概念车身框架结构有限元精细建模与截面几何形状优化设计

In order to reduce the design periods and manufacturing risk of car body at the conceptual design stage, refined finite element model and cross-sectional shape optimization for thin-walled skeleton structure are investigated in this project..Firstly, Vlasov's general coordinates are introduced to describe the cross-sectional deformation of warping and distortion. And then a new thin-walled beam element with eight degree of freedoms (DOFs) is derived from the Hellinger-Reissner mixed variational principle. .Secondly, a semi-rigid beam element that consists of the new beam element with six springs at the ends is exploited to simulate the flexibility of joint. Guyan reduction method condenses the semi-rigid beam element as a super element. By the above two steps, a refined finite element model of skeletal structure for car body is constructed. .Thirdly, the thin-walled skeletal structure is optimized to find the optimal thickness of plate and cross-sectional shape which fulfills the highest stiffness and hardness requirements at the lowest structural weight. The nodal displacements and frequency of the structure express the stiffness requirement; and the stress of beam element indicates the hardness requirement. The hybrid genetic algorithm and sequential linear programming method (Hybrid-GA-SLP) is developed to solve the highly nonlinear optimization problem with continuous and discrete variables. The Hybrid-GA-SLP has the ability to global and local optimization. The structural reanalysis method and parallel computation are applied to speed up the process of optimization. .At last, a special finite element software for structural modeling and analysis is developed to improve the design ability of car body structure. The unified modeling language and objected-oriented programming are employed to depict the classes and their relationship. The design patterns are identified and applied in the framework design to facilitate communication and system expansion. Microsoft DirectX and GDI+ implement graphics display of spatial thin-walled frame and planar thin-walled cross section, respectively.

为了缩短车身设计周期、降低制造风险，本项目旨在解决概念设计阶段车身薄壁框架结构有限元精细建模与截面形状优化设计难题，实现"轻量化、高刚度、高强度"的车身设计目标。首先基于Vlasov广义坐标原理，构造了可描述截面翘曲与畸变变形的位移模式；接着采用H-R混合变分原理推导出新型的8自由度薄壁梁有限元单元。其次为了方便模拟接头柔度，对两端连接有弹簧的梁单元进行自由度缩减，得到半刚性梁单元。以上两步实现车身框架有限元精细建模。然后以车身质量为目标函数，位移、应力与频率为约束条件，建立关于板料厚度与截面节点坐标的结构形状优化模型。采用遗传算法与序列线性规划相结合的混合优化算法求解关于离散-连续变量的非线性优化问题，实现全局与局部快速寻优。最后利用面向对象编程技术、UML建模机制、DirectX图形引擎、软件设计模式等自主开发车身框架结构建模与截面优化专用CAE软件，以提高我国轿车车身正向设计能力。

轿车结构轻量化设计是实现节能减排的主要途径，结构优化设计是结构轻量化设计的理论基础。轿车车身结构优化设计一般由：拓扑优化、截面形状优化、板厚尺寸优化三步完成。其中，车身复杂截面形状的确定目前依赖于工程经验，无理性的优化设计方法对其求解，该问题是困扰国际上车身结构设计领域的难题。. 本项目通过车身框架结构的精细有限元建模与截面形状优化，实现了“轻量化、高刚度、高强度”的车身设计目标。首先基于广义坐标原理，构造了可描述截面翘曲与畸变变形的位移模式；接着采用Hellinger-Reissner 混合变分原理推导出新型的8 自由度薄壁梁有限元单元。其次为了方便模拟接头柔度，对两端连接有弹簧的梁单元进行自由度缩减，得到半刚性梁超单元。以上两步实现车身框架有限元精细建模。. 为了解决以上车身截面几何形状优化难题，采用箱型截面作为中间变量，建立了双层协同优化模型：第一层优化模型：以车身的质量为目标函数，高刚度（位移、频率约束）与高强度（应力）为约束条件，建立关于箱梁截面长、宽、厚度尺寸参数的优化模型。采用基于组件灵敏度信息的序列线性规划求解该优化模型，得到箱梁截面最优尺寸，进而求得截面的最优几何特性：截面积，弯曲惯性矩与扭转惯性矩。第二层优化模型：以截面积最小为目标，第一层优化得到的弯曲惯性矩、扭转惯性矩以及制造工艺为约束条件，对梁截面的板料厚度（离散变量）、节点坐标（连续变量）进行截面形状优化研究。采用遗传算法求解该离散-连续变量的非线性有理式优化问题。. 最后自主开发了车身框架设计与优化专用CAE 软件VFDO。该成果已应用到一汽轿车股份有限公司的新车型的开发，可辅助设计人员在2-3天内完成整车梁截面的几何形状设计，1周内完成刚度、强度以及冲压工艺约束下的整车梁断面几何形状的优化。该研究解决了困扰汽车行业的车身框架断面形状优化难题，实现了轻量化目标，提升了我国轿车车身自主设计能力。

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