Parametric Topology Optimization Toward Rational Design and Efficient Prefabrication for Additive Manufacturing

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Long Jiang ◽  
Hang Ye ◽  
Chi Zhou ◽  
Shikui Chen
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Level Set ◽  
Rational Design ◽  
Computational Cost ◽  
Significant Advance ◽  
Free Form ◽  
Geometric Complexity ◽  
Original Design ◽  
Design And Manufacturing

The significant advance in the boosted fabrication speed and printing resolution of additive manufacturing (AM) technology has considerably increased the capability of achieving product designs with high geometric complexity and provided tremendous potential for mass customization. However, it is also because of geometric complexity and large quantity of mass-customized products that the prefabrication (layer slicing, path planning, and support generation) is becoming the bottleneck of the AM process due to the ever-increasing computational cost. In this paper, the authors devise an integrated computational framework by synthesizing the parametric level set-based topology optimization method with the stereolithography (SLA)-based AM process for intelligent design and manufacturing of multiscale structures. The topology of the design is optimized with a distance-regularized parametric level set method considering the prefabrication computation. With the proposed framework, the structural topology optimization not only can create single material structure designs but also can generate multiscale, multimaterial structures, offering the flexibility and robustness of the structural design that the conventional methods could not provide. The output of the framework is a set of mask images that can be directly used in the AM process. The proposed approach seamlessly integrates the rational design and manufacturing to reduce the numerical complexity of the computationally expensive prefabrication process. More specifically, the prefabrication-friendly design and optimization procedure are devised to drastically eliminate the redundant computations in the traditional framework. Two test examples, including a free-form 3D cantilever beam and a multiscale meta-structure, are utilized to demonstrate the performance of the proposed approach. Both the simulation and experimental results verified that the new rational design could significantly reduce the prefabrication computation cost without affecting the original design intent or sacrificing the original functionality.

Parametric Topology Optimization Toward Rational Design and Efficient Prefabrication for Additive Manufacturing

2017 ◽  
Author(s):  
Long Jiang ◽  
Hang Ye ◽  
Chi Zhou ◽  
Shikui Chen ◽  
Wenyao Xu
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Level Set ◽  
Manufacturing Process ◽  
Rational Design ◽  
Optimization Method ◽  
Significant Advance ◽  
Original Design ◽  
Computational Framework ◽  
Multi Scale

The significant advance in the boosted fabrication speed and printing resolution of additive technology has considerably increased the capability of achieving product designs with high geometric complexity. The prefabrication computation has been increasingly important and is coming to be the bottleneck in the additive manufacturing process. In this paper, the authors devise an integrated computational framework by synthesizing the parametric level set-based topology optimization method with the DLP-based SLA process for intelligent design and additive manufacturing of not only single material structures but also multi-scale, multi-functional structures. The topology of the design is optimized with a new distance-regularized parametric level set method considering the prefabrication computation. offering the flexibility and robustness of the structural design that the conventional methods could not provide. The output of the framework is a set of mask images which can be directly used in the additive manufacturing process. The proposed approach seamlessly integrates the rational design and manufacturing to reduce the complexity of the computationally-expensive prefabrication process. Two test examples, including a freeform 3D cantilever beam and a multi-scale meta-structure, are utilized to demonstrate the performance of the proposed approach. Both the simulation and experimental results verified that the new rational design could significantly reduce the prefabrication computation cost without affecting the original design intent or sacrificing original functionality.

