增材制造自支撑点阵-实体复合结构拓扑优化方法

A lattice-solid hybrid structure topology optimization method for support-free additive manufacturing

随着先进设计概念和增材制造技术的发展与革新,多尺度结构的设计及制造在学术界被广泛研究。点阵-实体复合结构兼具轻量化、高性能、多功能属性,展现了巨大的应用前景和科研价值。为此,提出了一种增材制造自支撑点阵-实体复合结构拓扑优化方法,通过建立一套创新的层级材料插值模型,分别定义了自支撑单元密度和单元内点阵单胞-实体材料的相对密度。其中,对自支撑单元密度进行增材制造滤波以实现结构的增材制造自支撑特性,利用计算均化方法及多项式插值,对点阵单胞-实体材料的等效刚度进行了点阵域-实体域统一插值,以此实现优化过程点阵-实体的无缝双向切换。最后,通过数值计算案例对所建立算法的有效性和先进性进行了论证,结果表明,自支撑的点阵-实体复合结构在力学承载能力上优于传统的单一尺度自支撑拓扑优化结果。

In light of the development of advanced design methods and additive manufacturing technologies,the design and manufacturing of multi-scale structures have been extensively investigated.Extensive research has been conducted on multi-scale structural optimization with both variable density lattices and topologically freeform micro structures.Their additively manufactured counterparts have undergone testing,showcasing excellent mechanical properties,as reported in a vast number of publications.Recently,by introducing solid phase into the design,it is found that the resulted mechanical performance of the multi-scale structures can be further enhanced.The lattice-solid hybrid multi-scale structures possess lightweight,high-performance,and multifunctional characteristics,demonstrating great potentials in applications and scientific research.Hence,in this paper,a topology optimization method on lattice-solid hybrid structures for support-free additive manufacturing was proposed.By proposing a novel hierarchical material interpolation model,this method defined two sets of densities:the external densities defining the overall material distribution for support-free effect and the internal relative densities defining the local structural details for lattice-solid phase interpolation.PDE filter is applied to smooth density distribution and thus eliminate the check board issue.Heaviside projection is adopted to create the clear cut structural boundary,preventing hard to process grey elements.Additive manufacturing filter was applied to the external densities to ensure the support-free capability by restricting the overhang inclination angle beyond 45 degree.The effective elastic properties of the lattice-solid materials were evaluated through numerical homogenization,and polynomial fittings were performed to establish the surrogate models of the equivalent elastic matrix components on the internal relative densities.One important characteristic of the above interpolation was that the material option could automatically switch between the lattice and solid phases,thus enabling the smooth gradient-based design optimization.Then,the optimization problem is formulated similar to the density based topology optimization scheme and sensitivities of both the objective and constraint functions are derived with the adjoint method.The method of moving asymptotes are adopted for design updating the two sets of density variables.Finally,the effectiveness of the proposed method was verified through a numerical case study.The numerical result indicated that the support-free lattice-solid hybrid structure outperformed the conventional single-scale self-support topological design in terms of load-bearing capability.