Topology optimization for additive manufacturing with self-supporting constraint

A review of topology optimization for additive manufacturing: Status and challenges

PurposeThe purpose of this paper is to communicate a method to perform simultaneous topology optimization of component and support structures considering typical metal additive manufacturing (AM) restrictions and post-print machining requirements.Design/methodology/approachAn integrated topology optimization is proposed using two density fields: one describing the design and another defining the support layout. Using a simplified AM process model, critical overhang angle restrictions are imposed on the design. Through additional load cases and constraints, sufficient stiffness against subtractive machining loads is enforced. In addition, a way to handle non-design regions in an AM setting is introduced.FindingsThe proposed approach is found to be effective in producing printable optimized geometries with adequate stiffness against machining loads. It is shown that post-machining requirements can affect optimal support structure layout.Research limitations/implicationsThis study uses a simplified AM process model based on geometrical characteristics. A challenge remains to integrate more detailed physical AM process models to have direct control of stress, distortion and overheating.Practical implicationsThe presented method can accelerate and enhance the design of high performance parts for AM. The consideration of post-print aspects is expected to reduce the need for design adjustments after optimization.Originality/valueThe developed method is the first to combine AM printability and machining loads in a single topology optimization process. The formulation is general and can be applied to a wide range of performance and manufacturability requirements.

The integration of topology optimization (TO) and additive manufacturing (AM) technologies can create significant synergy benefits, while the lack of AM-friendly TO algorithms is a serious bottleneck for the application of TO in AM. In this paper, a TO method is proposed to design self-supporting structures with an explicit continuous self-supporting constraint, which can be adaptively activated and tightened during the optimization procedure. The TO procedure is suitable for various critical overhang angles (COA), which is integrated with build direction assignment to reduce performance loss. Besides, a triangular directional self-supporting constraint sensitivity filter is devised to promote the downward evolution of structures and maintain stability. Two numerical examples are presented; all the test cases have successfully converged and the optimized solutions demonstrate good manufacturability. In the meanwhile, a fully self-supporting design can be obtained with a slight cost in performance through combination with build direction assignment.

Combining topology optimization and additive manufacturing (AM) is a promising approach to breaking through the limitations of conventional design and developing innovative structures with high performance. However, the unique manufacturing constraints in AM should be considered when developing the topology optimization algorithms for AM. Material anisotropy is one of the common characteristics of AM materials due to the layer-by-layer manufacturing techniques. This work proposes a topology optimization approach for AM with strength constraints considering anisotropy. The Hoffman failure criterion is adopted to represent the anisotropic strength behaviors of AM materials. Based on the Hoffman failure criteria and the p-norm measure aggregation function, a global strength constraint formulation is established. Under the framework of solid isotropic material with penalization, we develop a topology optimization methodology to minimize the structural weight or volume fraction subject to structural stiffness and strength constraints. Several two-dimensional (2D) or 3D numerical test cases are performed to validate the effectiveness and performance of the developed method. The results indicated that the proposed method could make full use of material properties by considering anisotropic strength. Besides, the topological optimization considering strength anisotropy could be combined with build direction optimization to further reduce the structural weight.

Topology optimization for additive manufacturing using a component of a humanoid robot

Topology optimization is widely recognized for its ability to determine the best distribution of material in a structure to optimize its stiffness. This process often leads to creative configurations that produce complicated geometries challenging to construct using traditional techniques. Additive manufacturing has recently received a lot of interest from academics as well as industry. When compared to traditional methods, additive manufacturing or 3D printing offers considerable benefits (direct manufacture, time savings, fabrication of complex geometries, etc.). Recently, additive manufacturing techniques are increasingly being employed in industry to create complex components that cannot be produced using standard methods. The primary benefit of these techniques is the amount of creative flexibility they give designers. Additive manufacturing technology with higher resolution output capabilities has created a wealth of options for bridging the topology optimization and product application gap. This paper is a preliminary attempt to determine the key aspects of research on the integration of topology optimization and additive manufacturing, to outline topology optimization methods for these aspects with a review of various scientific and industry applications during the last years.

This paper discusses the design of axisymmetric structures with self-supporting features that can be additively manufactured without requiring internal support structures. This is motivated by wire-fed additive manufacturing processes, many of which can fabricate designs with enclosed pores that inherently exist in many axisymmetric structures, such as double walled pressure vessels. Although enclosed pores are possible, features that rise at shallow angles from the build plate typically cannot be fabricated without the use of support structures, which require removal and thus are unfavorable in such applications. In this paper, an overhang constraint is applied to ensure that all designed features rise at a designer-prescribed self-supporting angle to eliminate the need for such support structures. This is achieved by coupling the projection-based overhang constraint approach with topology optimization and axisymmetric finite elements whose stiffness is interpolated using Solid Isotropic Material with Penalization (SIMP). Gradients are computed with the adjoint method and the Method of Moving Asymptotes (MMA) is employed as the gradient-based optimizer. Two numerical examples related to a canonical pressure vessel and an optical mirror support structure are used to demonstrate the approach. Solutions are shown to satisfy minimum feature size requirements and designer-prescribed (process dependent) overhang constraint angles, while providing clear and crisp representations of topology. As observed in past works on overhang constraints, a clear trade-off is illustrated between the magnitude of the overhang constraint angle and the structural performance (mass or stiffness), with more strict requirements producing designs with lower performance.

