Origami Design by Topology Optimization

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Kazuko Fuchi ◽  
Alejandro R. Diaz
Keyword(s):  
Topology Optimization ◽  
Design Method ◽  
Optimization Method ◽  
Optimal Combination ◽  
Ground Structure ◽  
Line Segments ◽  
Folding Pattern ◽  
Design Variables ◽  
3D Geometry ◽  
Dimensional Domain

An origami design method based on topology optimization is introduced. The design of a folding pattern is cast as a problem of assigning presence and type of fold to lines in a “ground structure,” using folding angles as design variables. A ground structure for origami design has lines drawn on a two dimensional domain, showing all line segments that may appear as crease lines in the folded geometry. For a given ground structure and folding angles, the 3D geometry of the folded sheet can be computed using the mathematics of origami. A topology optimization method is then used to find an optimal combination of folding angles, which results in a folding pattern with desired, target geometric properties.

scholarly journals Microstructural Topology Optimization of Constrained Layer Damping on Plates for Maximum Modal Loss Factor of Macrostructures

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zhanpeng Fang ◽  
Lei Yao ◽  
Shuxia Tian ◽  
Junjian Hou
Keyword(s):  
Topology Optimization ◽  
Loss Factor ◽  
Strain Energy ◽  
Design Method ◽  
Optimization Method ◽  
Constrained Layer Damping ◽  
Viscoelastic Materials ◽  
Modal Strain Energy ◽  
Design Variables ◽  
Microstructural Topology Optimization

This paper presents microstructural topology optimization of viscoelastic materials for the plates with constrained layer damping (CLD) treatments. The design objective is to maximize modal loss factor of macrostructures, which is obtained by using the Modal Strain Energy (MSE) method. The microstructure of the viscoelastic damping layer is composed of 3D periodic unit cells. The effective elastic properties of the unit cell are obtained through the strain energy-based method. The density-based topology optimization is adopted to find optimal microstructures of viscoelastic materials. The design sensitivities of modal loss factor with respect to the design variables are analyzed and the design variables are updated by Method of Moving Asymptotes (MMA). Numerical examples are given to demonstrate the validity of the proposed optimization method. The effectiveness of the optimal design method is illustrated by comparing a solid and an optimized cellular viscoelastic material as applied to the plates with CLD treatments.

A preliminary design method for axisymmetric turbomachinery disks based on topology optimization

2021 ◽  
pp. 095440622110395
Author(s):  
Bo Wang ◽  
Guangming Wang ◽  
Kuo Tian ◽  
Yunfeng Shi ◽  
Caihua Zhou ◽  
...  
Keyword(s):  
Topology Optimization ◽  
Optimization Problem ◽  
Design Method ◽  
Optimization Method ◽  
Preliminary Design ◽  
Optimal Result ◽  
Density Distribution Function ◽  
Design Variables ◽  
Turbine Disks ◽  
Controlling Element

The topology optimization can be used to obtain preliminary turbomachinery disk designs which meet strength requirement. In order to eliminate enclosed holes which challenge manufacturing processes and to ensure distinct solid-void interface in the optimal result obtained by the topology optimization, a density distribution function is introduced for each element column in the design domain. Then, a parameter in each function is used to determine the disk’s thickness at corresponding radial position by controlling element densities. Once thicknesses at all radial positions are optimized, the shape of disk is thus determined. In this way, the optimization problem can be simplified by using these parameters as design variables. Illustrative examples are carried out to demonstrate the effectiveness of the proposed method in designing both compressor disks and turbine disks in comparison to the software T-Axis Disk and shape optimization method.

scholarly journals Topology Optimization of Hard-Coating Thin Plate for Maximizing Modal Loss Factors

Coatings ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 774
Author(s):  
Haitao Luo ◽  
Rong Chen ◽  
Siwei Guo ◽  
Jia Fu
Keyword(s):  
Topology Optimization ◽  
Objective Function ◽  
Composite Plates ◽  
Optimization Method ◽  
Hard Coating ◽  
Design Variables ◽  
Coating Composite ◽  
Damping Materials ◽  
Topology Optimization Method ◽  
Loss Factors

