Multicomponent topology optimization of functionally graded lattice structures with bulk solid interfaces

Abstract

This article presents a topology optimization method for structures consisting of multiple lattice components under a certain size, which can be manufactured with an additive manufacturing machine with a size limit and assembled via conventional joining processes, such as welding, gluing, riveting, and bolting. The proposed method can simultaneously optimize overall structural topology, partitioning to multiple components and functionally graded lattices within each component. The functionally graded lattice infill with guaranteed connectivity is realized by applying the Helmholtz PDE filter with a variable radius on the density field in the solid isotropic material with penalization (SIMP) method.The partitioning of an overall structure into multiple components is realized by applying the discrete material optimization (DMO) method, in which each material is interpreted as each component, and the size limit for each component imposed by a chosen additive manufacturing machine. A gradient-free coating filter realizes bulk solid boundaries for each component, which provide continuous mating surfaces between adjacent components to enable the subsequent joining. The structural interfaces between the bulk solid boundaries are extracted and assigned a distinct material property, which model the joints between the adjacent components. Several numeral examples are solved for demonstration. K E Y W O R D Sbulk solid interfaces, lattice infill, multicomponent structures, topology optimization INTRODUCTIONLattice structures exhibit superior structural properties such as low stiffness-to-weight ratio, robustness for random direction loads, damage resistance against defects, and extreme physical properties such as large energy absorption, 1,2 negative Poisson's ratio, 3,4 large thermal expansion, 5,6 and special acoustic absorption. 7,8 Owing to the recent advancement in additive manufacturing processes, especially those in metals, the fabrication and testing of engineered lattice structures have become much more accessible to researchers. Thompson et al. 9 reviewed recent work on design for additive manufacturing including the design of engineered lattice structures. They pointed out there was still a lack of systematic design method to overcome the complexity of lattice structures whose dimension spans from the micro/meso-scale to macro-scale. In addition to the structural complexity, additively manufactured lattice structures for industrial applications

Functionally-graded Lattice Topology Optimization of Conformal Fluid Channels

“…In general, the adjoint method is applied to compute the sensitivity of target function. The sensitivity analysis of mean temperature, pressure drop constraint, displacement constraint, and local volume constraint can be easily found in (Andreasen, Gersborg et al 2009, Zhao, Zhou et al 2018, Yi, Zhou et al 2019, Yu, Ruan et al 2020, Yi and Saitou 2021. Because the limitation of length, only the sensitivity of thermal stress with respect to density 𝜌 𝑒 is demonstrated in detail.…”

“…Details are contained in Section 3.3. Although several groups of researchers (Wu, Aage et al 2018, Yi, Zhou et al 2019, Yi and Saitou 2021, Zhao and Zhang 2021 have explored the potential of this method in generating structurally robust geometry, few research have investigated thermal structures. Das and Sutradhar (Das and Sutradhar 2020) presented a lattice TO method to design heat dissipating structures subject to thermal and structural performance requirements.…”

“…We adopt a neighborhood mask approach (Wu, Aage et al 2018, Yi, Zhou et al 2019, Yi and Saitou 2021 for functionally-graded lattices, where lattice patters are generated by constraining the average element density within a small neighborhood of a design point. To achieve checkboard-free patterns and FE meshindependent results, the element density is regularized using a Helmholtz PDE filter and a smoothed Heaviside function (Kawamoto, Matsumori et al 2010) .…”

“…In the examples in Section 4, the radius is allowed to vary in a range between 𝑟 and 𝐶𝑟, where where 𝐶 is a scalar tuning parameter. Sensitivities of the constraint (21) with respect to 𝜌 and 𝑟 are detailed in (Yi, Zhou et al 2019, Yi andSaitou 2021). As done in Section 4.2, the left-hand side of Eq.…”

“…(A.20) into Eq. (A.6), the sensitivity of 𝜎 𝑝𝑛𝑜𝑟𝑚 with respect to element density 𝜌 can be obtained.Similarly, the sensitivity of the thermal stress constraint with respect to the locally varying averaging radius can be written as: given in(Yi, Zhou et al 2019, Yi andSaitou 2021) as: 𝑵 𝒋 is the vector of the 𝑗 𝑡ℎ element shape function and 𝑲 𝒇 (𝒓) is given as:𝑲 𝑓 (𝑟) = 𝐴 𝑒=1 𝑛 𝑒 [∫ −(∇𝑵 𝒆 ) ⊤ 𝑟 2 ∇𝑵 𝒆 + 𝑵 𝒆 ⊤ 𝑵 𝒆 ] 𝑑𝑥where 𝐴 𝑒=1 𝑛 𝑒 is the standard FEM operator.Substituting Eq. (A.22) and Eq.…”