A several cycles of design-verification-modification are needed during traditional design, which is very time-consuming. Topology optimization is rapidly expanding in the recent years in the field of structural mechanics. Currently it is widely applied to structural design. The combination of topology optimization and sizing and/or shape optimization has been adopted for flight vehicle structural design, which results possible better designs. In the paper, continuum structural topology optimizations as well as size optimization are combined for a folding wing structural design. A structure optimization problem is established using Solid Isotropic Material with Penalization (SIMP) method, it consists of the thickness variable of the skin and the relative element density variables of the tip part of the folding wing. The design objective is to minimize the compliance of the whole structure, and the constraints are structural mass constraints and stress constraints. The problem was solved based on commercial software package HyperWorks™. The resulting design shows that a new tip structure which satisfies the requirements of stiffness and strength was reconstructed.

The main goal of the present research is to propose an integrated methodology to address the fatigue performance of topology optimized components, produced by additive manufacturing. The main steps of the component design will be presented, specially the methods and parameters applied to the topology optimization and the post-smoothing process. The SIMP method was applied in order to obtain a lighter component and a suitable stiffness for the desired application. In addition, since residual stresses are intrinsic to every metallic additive manufacturing process, the influence of those stresses will be also analyzed. The Laser Powder Bed Fusion was numerically simulated aiming at evaluating the residual stresses the workpiece during the manufacturing process and to investigate how they could influence the fatigue behavior of the optimized component. The effect of the built orientation of the workpiece on the residual stresses at some selected potential critical points are evaluated. The final design solution presented a stiffness/volume ratio nearly 6 times higher when compared to the initial geometry. By choosing the built orientation, it is possible impact favorably in the fatigue life of the component.

Additive Manufacturing allows for considerably more form freedom compared to existing manufacturing technologies but still faces the limitation of building overhanging parts. The overhang limitation in additive manufacturing prevents the direct production of topology optimized parts. We present an overhang constraint that incorporates this manufacturing limitation into topology optimization. The overhanging regions in a design iteration are detected using front propagation and a global constraint is formulated by aggregating the local constraints within the design domain. Since the constraint is formulated in a continuous manner, it can be discretized for any type of mesh, and with an arbitrary minimum allowable overhang angle. Furthermore, it is easily extensible to 3D. The Ordered Upwind Method is used to solve the constraint, and adjoint sensitivities are used for efficient evaluation. The newly developed constraint is demonstrated on 2D examples having an unstructured mesh. Overhang free designs are obtained with smooth convergence behaviour.

In this work, topology optimization is used to optimize the compliance or eigenvalues of prestressed plates. The prestress is accounted for by including the force equivalent to the prestressing and adding the initial stress stiffness matrix to the original stiffness matrix. The calculation of the sensitivities is complicated because of the initial stress stiffness matrix, but the computational cost can be kept low by using the adjoint method. The topology optimization problem is solved using the solid isotropic material with penalization (SIMP) method in combination with method of moving asymptotes (MMA). Numerical examples of minimizing compliance or maximizing the first eigenvalue of plates are given. One example is a micro electro mechanical systems (MEMS) application involving a backplate used in a microphone in a hearing aid. Copyright © 2001 John Wiley & Sons, Ltd.

In this work, topology optimization is used to optimize the compliance or eigenvalues of prestressed plates. The prestress is accounted for by including the force equivalent to the prestressing and adding the initial stress stiffness matrix to the original stiffness matrix. The calculation of the sensitivities is complicated because of the initial stress stiffness matrix, but the computational cost can be kept low by using the adjoint method. The topology optimization problem is solved using the solid isotropic material with penalization (SIMP) method in combination with method of moving asymptotes (MMA). Numerical examples of minimizing compliance or maximizing the first eigenvalue of plates are given. One example is a micro electro mechanical systems (MEMS) application involving a backplate used in a microphone in a hearing aid. Copyright © 2001 John Wiley & Sons, Ltd.

Topological optimization is an innovative method to realize the lightweight design. This paper proposes a hybrid topology optimization method that combines the SIMP (solid isotropic material with penalization) method and genetic algorithm (GA), called the SIMP-GA method. In the method, SIMP is used to update the chromosomes, which can accelerate convergence. The filtering scheme in the SIMP method can filter unconnected elements to ensure the connectivity of the structure. We studied the influence of varying the filtering radius on the optimized structure. Simultaneously, in the SIMP-GA method, each element is regarded as a gene, which controls the population number to a certain extent, reduces the amount of calculation, and improves the calculation efficiency. The calculation of some typical examples proves that the SIMP-GA method can obtain a better solution than the gradient-based method. Compared with the conventional genetic algorithm and GA-BESO (Bi-directional Evolutionary Structural Optimization) method, the calculation efficiency of the proposed method is higher and similar results are obtained. The innovative topology optimization method could be an effective way for structural lightweight design.

Research on multi-stage topology optimization method based on latent diffusion model

• A modified Tsai-Hill stress interpolation model for lattices is proposed. • Multiscale lattice structure topology optimization under stress constraints for static and dynamic loads is addressed. • Full-scale analysis and experimental validation of the optimized structures are conducted. This study presents a topology optimization method for heterogeneous lattice structures subject to stress constraints. The proposed approach extends the ordered SIMP (Solid Isotropic Material with Penalization) framework to incorporate a composite material failure criterion. Specifically, a modified Tsai–Hill yield criterion is employed to characterize the anisotropic yielding behavior of the heterogeneous lattice, which is subsequently integrated into the optimization as a stress constraint. To address the variation in yield strength across different lattice configurations, a normalization strategy is applied to the stress field. Additionally, a P-norm aggregation scheme is introduced to efficiently handle local stress constraints while reducing computational cost. The equivalent elastic tensor and yield strength of each lattice configuration are obtained using a representative volume element (RVE) based on homogenization theory. The effectiveness of the proposed method is demonstrated through a series of 2D cases, achieving lightweight structural designs that satisfy stress constraints. Finally, full-scale mechanical analysis and 3D printing experimental validation further confirm the strength reinforcement of the optimized results.