利用有限元构造Michell桁架的一种方法

A METHOD OF CONSTRUCTING MICHELL TRUSS USING FINITE ELEMENT METHOD

提出了一种新的形成Michell桁架的有限元分析方法.该方法以纤维增强正交各向异性复合板为材料模型,根据有限元分析结果调整各单元的纤维密度和方向.采用所提出的一种迭代格式,经过少量迭代,形成满足Michell准则的应变、内力场.该方法适于不同几何形状、支撑条件及荷载情况.算例结果表明该方法是有效的.

A new method of constructing Michell truss based on finite element analysis was presented. The orthotropic composite plates with fibre-reinforcement was used as the material model. The direction and density of fibre, which determining the constitutive parameters of the materials, were taken as design variables. A iterating schemes was suggested by this paper to determine these variables. According to the results of finite element analysis, the direction of the fibre in each finite element was turned to the direction of principal strain, and the density of fibre in each finite element was increased (or decreased) when the strain in the same direction is greater (or less) than allowable strain. It induced the changing of the stiffness in the two orthogonal direction in each element during the process of the iteration. The strain and internal force field satisfying Michell criteria was formed after several iteration. At the same time, the across areas and the direction of the bar in the continuum body were obtained. According to these results, the optimum truss is formed. By this method, the structure in any shapes, with any supporting and loading condition can be calculated. The checkerboard problem was avoid and more detail structural can be obtain by using less elements. Several examples are used to demonstrate the efficiency and effectiveness of the proposed method.