Forming Michell Truss in Therr-Dimensions by Finite Element Method
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摘要: 提出了形成三维Michell桁架的有限元方法.采用正交异性纤维增强复合材料模型模拟Michell桁架.纤维在节点处的密度和方向作为基本设计变量.根据有限元分析得到节点位置的应力和应变.采用迭代方法,将纤维方向调整到主应力方向;根据纤维方向的应变改变纤维密度. 仅需少量迭代即可得到满足Michell准则的应变场和类桁架连续体.最后根据节点处的纤维方向用连续线表示出Michell桁架.几个算例表明了算法的有效性和计算效率.Abstract: The finite element method to form Michell truss in three-dimensions is presented. The orthotropic composite with fiber-reinforcement is employed as the material model to simulate Michell truss. The orientation and densities of fibers at nodes are taken as basic design variables. The stresses and strains at nodes are calculated by finite element method. An iteration scheme is suggested to adjust the orientations of fibers to be along the orientations of principal stresses, and the densities of fibers according to the strains in the orientations of fibers. The strain field satisfying Michell criteria and truss-like continuum are achieved after several iterations. Lastly, the Michell truss is showed by continuous lines, which are formed according to the orientations of fibers at nodes. Several examples are used to demonstrate the efficiency of the presented approach.
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