Computational Design and Additive Manufacturing of Conformal Metasurfaces by Combining Topology Optimization With Riemann Mapping Theorem

2017 ◽  
Author(s):  
Panagiotis Vogiatzis ◽  
Ming Ma ◽  
Shikui Chen ◽  
Xianfeng David Gu
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Conformal Mapping ◽  
Level Set ◽  
Computational Design ◽  
Unit Cell ◽  
Free Form ◽  
Computational Framework ◽  
Riemann Mapping Theorem ◽  
Free Form Surfaces

In this paper, we present a computational framework for computational design and additive manufacturing of spatial free-form periodic metasurfaces. The proposed scheme rests on the level-set based topology approach and the conformal mapping theory. A 2D unit cell of metamaterial with tailored effective properties is created using the level-set based topology optimization method. The achieved unit cell is further mapped to the 3D quad meshes on a free-form surface by applying the conformal mapping method which can preserve the local shape and angle when mapping the 2D design to a 3D surface. The proposed level-set based optimization methods not only can act as a motivator for design synthesis, but also can be seamlessly hooked with additive manufacturing with no need of CAD reconstructions. The proposed computational framework provides a solution to increasing applications involving innovative metamaterial designs on free-form surfaces in different fields of interest. The performance of the proposed scheme is illustrated through a benchmark example where a negative-Poisson’s-ratio unit cell pattern is mapped to a 3D human face and fabricated through additive manufacturing.

scholarly journals Optimal and continuous multilattice embedding

2021 ◽  
Vol 7 (16) ◽  
pp. eabf4838
Author(s):  
E. D. Sanders ◽  
A. Pereira ◽  
G. H. Paulino
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Hierarchical Structures ◽  
Free Form ◽  
Structural Hierarchy ◽  
Design And Manufacturing ◽  
Surface Representations ◽  
Material Space ◽  
Spatially Varying ◽  
Biomimetic Structures

Because of increased geometric freedom at a widening range of length scales and access to a growing material space, additive manufacturing has spurred renewed interest in topology optimization of parts with spatially varying material properties and structural hierarchy. Simultaneously, a surge of micro/nanoarchitected materials have been demonstrated. Nevertheless, multiscale design and micro/nanoscale additive manufacturing have yet to be sufficiently integrated to achieve free-form, multiscale, biomimetic structures. We unify design and manufacturing of spatially varying, hierarchical structures through a multimicrostructure topology optimization formulation with continuous multimicrostructure embedding. The approach leads to an optimized layout of multiple microstructural materials within an optimized macrostructure geometry, manufactured with continuously graded interfaces. To make the process modular and controllable and to avoid prohibitively expensive surface representations, we embed the microstructures directly into the 3D printer slices. The ideas provide a critical, interdisciplinary link at the convergence of material and structure in optimal design and manufacturing.

Utilizing Design for Metal Additive Manufacturing and Topology Optimization to Improve Product Designs

2019 ◽  
Author(s):  
Martin L. Tanaka ◽  
Jeremy J. Smith
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Yield Strength ◽  
Maximum Stress ◽  
Optimized Design ◽  
Original Design ◽  
Optimization Software ◽  
Metal Additive Manufacturing ◽  
Fea Model ◽  
Metal Additive

Abstract Metal additive manufacturing has transformed the product design process by enabling the fabrication of components with complex geometries that cannot be manufactured using conventional methods. Initial designs can be further enhanced by employing topology optimization software and Design for Metal Additive Manufacturing (DFMAM) guidelines. In this study, a commercially available bicycle spider-crank was optimized for three-dimensional (3D) metal manufacturing. The 3D surface geometry of the original spider-crank was acquired using a white light scanner and used to generate a 3D solid model of the part. Boundary conditions were obtained from cycling loads found in published literature and applied to an ANSYS Finite Element Analysis (FEA) model. The FEA model was analyzed to determine the von Mises stress throughout the part. ANSYS Topology Optimization software was applied to the model. The software uses an iterative process to remove low stress material and recalculate stress within the part until no more material can be removed without exceeding a target maximum stress value. Following topology optimization, DFMAM principles were applied to enable the part to be 3D printed. Results from the FEA showed the DFMAM optimized design to be 41.5% lighter than the original design. The maximum stress increased from 41.2% of the material yield strength to 61.5% in the DFMAM optimized design, which exceeded the target optimization value of 50% yield strength. Analysis results were verified experimentally. The original design and DFMAM optimized design were printed using an EOS M 290 metal additive manufacturing machine. Parts were separated from the support structure and tested on a universal testing machine. A custom testing apparatus was designed and built to conduct the testing. Testing was performed at 15 degrees intervals throughout the range of motion. Strain gages attached to the arm of the crank were used to obtain stress values at specific locations and dial indicators were used to measure the deflection of the crank arm under load. Experimental results closely matched results obtained from the FEA, validating the model. With the model validated at specific locations, it was assumed that the stress calculated by the FEA at the critical points were also accurate. The results showed the topology optimization software to be an effective and useful tool for optimizing the design of 3D metal printed parts. However, topology optimization alone was not enough to finalize a design prior to printing. The application of DFMAM principles were needed to ensure that the overhanging structures would not collapse during printing. Because the determination of what constitutes an overhang is determined by the part orientation when printed, some modification will generally be required prior to printing. In conclusion, using a bicycle spider-crank as an example, this research has shown that the use of topology optimization software and Design for Metal Additive Manufacturing principles is able to reduce the weight of a 3D metal printed part while simultaneously achieving a maximum stress near a target value.

