论文标题
基于投影的隐式建模方法（PIMM），用于功能分级的晶格优化
Projection-based Implicit Modeling Method (PIMM) for Functionally Graded Lattice Optimization
论文作者
论文摘要
本文提出了一种基于投影的隐式建模方法（PIMM），用于功能分级的晶格优化，该方法不需要任何均质化技术。在此方法中，提出了一个参数投影函数，以将功能分级晶格的隐式函数与有限元背景网格联系起来。为了减少设计变量的数量，径向基函数（RBF）用于插值隐式设计字段。三个周期性最小表面（TPM）晶格用于证明所提出的方法。与常规的基于均匀化的拓扑优化相比，提出的方法可以有效地解决应力约束的晶格设计。例如，优化后从初始设计中删除尖角。提出了几个二维晶格设计示例，以解决合规性和应力约束问题，以此为基于GPU的计算来加速有限元分析。提出的PIMM方法是灵活的，可以扩展到设计分级的不规则多孔支架和非周期性晶格填充设计。
This paper proposes a projection-based implicit modeling method (PIMM) for functionally graded lattice optimization, which does not require any homogenization techniques. In this method, a parametric projection function is proposed to link the implicit function of functionally graded lattice with the finite element background mesh. To reduce the number of design variables, the radial basis function (RBF) is utilized to interpolate the implicit design field. The triply periodic minimal surface (TPMS) lattice is employed to demonstrate the proposed method. Compared with conventional homogenization-based topology optimization, the proposed method can effectively resolve the stress-constrained lattice design; for example, sharp corners are removed from the initial design after optimization. Several two- and three-dimensional lattice design examples are presented to solve the compliance and stress-constrained problems, for which GPU-based computing is adopted to accelerate the finite element analysis. The proposed PIMM method is flexible and can potentially be extended to design graded irregular porous scaffold and non-periodic lattice infill designs.
