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.

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 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.

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.

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.

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.

scholarly journals Design Right Once for Additive Manufacturing

2018 ◽  
Vol 188 ◽  
pp. 03020
Author(s):  
Antonios Tsakiris ◽  
Christos Salpistis ◽  
Athanassios Mihailidis
Keyword(s):  
Additive Manufacturing ◽  
Weight Reduction ◽  
Variable Density ◽  
Free Form ◽  
Structure Generation ◽  
Innovative Design ◽  
Key Factor ◽  
Traditional Manufacturing ◽  
Manufacturing Technologies ◽  
Free Form Surfaces

Additive Manufacturing (AM) has been widely considered a key factor for innovative design. However, the utilization of AM has not been as high as expected, although the technology offers key innovative design capabilities, weight reduction, parts count and assembly consolidation as well as material saving. This low utilization is attributed to the lack of AM understanding, mature CAE/CAM software tools addressing AM specific issues such as design support structure generation and removal, residual stresses, surface quality. In most cases, Design for AM (DfAM) is a crucial requisite for a “Design Right Once” approach. Such an approach is shown in the current study using three parts as example: an arthropod’s leg, a gearshift drum and an electric motor mounting frame. The implementation of geometrical conformal lattice structures and lattices with variable density are discussed. A structured design approach is presented and design dilemmas are solved in terms of a DfAM approach. Primary design optimizations are evaluated. Weight reduction is considered throughout the design and free form surfaces are being used. “Freedom to Design” principle is also portrayed and assembly parts consolidation occurs as a natural process of DfAM in comparison with previous design practices. It is concluded that, even from the primary design phase the design engineer can reveal his creativity because of the absence of constraints set by the traditional manufacturing technologies.

Lattice Structure Design for Additive Manufacturing: Unit Cell Topology Optimization

2019 ◽  
Author(s):  
Bradley Hanks ◽  
Mary Frecker
Keyword(s):  
Topology Optimization ◽  
Additive Manufacturing ◽  
Lattice Structure ◽  
Optimization Method ◽  
Structure Design ◽  
Unit Cell ◽  
Lattice Structures ◽  
Design For Additive Manufacturing ◽  
Structure Topology

Abstract Additive manufacturing is a developing technology that enhances design freedom at multiple length scales, from the macroscale, or bulk geometry, to the mesoscale, such as lattice structures, and even down to tailored microstructure. At the mesoscale, lattice structures are often used to replace solid sections of material and are typically patterned after generic topologies. The mechanical properties and performance of generic unit cell topologies are being explored by many researchers but there is a lack of development of custom lattice structures, optimized for their application, with considerations for design for additive manufacturing. This work proposes a ground structure topology optimization method for systematic unit cell optimization. Two case studies are presented to demonstrate the approach. Case Study 1 results in a range of unit cell designs that transition from maximum thermal conductivity to minimization of compliance. Case Study 2 shows the opportunity for constitutive matching of the bulk lattice properties to a target constitutive matrix. Future work will include validation of unit cell modeling, testing of optimized solutions, and further development of the approach through expansion to 3D and refinement of objective, penalty, and constraint functions.

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.

Generative Design of Multi-Material Hierarchical Structures via Concurrent Topology Optimization and Conformal Geometry Method

2019 ◽  
Author(s):  
Long Jiang ◽  
Shikui Chen ◽  
Xianfeng David Gu
Keyword(s):  
Topology Optimization ◽  
Conformal Mapping ◽  
Level Set ◽  
Basis Function ◽  
Material Properties ◽  
Structural Topology Optimization ◽  
Structural Topology ◽  
Signed Distance ◽  
Level Set Function ◽  
Set Function

Abstract Topology optimization has been proved to be an automatic, efficient and powerful tool for structural designs. In recent years, the focus of structural topology optimization has evolved from mono-scale, single material structural designs to hierarchical multimaterial structural designs. In this research, the multi-material structural design is carried out in a concurrent parametric level set framework so that the structural topologies in the macroscale and the corresponding material properties in mesoscale can be optimized simultaneously. The constructed cardinal basis function (CBF) is utilized to parameterize the level set function. With CBF, the upper and lower bounds of the design variables can be identified explicitly, compared with the trial and error approach when the radial basis function (RBF) is used. In the macroscale, the ‘color’ level set is employed to model the multiple material phases, where different materials are represented using combined level set functions like mixing colors from primary colors. At the end of this optimization, the optimal material properties for different constructing materials will be identified. By using those optimal values as targets, a second structural topology optimization is carried out to determine the exact mesoscale metamaterial structural layout. In both the macroscale and the mesoscale structural topology optimization, an energy functional is utilized to regularize the level set function to be a distance-regularized level set function, where the level set function is maintained as a signed distance function along the design boundary and kept flat elsewhere. The signed distance slopes can ensure a steady and accurate material property interpolation from the level set model to the physical model. The flat surfaces can make it easier for the level set function to penetrate its zero level to create new holes. After obtaining both the macroscale structural layouts and the mesoscale metamaterial layouts, the hierarchical multimaterial structure is finalized via a local-shape-preserving conformal mapping to preserve the designed material properties. Unlike the conventional conformal mapping using the Ricci flow method where only four control points are utilized, in this research, a multi-control-point conformal mapping is utilized to be more flexible and adaptive in handling complex geometries. The conformally mapped multi-material hierarchical structure models can be directly used for additive manufacturing, concluding the entire process of designing, mapping, and manufacturing.

Sign in / Sign up

Export Citation Format

Share Document