At present, hard coating structures are widely studied as a new passive damping method. Generally, the hard coating material is completely covered on the surface of the thin-walled structure, but the local coverage cannot only achieve better vibration reduction effect, but also save the material and processing costs. In this paper, a topology optimization method for hard coated composite plates is proposed to maximize the modal loss factors. The finite element dynamic model of hard coating composite plate is established. The topology optimization model is established with the energy ratio of hard coating layer to base layer as the objective function and the amount of damping material as the constraint condition. The sensitivity expression of the objective function to the design variables is derived, and the iteration of the design variables is realized by the Method of Moving Asymptote (MMA). Several numerical examples are provided to demonstrate that this method can obtain the optimal layout of damping materials for hard coating composite plates. The results show that the damping materials are mainly distributed in the area where the stored modal strain energy is large, which is consistent with the traditional design method. Finally, based on the numerical results, the experimental study of local hard coating composites plate is carried out. The results show that the topology optimization method can significantly reduce the frequency response amplitude while reducing the amount of damping materials, which shows the feasibility and effectiveness of the method.

Structural topology optimization of bridge girders in cable supported bridges

2018 ◽  
Author(s):  
Mads Baandrup ◽  
Ole Sigmund ◽  
Niels Aage
Keyword(s):  
Topology Optimization ◽  
Large Scale ◽  
Design Method ◽  
Optimization Method ◽  
Bridge Girders ◽  
Structural Topology ◽  
Box Girders ◽  
Box Girder ◽  
Fine Mesh ◽  
Further Development

<p>This work applies a ultra large scale topology optimization method to study the optimal structure of bridge girders in cable supported bridges.</p><p>The current classic orthotropic box girder designs are limited in further development and optimiza­ tion, and suffer from substantial fatigue issues. A great disadvantage of the orthotropic girder is the loads being carried one direction at a time, thus creating stress hot spots and fatigue problems. Hence, a new design concept has the potential to solve many of the limitations in the current state­ of-the-art.</p><p>We present a design method based on ultra large scale topology optimization. The highly detailed structures and fine mesh-discretization permitted by ultra large scale topology optimization reveal new design features and previously unseen eff ects. The results demonstrate the potential of gener­ ating completely different design solutions for bridge girders in cable supported bridges, which dif­ fer significantly from the classic orthotropic box girders.</p><p>The overall goal of the presented work is to identify new and innovative, but at the same time con­ structible and economically reasonable, solutions tobe implemented into the design of future cable supported bridges.</p>

Topology Optimization Algorithm for Plates and Shells Subjected to Plastic Deformations

1998 ◽  
Author(s):  
Kohei Yuge ◽  
Nobuhiro Iwai ◽  
Noboru Kikuchi
Keyword(s):  
Topology Optimization ◽  
Optimization Method ◽  
Homogenization Method ◽  
Finite Deformations ◽  
Thin Shells ◽  
Plastic Deformations ◽  
Material Tensor ◽  
Design Variables ◽  
Interpolation Technique ◽  
Plates And Shells

Abstract A topology optimization method for plates and shells subjected to plastic deformations is presented. The algorithms is based on the generalized layout optimization method invented by Bendsϕe and Kikuchi (1988), where an admissible design domain is assumed to be composed of microstructures with periodic cavities. The sizes of the cavities and the rotational angles of the microstructures are design variables which are optimized so as to minimize the applied work. The macroscopic material tensor for the porous material is numerically calculated by the homogenization method for the sensitivity analysis. In this paper, the method is applied to two-dimensional elasto-plastic problems. A database of the material tensor and its interpolation technique are presented. The algorithm is expanded into thin shells subjected to finite deformations. Several numerical examples are shown to demonstrate the effectiveness of these algorithms.

