In this article, Modern Design for Manufacturing (MDfM) refers to the confluence of two nascent technologies, namely, topology optimization (TO) and additive manufacturing (AM). The two share a symbiotic relationship wherein TO reduces the amount of material required to meet design objectives, while AM is ideally suited for fabricating complex designs generated via TO. The objective of this article is to highlight the challenges and opportunities underlying this symbiotic relationship. The state-of-the-art capabilities of TO are presented, specifically focusing on multi-material, and multi-scale TO. This is followed by a discussion on some of the challenges posed by AM that must be accounted for, during TO, to ensure part manufacturability. Recent efforts to bridge the gap between these two technologies are summarized.

Multi-scale topology optimization (MTO) is exploited today in applications that require designs with large surface-to-volume ratio. Further, with the advent of additive manufacturing, MTO has gained significant prominence. However, a major drawback of MTO is that it is computationally expensive. As an alternate, graded MTO has been proposed where the design features at the smaller scale are graded variations of a single microstructure. This leads to significant reduction in computational cost, while retaining many of the benefits of MTO. Graded MTO fundamentally rests on interpolation of elasticity matrices. The direct method of interpolation used today unfortunately does not guarantee positive-definiteness of the resulting matrices. Consequently, during the graded MTO algorithm the strain energy may become negative and non-physical. In this paper, we propose a simple but effective spectral decomposition-based approach which guarantees positive-definite elasticity matrices. The proposed method relies on a spectral (eigen) decomposition of instances of the elasticity matrices, followed by regression of eigenvalues and interpolation of eigenvector orientations. The resulting elasticity matrix can then be used for stable optimization. The direct and spectral decomposition methods are compared here for robustness, accuracy and speed, through several numerical experiments. (C) 2021 Elsevier B.V. All rights reserved.

In topology optimization, the bisection method is typically used for computing the Lagrange multiplier associated with a constraint. While this method is simple to implement, it leads to oscillations in the objective and could possibly result in constraint failure if proper scaling is not applied. In this paper, we revisit an alternate and direct method to overcome these limitations. The direct method of Lagrange multiplier computation was popular in the 1970s and 1980s but was later replaced by the simpler bisection method. In this paper, we show that the direct method can be generalized to a variety of linear and nonlinear constraints. Then, through a series of benchmark problems, we demonstrate several advantages of the direct method over the bisection method including (1) fewer and faster update iterations, (2) smoother and robust convergence, and (3) insensitivity to material and force parameters. Finally, to illustrate the implementation of the direct method, drop-in replacements to the bisection method are provided for popular Matlab-based topology optimization codes.

Additive manufacturing (AM) has enabled the fabrication of artifacts with unprecedented geometric and material complexity. The focus of this paper is on the build the optimization of short fiber reinforced polymers (SFRP) AM components. Specifically, we consider optimization of the build direction, topology, and fiber orientation of SFRP components. All three factors have a significant impact on the functional performance of the printed part. While significant progress has been made on optimizing these independently, the objective of this paper is to consider all three factors simultaneously and explore their interdependency, within the context of thermal applications. Towards this end, the underlying design parameters are identified, appropriate sensitivity equations are derived, and a formal optimization problem is posed as an extension to the popular Solid Isotropic Material with Penalization (SIMP). Results from several numerical experiments are presented, highlighting the impact of build direction, topology, and fiber orientation on the performance of SFRP components.

Microstructural topology optimization (MTO) is the simultaneous optimization of macroscale topology and microscale structure. MTO holds the promise of enhancing product-performance beyond what is possible today. Furthermore, with the advent of additive manufacturing, the resulting multiscale structures can be fabricated with relative ease. There are however two significant challenges associated with MTO: (1) high computational cost, and (2) potential loss of microstructural connectivity. In this paper, a novel density-and-strain-based K-means clustering method is proposed to reduce the computational cost of MTO. Further, a rotational degree of freedom is introduced to fully utilize the anisotropic nature of microstructures. Finally, the connectivity issue is addressed through auxiliary finite element fields. The proposed concepts are illustrated through several numerical examples applied to two-dimensional single-load problems.