scholarly journals An Open Source Framework for Integrated Additive Manufacturing and Level-Set-Based Topology Optimization

2017 ◽  
Vol 17 (4) ◽  
Author(s):  
Panagiotis Vogiatzis ◽  
Shikui Chen ◽  
Chi Zhou
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
3D Printing ◽  
Open Source ◽  
Level Set ◽  
Optimization Procedure ◽  
Computational Design ◽  
Standard Format ◽  
Practical Algorithms ◽  
Open Source Framework

Topology optimization has been considered as a promising tool for conceptual design due to its capability of generating innovative design candidates without depending on the designer's intuition and experience. Various optimization methods have been developed through the years, and one of the promising options is the level-set-based topology optimization method. The benefit of this alternative method is that the design is characterized by its clear boundaries. This advantage can avoid postprocessing work in conventional topology optimization process to a large extent and realize direct integration between topology optimization and additive manufacturing (AM). In this paper, practical algorithms and a matlab-based open source framework are developed to seamlessly integrate the level-set-based topology optimization procedure with AM process by converting the design to STereoLithography (STL) files, which is the de facto standard format for three-dimensional (3D) printing. The proposed algorithm and code are evaluated by a proof-of-concept demonstration with 3D printing of both single and multimaterial topology optimization results. The algorithm and the open source framework proposed in this paper will be beneficial to the areas of computational design and AM.

scholarly journals Topology optimization subject to additive manufacturing constraints

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Moritz Ebeling-Rump ◽  
Dietmar Hömberg ◽  
Robert Lasarzik ◽  
Thomas Petzold
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Computational Cost ◽  
Ginzburg Landau ◽  
First Order ◽  
Manufacturing Constraint ◽  
External Forces ◽  
The Cost ◽  
Low Computational Cost ◽  
The Ideal

AbstractIn topology optimization the goal is to find the ideal material distribution in a domain subject to external forces. The structure is optimal if it has the highest possible stiffness. A volume constraint ensures filigree structures, which are regulated via a Ginzburg–Landau term. During 3D printing overhangs lead to instabilities. As a remedy an additive manufacturing constraint is added to the cost functional. First order optimality conditions are derived using a formal Lagrangian approach. With an Allen-Cahn interface propagation the optimization problem is solved iteratively. At a low computational cost the additive manufacturing constraint brings about support structures, which can be fine tuned according to demands and increase stability during the printing process.

