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This paper proposes a topology optimization formulation for additive manufacturing, in which the part, supports and their machining directions are simultaneously optimized. The part and supports are represented by two groups of density fields. The support structures are optimized for heat dissipation efficiency by solving a pseudo heat conduction problem under heat flux boundary loading and constraining the maximum temperature. The temperature constraint allows us to obtain self-supporting overhangs or non-self-supporting overhangs with support structures underneath. During the optimization, the support structures are further filtered by the solution fields from the advection-diffusion equations to ensure their accessibility to the machining tools. Based on the developed formulation, the optimized support structures would be distributed in the machinable regions of the part to enhance heat transfer in the manufacturing process. The unmachinable regions of the part, including enclosed voids, are self-supported for additive manufacturing. The sensitivity of the manufacturing constraint with respect to the design variables of the part, supports and the machining directions is derived through the adjoint method. We validate the effectiveness of the proposed formulation through several examples in 2D and 3D cases. [ABSTRACT FROM AUTHOR]

This paper introduces a density penalty-based topology optimization method for designing shell–infill structures. During the optimization, the shell is identified by simultaneously penalizing density variables of both the solid and the void phases. Two-phase density filtering and Boolean operations are further applied to model the shell–infill structure. In the optimization of shell–infill structures, the shell thickness is controlled through density filtering and the density penalty. For explicit control of the shell thickness, its analytical relationship with the filter radius and the penalty parameter is derived. Both 2D and 3D numerical examples are investigated to showcase the effectiveness of the shell–infill optimization approach. The effects of mass constraints, filter radius, penalty parameter, mesh resolution, and material properties are thoroughly studied. The results demonstrate that the density penalty-based method can efficiently identify interfaces for different settings in shell–infill optimization. The presented formulations can be directly integrated into the optimization process, offering a new perspective for the design of shell–infill structures. [ABSTRACT FROM AUTHOR]

The alternating active-phase algorithm (AAPA) is widely recognized as being efficient for multi-material topology optimization. It has the advantages of easy implementation and broad applicability, but faces shortcomings, such as a uniform punishment intensity for all elements, excessive gray elements, and slow optimization convergence. To overcome these shortcomings, proposed here is an enhanced AAPA (EAAPA), the core ideas of which are as follows. (1) A new equal-scale Heaviside projection function (EHPF) is proposed, with the scale factor introduced to adjust the physical density adaptively to overcome the challenges of the invariance of the density sum and the uniqueness of projecting faced by the traditional Heaviside projection function. This adaptation reduces the number of gray elements and accelerates the convergence. (2) An innovative solid isotropic material with exponential sigmoid function (SIMESF) is constructed, with a penalty threshold and a steepness factor introduced to divide different penalty intensity regions and control their transition steepness. This improves the applicability and flexibility of the interpolation model, addressing the issue of a single punishment intensity in the solid isotropic material with penalization. The parameter values of the SIMESF model are explored via the design of a bridge, and the performances of AAPA and EAAPA are evaluated via the designs of simply supported and cantilever beams. The results show clearly that EAAPA has significant advantages in terms of optimization effectiveness and convergence speed. [ABSTRACT FROM AUTHOR]

The paper presents a formulation for simultaneous optimization of part and support in additive manufacturing. A pseudo heat conduction problem is solved to simulate heat transfer between the part and support. In the pseudo problem, a surface slope-dependent heat flux is applied on the part/support interfaces. The input heat is then transferred through the part and support to the build plate, which is treated as the heat sink. Since the density-based topology optimization does not involve explicit surface representation, the heat flux is implicitly imposed through a domain integration of a Heaviside projected density gradient. The proposed formulation has the inherent ability to control surface slope, which allows us to obtain self-supported enclosed voids and put removable external supports only on the open surfaces. Self-supporting supports can also be obtained by controlling the anisotropic thermal conductivity of the supports. Three different objective functions related to heat dissipation efficiency of the support are investigated. Both 2D and 3D numerical examples are presented to demonstrate the validity and efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

One way to solve topology optimization of continuum structures under design-dependent pressure loads is to recover the loading surface at each step of the minimization process. During the topology evolution, the intermediate topologies obtained by using the SIMP (Solid Isotropic Material with Penalization) method actually can be regarded as gray scale images, for which the paper proposes a new material boundary identification scheme based on image segmentation technique. The Distance Regularized Level Set Evolution (DRLSE) method proposed by Li et al., IEEE Trans Image Process 19(12):3243-3254 (2010) is utilized to detect the image edge. Then the pressure boundary is represented as the zero level contour of a level set function (LSF). Inheriting the merits of the level set method, the current scheme can handle the topological change of the pressure boundary efficiently and be easily extended to the three-dimensional problems. In addition, the scheme is more stable compared with the conventional loading surface searching methods since it works well for the intermediate topologies with local scattered densities. A new optimization framework is also proposed to avoid the load sensitivity analysis. Four numerical examples are presented to show the validity and advantages of the proposed scheme. [ABSTRACT FROM AUTHOR]