scholarly journals Multiscale, thermomechanical topology optimization of self-supporting cellular structures for porous injection molds

2019 ◽  
Vol 25 (9) ◽  
pp. 1482-1492
Author(s):  
Tong Wu ◽  
Andres Tovar
Keyword(s):  
Topology Optimization ◽  
Mechanical Performance ◽  
Mechanical Load ◽  
Design Method ◽  
Three Dimensional ◽  
Optimization Method ◽  
Cellular Structures ◽  
Injection Mold ◽  
Computationally Efficient ◽  
Content Type

Purpose This paper aims to establish a multiscale topology optimization method for the optimal design of non-periodic, self-supporting cellular structures subjected to thermo-mechanical loads. The result is a hierarchically complex design that is thermally efficient, mechanically stable and suitable for additive manufacturing (AM). Design/methodology/approach The proposed method seeks to maximize thermo-mechanical performance at the macroscale in a conceptual design while obtaining maximum shear modulus for each unit cell at the mesoscale. Then, the macroscale performance is re-estimated, and the mesoscale design is updated until the macroscale performance is satisfied. Findings A two-dimensional Messerschmitt Bolkow Bolhm (MBB) beam withstanding thermo-mechanical load is presented to illustrate the proposed design method. Furthermore, the method is implemented to optimize a three-dimensional injection mold, which is successfully prototyped using 420 stainless steel infiltrated with bronze. Originality/value By developing a computationally efficient and manufacturing friendly inverse homogenization approach, the novel multiscale design could generate porous molds which can save up to 30 per cent material compared to their solid counterpart without decreasing thermo-mechanical performance. Practical implications This study is a useful tool for the designer in molding industries to reduce the cost of the injection mold and take full advantage of AM.

Aerodynamic Automobile Shape Optimization by Incorporating Reverse Shape Design Method With CFD Analysis

2017 ◽  
Author(s):  
Kisun Song ◽  
Kyung Hak Choo ◽  
Jung-Hyun Kim ◽  
Dimitri N. Mavris
Keyword(s):  
Design Optimization ◽  
Aerodynamic Drag ◽  
Design Method ◽  
Shape Design ◽  
Cfd Analysis ◽  
Simple Arithmetic ◽  
Design Variables ◽  
3D Geometry ◽  
Geometric Entity ◽  
Aerodynamic Drag Reduction

In modern automotive industry market, there have been a lot of state-of-art methodologies to perform a conceptual design of a car; functional methods and 3D scanning technology are widely used. Naturally, the issues frequently boiled down to a trade-off decision making problem between quality and cost. Besides, to incorporate the design method with advanced optimization methodologies such as design-of-experiments (DOE), surrogate modeling, how efficiently a method can morph or recreate a vehicle’s shape is crucial. This paper accomplishes an aerodynamic design optimization of rear shape of a sedan by incorporating a reverse shape design method (RSDM) with the aforementioned methodologies based on CFD analysis for aerodynamic drag reduction. RSDM reversely recovers a 3D geometry of a car from several 2D schematics. The backbone boundary lines of 2D schematic are identified and regressed by appropriate interpolation function and a 3D shape is yielded by a series of simple arithmetic calculations without losing the detail geometric features. Besides, RSDM can parametrize every geometric entity to efficiently manipulate the shape for application to design optimization studies. As the baseline, an Audi A6 is modeled by RSDM and explored through CFD analysis for model validation. Choosing six design variables around the rear shape, 77 design points are created to build neural networks. Finally, a significant amount of CD reduction is obtained and corresponding configuration is validated via CFD.

