Sensitivity analysis and lattice density optimization for sequential inherent strain method used in additive manufacturing process
Sensitivity analysis and lattice density optimization for sequential inherent strain method used in additive manufacturing process
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DOI：
10.1016/j.cma.2020.113231
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发表时间：
2020-10
影响因子：
7.2
通讯作者：
A. Takezawa;A. To;Qiang Chen;Xuan Liang;Florian Dugast;Xiaopeng Zhang;M. Kitamura
中科院分区：
文献类型：
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作者：
A. Takezawa;A. To;Qiang Chen;Xuan Liang;Florian Dugast;Xiaopeng Zhang;M. Kitamura
金属添加剂制造过程中产生的热变形的补偿是金属添加剂制造领域的一个重要问题。针对在物体内部形成晶格结构以减少热变形的问题，提出了一种晶格体积分数分布优化方法。假定线弹性问题是用有限元方法求解的，将利用有限元过程中的单元激活的逐层处理的固有应变法形成为递推关系，并基于伴随方法导出目标函数的灵敏度。单元格子形状为带有立方体或球状气孔的简单立方体，并以其周围最小壁厚为设计变量对其分布进行优化。用齐次化方法得到了晶格的有效刚度张量。有效属性关于设计变量的函数用多项式函数来逼近。将优化问题表示为无约束极小化问题。采用移动渐近线的方法对设计变量进行优化。在此，基于准二维和三维数值研究，包括通过全尺度热力分析进行再分析，讨论了所提出方法的有效性。
Compensation of the thermal distortion that occurs during the fabrication process is an important issue in the field of metal additive manufacturing. Considering the problem in forming a lattice structure inside an object to reduce the thermal distortion, we developed a lattice volume fraction distribution optimization method. Assuming that the linear elastic problem is solved using the finite element method (FEM), an inherent strain method applying a layer-by-layer process utilizing the element activation during the FEM is formed as a recurrence relation, and the sensitivity of an objective function is derived based on the adjoint method. The unit lattice shape is a simple cube with a cube or a sphere-shaped air hole, and its distribution is optimized by considering the minimum thickness of the wall surrounding it as a design variable. The effective stiffness tensor of the lattice is derived using a homogenization method. The functions of the effective properties with respect to the design variables are approximated through polynomial functions. The optimization problem is formulated as an unconstrained minimization problem. The design variables are optimized using the method of moving asymptotes. Herein, the validity of the proposed method is discussed based on quasi two-dimensional and three-dimensional numerical studies including a re-analysis through full-scale thermo-mechanical analysis.