张拉整体基本形体稳定构型理论

发布时间：2019-05-25 04:43

【摘要】：提出用统一的几何参数描述一维、二维、三维不同空间维数结构,通过几何参数变化,实现不同维数结构的无缝演化。以基本形体结构的几何参数和分形参数为基础,提出应用节点力平衡法,构建张拉整体基本形体稳定构型理论。建立了主分形参数与辅助分形参数及构件空间位置、结构几何参数的数学分析模型。确立出主分形参数与辅助分形参数构建自应力稳定基本单元结构,必须满足的映射关系。分析得出自应力稳定状态下,各个构件力密度间的函数关系。应用节点广义坐标结合构件连接矩阵、构件内力密度、系统力平衡,编写Matlab程序;输入基本体包络几何参数和主分形参数,程序即可自动完成辅助分形参数确定及所有构件矢量计算及其空间布置方式,实现自应力稳定基本单元自动构型。对于不同的分形参数构建起的自应力稳定结构进行分析比较,给出分形参数与结构几何参数、力密度、辅助形体参数之间的函数关系及变化趋势。
[Abstract]:In this paper, unified geometric parameters are used to describe one-dimensional, two-dimensional and three-dimensional spatial dimension structures, and the seamless evolution of different dimension structures is realized by changing geometric parameters. Based on the geometric parameters and fractal parameters of the basic body structure, the theory of stable configuration of the tensioned whole body is constructed by using the node force balance method. The mathematical analysis models of main fractal parameters and auxiliary fractal parameters, spatial position of components and structural geometric parameters are established. The mapping relationship between the main fractal parameters and the auxiliary fractal parameters to construct the basic unit structure of self-stress stability is established. The functional relationship between the force density of each component under the condition of self-stress stability is obtained. The Matlab program is written by combining the joint generalized coordinates with the connection matrix of the component, the internal force density of the component, and the force balance of the system. By inputting the geometric parameters of the basic body envelope and the main fractal parameters, the program can automatically complete the auxiliary fractal parameter determination, the vector calculation of all components and their spatial arrangement, and realize the automatic configuration of the basic unit of self-stress stability. The self-stress stable structures constructed by different fractal parameters are analyzed and compared, and the functional relationship and changing trend between fractal parameters and structural geometric parameters, force density and auxiliary body parameters are given.
【作者单位】：哈尔滨工程大学机电工程学院;加州大学圣地亚哥分校机械与航空系;
【基金】：国家自然科学基金(51605111,51675114) 黑龙江省自然基金(11202128)资助项目
【分类号】：TU311.2

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