Design and Manufacturing Functionally Gradient Material Objects With an Off the Shelf Three-Dimensional Printer: Challenges and Solutions

2015 ◽  
Vol 137 (11) ◽  
Author(s):  
Anthony Garland ◽  
Georges Fadel
Keyword(s):  
Genetic Algorithm ◽  
Topology Optimization ◽  
Level Set ◽  
Gradient Material ◽  
Future Research ◽  
Functionally Gradient Material ◽  
Topology Optimization Problem ◽  
Fused Deposition ◽  
Level Set Function ◽  
Functionally Gradient

This paper presents the challenges and solutions encountered while designing and then printing functionally gradient material (FGM) objects using an off the shelf fused deposition modeling (FDM) 3D printer. The printer, Big Builder Dual-Feed Extruder from 3dprinter4u, Noordwijkerhout, The Netherlands, has the unique design of extruding two different filaments out of one nozzle. By controlling the rate at which the two filaments are pulled into the melt chamber, FGM objects can be printed. Software challenges associated with process planning required to print an FGM object are solved by showing a method for printing a discretized gradient and by designing an open-loop control mechanism for the extruder motors. A design method is proposed that models an object using a level-set function (LSF) with a material gradient. Instead of merely identifying the boundaries of the object, the level set also models the material gradient within the object. This representation method along with a genetic algorithm finds an optimal design for an FGM cantilever beam that is then printed on the FDM printer. The model and genetic algorithm are also used to solve a standard topology optimization problem. The results are compared to a similar FGM topology optimization method in the literature. All the codes for this paper are made open source to facilitate future research.

Multi-Objective Optimal Design of Functionally Gradient Materials

2016 ◽  
Author(s):  
Anthony Garland ◽  
Georges Fadel
Keyword(s):  
Topology Optimization ◽  
Material Design ◽  
Optimal Placement ◽  
Gradient Material ◽  
Gradient Materials ◽  
Functionally Gradient Material ◽  
Topology Optimization Problem ◽  
Functionally Gradient ◽  
Conflicting Objectives ◽  
Single Part

The objective of this research is to optimally design both the topology and material distribution of functionally gradient material objects while considering more than one objective. Many techniques exist for both topology optimization and optimal placement of functionally gradient material within a single object, but combining the two is challenging. In addition, gradient materials allow customization of individual regions of a single part in order to achieve conflicting objectives or constraints. This paper shows a technique for concurrent topology and material gradient optimization within a single part while considering two conflicting objectives. The algorithm is applied to a standard topology optimization problem. The resulting gradient material designs have regions with distinct functionality and the material in these regions is chosen based on the regions function. In addition, a comparison of the gradient material design and a corresponding homogenous material design shows a significant improvement in the objective value for the gradient material design.

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.

Improvement of topology optimization method based on level set function in magnetic field problem

2018 ◽  
Vol 37 (2) ◽  
pp. 630-644 ◽  
Author(s):  
Yoshifumi Okamoto ◽  
Hiroshi Masuda ◽  
Yutaro Kanda ◽  
Reona Hoshino ◽  
Shinji Wakao
Keyword(s):  
Magnetic Field ◽  
Topology Optimization ◽  
Level Set ◽  
Jacobi Equation ◽  
Field Problem ◽  
Content Type ◽  
Topology Optimization Problem ◽  
Level Set Function ◽  
Set Function ◽  
Hamilton Jacobi Equation

PurposeThe purpose of this paper is the improvement of topology optimization. The scope of the paper is focused on the speedup of optimization. Design/methodology/approachTo achieve the speedup, the method of moving asymptotes (MMA) with constrained condition of level set function is applied instead of solving the Hamilton–Jacobi equation. FindingsThe acceleration of convergence of objective function is drastically improved by the implementation of MMA. Originality/valueNormally, the level set method is solved through the Hamilton–Jacobi equation. However, the possibility of introducing mathematical programming is clear by the constrained condition. Furthermore, the proposed method is suitable for efficiently solving the topology optimization problem in the magnetic field system.

Manufacturing Functionally Gradient Material Objects With an Off the Shelf 3D Printer: Challenges and Solutions

2015 ◽  
Author(s):  
Anthony Garland ◽  
Georges Fadel
Keyword(s):  
Fused Deposition Modeling ◽  
Gradient Material ◽  
3D Printer ◽  
Unique Problem ◽  
Functionally Gradient Material ◽  
Fused Deposition ◽  
Functionally Gradient ◽  
Deposition Modeling ◽  
Material Gradation ◽  
Gradient Change

This paper presents the challenges and solutions encountered while printing functionally gradient material (FGM) objects using an off the shelf Fused Deposition Modeling (FDM) 3D printer. The printer, Build Builder Dual-Feed Extruder from 3dprinter4u, has the unique design of extruding two different filaments out of one nozzle. Two separate motors independently pull two different filaments into one chamber causing plastic to extrude out of one nozzle. By using different filaments with different properties, an object with a material properties gradient can be manufactured. These material property gradients can help minimize the difficulty of bonding two different materials directly to each other, and give the designer the ability to tailor individual regions of one object to have different physical properties. Finding an optimal object design that can take advantage of this gradation is a unique problem that goes beyond the traditional solid modeling found in most CAD software. Once a design is obtained, slicing the object and creating an optimal build path is challenging because the gradation must be considered. Several objects were designed and manufactured to test the printers ability to print FGM objects. The python code used to add gradient change commands to the existing Gcode, and to slice a FGM flywheel while taking into account the material gradation has been made open source.

scholarly journals An interface-enriched generalized finite element method for level set-based topology optimization

2020 ◽  
Vol 63 (1) ◽  
pp. 1-20
Author(s):  
S. J. van den Boom ◽  
J. Zhang ◽  
F. van Keulen ◽  
A. M. Aragón
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Topology Optimization ◽  
Level Set ◽  
Element Formulation ◽  
Generalized Finite Element Method ◽  
Level Set Function ◽  
Analytical Sensitivities ◽  
Generalized Finite Element ◽  
Element Method

AbstractDuring design optimization, a smooth description of the geometry is important, especially for problems that are sensitive to the way interfaces are resolved, e.g., wave propagation or fluid-structure interaction. A level set description of the boundary, when combined with an enriched finite element formulation, offers a smoother description of the design than traditional density-based methods. However, existing enriched methods have drawbacks, including ill-conditioning and difficulties in prescribing essential boundary conditions. In this work, we introduce a new enriched topology optimization methodology that overcomes the aforementioned drawbacks; boundaries are resolved accurately by means of the Interface-enriched Generalized Finite Element Method (IGFEM), coupled to a level set function constructed by radial basis functions. The enriched method used in this new approach to topology optimization has the same level of accuracy in the analysis as the standard finite element method with matching meshes, but without the need for remeshing. We derive the analytical sensitivities and we discuss the behavior of the optimization process in detail. We establish that IGFEM-based level set topology optimization generates correct topologies for well-known compliance minimization problems.

Effect of B4C Particle Size on the Properties of Al/(Al–B4C)/Al Functionally Gradient Material

2020 ◽  
Vol 58 (11-12) ◽  
pp. 737-742
Author(s):  
Yingshui Yu ◽  
Chenglong Yao ◽  
Yubo Zhang ◽  
Guangye Xu ◽  
Tingju Li ◽  
...  
Keyword(s):  
Particle Size ◽  
Gradient Material ◽  
Functionally Gradient Material ◽  
Functionally Gradient ◽  
B4c Particle
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