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Orientation optimization in anisotropic materials using gradient descent method

机译:梯度下降法优化各向异性材料的取向

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The rapid advancement in additive manufacturing makes it feasible to manipulate material orientation locally to construct optimized structure. The remaining question becomes: how to find such material orientation distribution to minimize/maximize properties of a additively manufactured structure? Despite much research has been done to solve this problem, they all have constraints and especially lack the study of optimization algorithm at the fundamental level. In this work, the objective is to use gradient descent method to find the optimal distribution of material orientation for anisotropic materials to minimize/maximize compliance under plane stress condition. We propose a rationalized formula referred to as normalized gradient by maximum (NGM) to calculate step length. Gradient descent method has been demonstrated at the fundamental level that it is well suited for solving this problem provided that a proper step length can be calculated. NGM calculates step length at nearly no extra cost to guarantee that iterative process convergences to a local/global extreme. NGM method is validated by a tensile and shear condition.
机译:增材制造的飞速发展使得在本地操纵材料取向以构造优化的结构成为可能。剩下的问题变成:如何找到这样的材料取向分布以最小化/最大化增材制造结构的性能?尽管已经进行了大量的研究来解决这个问题,但是它们都具有约束条件,尤其是在基础层面上缺乏对优化算法的研究。在这项工作中,目标是使用梯度下降法来寻找各向异性材料的材料取向的最佳分布,以在平面应力条件下最小化/最大化柔顺性。我们提出了一种合理的公式,称为最大归一化梯度(NGM),以计算步长。在基本水平上已经证明了梯度下降方法,只要可以计算出适当的步长,它就非常适合解决该问题。 NGM几乎无需额外成本即可计算步长,以确保迭代过程收敛到本地/全局极限。 NGM方法通过拉伸和剪切条件验证。

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