Conformal Topology Optimization of Heat Conduction Problems on Manifolds Using an Extended Level Set Method (X-LSM)

2021 ◽  
Author(s):  
Xiaoqiang Xu ◽  
Shikui Chen ◽  
Xianfeng David Gu ◽  
Michael Yu Wang
Keyword(s):  
Topology Optimization ◽  
Heat Conduction ◽  
Level Set ◽  
Rectangular Domain ◽  
Free Form ◽  
Topology Optimization Problem ◽  
Parameter Domain ◽  
Covariant Derivatives ◽  
3D Topology ◽  
Free Form Surfaces

Abstract In this paper, the authors propose a new dimension reduction method for level-set-based topology optimization of conforming thermal structures on free-form surfaces. Both the Hamilton-Jacobi equation and the Laplace equation, which are the two governing PDEs for boundary evolution and thermal conduction, are transformed from the 3D manifold to the 2D rectangular domain using conformal parameterization. The new method can significantly simplify the computation of topology optimization on a manifold without loss of accuracy. This is achieved due to the fact that the covariant derivatives on the manifold can be represented by the Euclidean gradient operators multiplied by a scalar with the conformal mapping. The original governing equations defined on the 3D manifold can now be properly modified and solved on a 2D domain. The objective function, constraint, and velocity field are also equivalently computed with the FEA on the 2D parameter domain with the properly modified form. In this sense, we are solving a 3D topology optimization problem equivalently on the 2D parameter domain. This reduction in dimension can greatly reduce the computing cost and complexity of the algorithm. The proposed concept is proved through two examples of heat conduction on manifolds.

Topology Optimization of Conformal Structures Using Extended Level Set Methods and Conformal Geometry Theory

2018 ◽  
Author(s):  
Qian Ye ◽  
Yang Guo ◽  
Shikui Chen ◽  
Xianfeng David Gu ◽  
Na Lei
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Differential Operators ◽  
Conformal Geometry ◽  
Level Set Methods ◽  
Free Form ◽  
Computational Framework ◽  
Covariant Derivatives ◽  
Free Form Surface ◽  
Free Form Surfaces

In this paper, we propose a new method to approach the problem of structural shape and topology optimization on manifold (or free-form surfaces). A manifold is conformally mapped onto a 2D rectangle domain, where the level set functions are defined. With conformal mapping, the corresponding covariant derivatives on a manifold can be represented by the Euclidean differential operators multiplied by a scalar. Therefore, the topology optimization problem on a free-form surface can be formulated as a 2D problem in the Euclidean space. To evolve the boundaries on a free-form surface, we propose a modified Hamilton-Jacobi equation and solve it on a 2D plane following the conformal geometry theory. In this way, we can fully utilize the conventional level-set-based computational framework. Compared with other established approaches which need to project the Euclidean differential operators to the manifold, the computational difficulty of our method is highly reduced while all the advantages of conventional level set methods are well preserved. We hope the proposed computational framework can provide a timely solution to increasing applications involving innovative structural designs on free-form surfaces in different engineering fields.

scholarly journals Design of stiffened panels for stress and buckling via topology optimization

2021 ◽  
Author(s):  
Sheng Chu ◽  
Carol Featherston ◽  
H. Alicia Kim
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Free Form ◽  
Analytical Sensitivity ◽  
Element Mesh ◽  
Stiffened Panels ◽  
Set Functions ◽  
Plate Elements ◽  
Analytical Sensitivity Analysis ◽  
Level Set Functions

AbstractThis paper investigates the weight minimization of stiffened panels simultaneously optimizing sizing, layout, and topology under stress and buckling constraints. An effective topology optimization parameterization is presented using multiple level-set functions. Plate elements are employed to model the stiffened panels. The stiffeners are parametrized by implicit level-set functions. The internal topologies of the stiffeners are optimized as well as their layout. A free-form mesh deformation approach is improved to adjust the finite element mesh. Sizing optimization is also included. The thicknesses of the skin and stiffeners are optimized. Bending, shear, and membrane stresses are evaluated at the bottom, middle, and top surfaces of the elements. A p-norm function is used to aggregate these stresses in a single constraint. To solve the optimization problem, a semi-analytical sensitivity analysis is performed, and the optimization algorithm is outlined. Numerical investigations demonstrate and validate the proposed method.

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