A MATLAB Code for Integrated Additive Manufacturing and Level-Set Based Topology Optimization

2016 ◽  
Author(s):  
Panagiotis Vogiatzis ◽  
Shikui Chen ◽  
Chi Zhou
Keyword(s):  
Topology Optimization ◽  
3D Printing ◽  
Level Set ◽  
Design Procedure ◽  
Optimization Procedure ◽  
Optimization Method ◽  
Matlab Code ◽  
Level Set Function ◽  
Final Design ◽  
3D Printers

Since topology optimization has become an important part of the design procedure, various optimization methods have been developed through the years. One of the promising options is the use of level-set based topology optimization method. In this method, the design is the zero level of a one higher dimension level-set function Φ. The benefit of this alternative method is that the final design is characterized by its clear boundaries. This advantage is based on the fact that post-processing work is not needed on the final design and it can be directly sent to the manufacturing line. The designers, in order to visualize their innovative results, often build prototypes using 3D printers, given that the designs may have complicated features. Furthermore, cost permitting, 3D printing can also be considered for mass customization. Either way, the result of the optimization has to be translated to a file that 3D printers can recognize. In this paper, the authors have developed a MATLAB code that can be integrated in the topology optimization procedure and convert the design to an STL file (STereoLithography), which is the de facto format for 3D printing.

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.

Design of Mechanical Structures Considering Harmonic Loads Using Level Set-Based Topology Optimization

2012 ◽  
Author(s):  
Takayuki Yamada ◽  
Toshiro Matsumoto ◽  
Shinji Nishiwaki
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Design Method ◽  
Optimization Method ◽  
Adjoint Equations ◽  
Topology Optimization Problem ◽  
Level Set Function ◽  
Elastic Design ◽  
Objective Functional ◽  
Topology Optimization Method

This paper presents an optimum design method for mechanical structures considering harmonic loads using a level set-based topology optimization method and the Finite Element Method (FEM). First, we briefly discuss the level set-based topology optimization method. Second, a topology optimization problem is formulated for a dynamic elastic design problem using level set boundary expressions. The objective functional is set to minimize the displacement at specific boundaries. Based on this formulation, the topological sensitivities of the objective functional are derived. Next, a topology optimization algorithm is proposed that uses the FEM to solve the equilibrium and adjoint equations, and when updating the level set function. Finally, several numerical examples are provided to confirm the validity and utility of the proposed method.

Level Set-Based Topology Optimization Method for Thermal Problems Considering Design-Dependent Boundary Effects

2009 ◽  
Author(s):  
Takayuki Yamada ◽  
Shinji Nishiwaki ◽  
Atsuro Iga ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Field Theory ◽  
Topology Optimization ◽  
Level Set ◽  
Phase Field ◽  
Three Dimensional ◽  
Optimization Method ◽  
Interface Energy ◽  
Total Potential ◽  
Level Set Function ◽  
Topology Optimization Method

This paper proposes a new level set-based topology optimization method for thermal problems that deal with generic heat transfer boundaries including design-dependent boundary conditions, based on the level set method and the concept of the phase field theory. First, a topology optimization method using a level set model incorporating a fictitious interface energy derived from the concept of the phase field theory is briefly discussed. Next, a generic optimization problem for thermal problems is formulated based on the concept of total potential energy. An optimization algorithm that uses the Finite Element Method when solving the equilibrium equation and updating the level set function is then constructed. Finally, several three-dimensional numerical examples are provided to confirm the utility and validity of the proposed topology optimization method.

Electromagnetic Design of In-Vehicle Reactor Using a Level-Set Based Topology Optimization Method

2014 ◽  
Author(s):  
Shintaro Yamasaki ◽  
Atsushi Kawamoto ◽  
Akira Saito ◽  
Masakatsu Kuroishi ◽  
Kikuo Fujita
Keyword(s):  
Topology Optimization ◽  
Level Set ◽  
Design Problem ◽  
Design Method ◽  
Reactor Core ◽  
Optimization Method ◽  
State Variables ◽  
Boundary Tracking ◽  
Level Set Function ◽  
Topology Optimization Method

In this paper, we propose a level-set based topology optimization method for designing a reactor, which is used as a part of the DC-DC converter in electric and hybrid vehicles. Since it realizes a high-power driving motor and its performance relies on its component, i.e., reactor core, it is valuable to establish a reasonable design method for the reactor core. Boundary tracking type level-set topology optimization is suitable for this purpose, because the shape and topology of the target structure is clearly represented by the zero boundary of the level-set function, and the state variables are accurately computed using the zero boundary tracking mesh. We formulate the design problem on the basis of electromagnetics, and derive the design sensitivities. The derived sensitivities are linked with boundary tracking type level-set topology optimization, and as a result, a useful structural optimization method for the reactor core design problem is developed.

Applications of 3D Level Set Topology Optimization

2012 ◽  
Author(s):  
Christopher J. Brampton ◽  
Hyunsun A. Kim ◽  
James L. Cunningham
Keyword(s):  
Topology Optimization ◽  
Internal Structure ◽  
Level Set ◽  
Bone Structure ◽  
Optimal Solution ◽  
Optimization Procedure ◽  
Optimal Structure ◽  
Os Calcis ◽  
Level Set Function ◽  
Set Function

Level set topology optimization defines the solution using the level set function values stored at the nodes of a regular finite element grid. These values represent a signed distance function which indicates the distance from each node to the structural boundaries. During optimization, nodal sensitivities are used to update the level set function values, moving the boundaries to create a more optimal structure. This paper presents two applications of the 3D level set topology optimization procedure aiming to minimize structural compliance subject to a volume constraint. The first application is the internal structure of a light subsonic aircraft wing. The results suggest that an alternative arrangement of ribs and sparse may be a more optimal solution for wing structures. The second application is the internal trabecular bone structure of an os-calcis. Comparison of the modeled optimal structure and the real internal structure suggest the internal bone structure is mechanically optimal.

A Level Set-Based Topology Optimization Method for Maximizing Thermal Diffusivity in Problems Including Design-Dependent Effects

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Takayuki Yamada ◽  
Kazuhiro Izui ◽  
Shinji Nishiwaki
Keyword(s):  
Topology Optimization ◽  
Thermal Diffusivity ◽  
Level Set ◽  
Design Method ◽  
Optimization Method ◽  
Interface Energy ◽  
Total Potential ◽  
Level Set Function ◽  
Set Function ◽  
Topology Optimization Method

This paper proposes an optimum design method, based on our level set-based topology optimization method, for maximizing thermal diffusivity in problems dealing with generic heat transfer boundaries that include design-dependent boundary conditions. First, a topology optimization method using a level set model incorporating a fictitious interface energy for regularizing the topology optimization is briefly discussed. Next, an optimization method for maximizing thermal diffusivity is formulated based on the concept of total potential energy. An optimization algorithm that uses the finite element method when solving the equilibrium equation and updating the level set function is then constructed. Finally, several numerical examples are provided to confirm the utility and validity of the proposed topology optimization method.

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