扑优化问题的难度更大，取得的经济效益更大，对工程设计人员更具吸引力类格栅连续体理论是拓扑优化的重要研究领域， 是继类桁架理论之后的60年代才开始发展起来。

相对于类桁架理论，类格栅连续体理论的优化结果更易于在工程上直接使用 本文研究了应力约束下类格栅连续体结构的拓扑优化方法采用正交异性增强复合材料模型模拟类格栅连续体（或加肋板）的本构关系，优化结果与类格栅连续体有明确的对应关系，克服了一般复合材料模型优化结果没有实际意义的问题同时它比各向同性材料模型具有更大的设计空间，可以得到更合理的结果 首先研究了单工况应力约束下的类格栅连续体结构的优化方法优化目标结构是由无限细无限密的梁（或肋）构成的类格栅连续体（或加肋板） 以梁（或肋）在结点处的密度和方向作为设计变量，梁（或肋）在设计域内连续分布建立了材料模型及其对应的弹性矩阵和刚度矩阵根据有限元分析结果，采用满应力准则法，经过少量迭代建立材料的连续分布场以几个算例演示拓扑优化过程用优化结果与解析解对比证明本文采用的方法有效 然后提出一种多工况应力约束下的类格栅连续体结构的拓扑优化方法先优化各单工况下梁（或肋）的分布假设结构达到最优华侨大学硕士学位论文 4时的方向刚度与各单工况下的方向刚度最大值的差值最小，优化多工况下梁（或肋）的分布经过少量迭代建立优化的材料连续分布场仍以算例演示拓扑优化的过程，并给出结点处梁（或肋）的密度和方向分布。

最后研究了单工况类格栅连续体理论的应用分析椅面板和筏型地基板在不同约束下的传力路径，指导椅面板加肋和筏型地基板加强梁的分布和走向，形成加肋板板的挠度减小，可以在原有基础上适当减小板的厚度，节省材料 关键词：板，拓扑优化，多工况，应力约束，格栅 华侨大学硕士学位论文 5ABSTRACT Topology optimization is one of the major research fields of structural optimization research up to date. It is much more difficulty usually than size optimization and shape optimization. However, it can achieve more benefit so that it is more attractive for design engineer. Grillage- like continua optimization theory is an important branch of topology optimization. It has been developed since 1960’ s after truss- like continua are studied. It is much more easily to be applied in engineering than that of truss- like continua. The method to optimize topology of grillage structures with stress constraints is studied. Fiber- reinforced orthotropic composite is employed as the material model to simulate the constitutive relation of grillage- like continua/ plate reinforcement. Using this material model, the optimum results explicitly correspond with grillage- like continua. The problem that the optimum results given by free material optimization have not any meaning in practice is solved. On the other hand, this material model provides larger design space than isotropic material model and may achieve more reasonable results. Firstly, grillage structures with stress constraints for single load case are optimized. The optimal structures are grillage- like continua/plate reinforcement containing infinite number of beams/ribs of infinitesimal 华侨大学硕士学位论文 6spacing. The beams/ribs densities and orientations at the nodes are taken as design variables. Material distributive field is continuous. Elastic matrix and stiffness matrix is developed. The material distribution is optimized by fully- stressed criterion based on finite element analysis. Some examples are presented to demonstrate the processes of topology optimization. Comparison between optimal solutions and analytic solutions demonstrate the effectiveness of the proposed approach. Then a method to optimize the topology of grillage structure under multiple load cases with stress constraints is presented. The beams/ribs distribution for single load case is optimized. With assumption that the directional stiffness of the optimal structures under multiple load cases approach to the biggest of the stiffness defined for single load case, the beams/ribs distribution for multiple load case is optimized. The optimal continuous material distributive field is achieved after several iterations. Three examples are presented to demonstrate the processes of the topology optimization. The beams/ribs densities and orientations distribution at the nodes are given finally. At last, applications of grillage structures for single load case are studied. The paths of load transfer both on chair faceplate and on r aft foundation plate with different constraints are studied, which can decide the distributions and orientations of beams/ribs on the plate. Plate reinforcement causes the deflections of the plate depressed, and the 华侨大学硕士学位论文 7thickness of the plate could be reduced appropriately to save materials. Keywords: plate, topology optimization, multiple load cases, stress constraints, grillage 华侨大学硕士学位论文 11第一章 绪论 1.1 引言 长期以来，结构设计依靠采用较大安全系数的方法实现安全设计，这种方法不能充分地利用能源和材料。

在现今能源紧缺的情况下，寻求最佳结构设计，优化结构各部分参数，具有重要的理论意义和应用价值许多学者者深入研究了结构优化设计问题结构优化设计是力学理论与数学规划理论在结构工程中的应用优化设计方法广范应用于各类结构，如航空航天器、船舶、车辆、建筑和精密机械等 按照设计变量的类型和求解问题的难易程度， 结构优化可分为尺寸优化 （尺寸变量） 、形状优化（形状变量）和拓扑优化（拓扑变量）三个层次分别对应于三个不同的产品设计阶段，即概念设计、基本设计和详细设计三个阶段，如图 1.1 所示[1] 尺寸优化（Sizing optimization） ：优化变量为杆件的横截面面积，或板壳的厚度分布在保持结构的形状和拓扑结构不变的情况下，寻求结构组件的最佳截面尺寸以及最佳材料性能的组合关系，优化横截面的面积（如桁架） ，选择板的最佳厚度等其特点是：设计变量容易表达，求解理论和方法成熟 图 1.1 结构优化的三个阶段 Structure Optimization （结构优化）Size Optimization （尺寸优化） Shape Optimization （形状优化） Topology Optimization （拓扑优化） Detailed Design Stage （详细设计阶段） Preliminary Design Stage （基本设计阶段） Conceptual Design Stage （概念设计阶段） 华侨大学硕士学位论文 12形状优化（Shape optimizati。