Topology Optimization of Compliant Mechanisms Using Hybrid Discretization Model

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Hong Zhou
Keyword(s):  
Topology Optimization ◽  
Compliant Mechanisms ◽  
Compliant Mechanism ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Diagonal Element ◽  
Initial Guess ◽  
Stress Constraint ◽  
Design Variables ◽  
Hybrid Discretization

The hybrid discretization model for topology optimization of compliant mechanisms is introduced in this paper. The design domain is discretized into quadrilateral design cells. Each design cell is further subdivided into triangular analysis cells. This hybrid discretization model allows any two contiguous design cells to be connected by four triangular analysis cells whether they are in the horizontal, vertical, or diagonal direction. Topological anomalies such as checkerboard patterns, diagonal element chains, and de facto hinges are completely eliminated. In the proposed topology optimization method, design variables are all binary, and every analysis cell is either solid or void to prevent the gray cell problem that is usually caused by intermediate material states. Stress constraint is directly imposed on each analysis cell to make the synthesized compliant mechanism safe. Genetic algorithm is used to search the optimum and to avoid the need to choose the initial guess solution and conduct sensitivity analysis. The obtained topology solutions have no point connection, unsmooth boundary, and zigzag member. No post-processing is needed for topology uncertainty caused by point connection or a gray cell. The introduced hybrid discretization model and the proposed topology optimization procedure are illustrated by two classical synthesis examples of compliant mechanisms.

scholarly journals Substructure-Based Topology Optimization for Symmetric Hierarchical Lattice Structures

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 678
Author(s):  
Zijun Wu ◽  
Renbin Xiao
Keyword(s):  
Topology Optimization ◽  
High Efficiency ◽  
Spline Interpolation ◽  
Optimization Method ◽  
Optimality Criteria ◽  
Lattice Structures ◽  
Hierarchical Lattice ◽  
B Spline ◽  
Design Variables ◽  
Optimality Criteria Method

This work presents a topology optimization method for symmetric hierarchical lattice structures with substructuring. In this method, we define two types of symmetric lattice substructures, each of which contains many finite elements. By controlling the materials distribution of these elements, the configuration of substructure can be changed. And then each substructure is condensed into a super-element. A surrogate model based on a series of super-elements can be built using the cubic B-spline interpolation. Here, the relative density of substructure is set as the design variable. The optimality criteria method is used for the updating of design variables on two scales. In the process of topology optimization, the symmetry of microstructure is determined by self-defined microstructure configuration, while the symmetry of macro structure is determined by boundary conditions. In this proposed method, because of the educing number of degree of freedoms on macrostructure, the proposed method has high efficiency in optimization. Numerical examples show that both the size and the number of substructures have essential influences on macro structure, indicating the effectiveness of the presented method.

scholarly journals Size and Topology Optimization for Trusses with Discrete Design Variables by Improved Firefly Algorithm

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Yue Wu ◽  
Qingpeng Li ◽  
Qingjie Hu ◽  
Andrew Borgart
Keyword(s):  
Topology Optimization ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Optimization Method ◽  
Structural Topology ◽  
Discrete Variables ◽  
And Topology ◽  
Design Variables ◽  
Improved Firefly Algorithm ◽  
Discrete Design Variables

Firefly Algorithm (FA, for short) is inspired by the social behavior of fireflies and their phenomenon of bioluminescent communication. Based on the fundamentals of FA, two improved strategies are proposed to conduct size and topology optimization for trusses with discrete design variables. Firstly, development of structural topology optimization method and the basic principle of standard FA are introduced in detail. Then, in order to apply the algorithm to optimization problems with discrete variables, the initial positions of fireflies and the position updating formula are discretized. By embedding the random-weight and enhancing the attractiveness, the performance of this algorithm is improved, and thus an Improved Firefly Algorithm (IFA, for short) is proposed. Furthermore, using size variables which are capable of including topology variables and size and topology optimization for trusses with discrete variables is formulated based on the Ground Structure Approach. The essential techniques of variable elastic modulus technology and geometric construction analysis are applied in the structural analysis process. Subsequently, an optimization method for the size and topological design of trusses based on the IFA is introduced. Finally, two numerical examples are shown to verify the feasibility and efficiency of the proposed method by comparing with different deterministic methods.

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