Optimal Design of Functionally Graded Parts
Abstract
:1. Introduction
2. Evolution of Design Methods
2.1. Prior to 2002
2.2. 2003–2009
2.3. 2010–2015
2.4. 2016–2022
3. Homogenization Approaches
3.1. Rule of Mixture
3.2. Mori-Tanaka Scheme
3.3. Levin’s Model
3.4. Maxwell Scheme
3.5. Temperature-Dependent Properties
3.6. Finite Element Model
3.7. Tamura-Tomota-Ozawa Model
4. Representation Techniques
4.1. Voxel-Based Models
4.2. Volume-Mesh Models
4.3. Explicit Function-Based Models
4.4. Control Point-Based Models
4.5. Implicit Function-Based Models
4.6. Composite Models
4.7. Material Primitive-Based Models
4.8. Comparison
5. Finite Element Analysis Approaches
5.1. Commercial Software
5.2. Indigenously-Developed Codes
5.3. FEM Integrated with CAD
6. Optimization Algorithms
7. Most Advanced Design Methods
8. Manufacturing Techniques
8.1. Direct Energy Deposition
8.2. Material Extrusion
8.3. Material Jetting
9. Conclusions and Future Directions
- With the advent of AM, FGM with a complex geometry and material distribution can be fabricated. To get the most out of this, we need advanced methodologies to design and fabricate parts with optimal material distributions and/or geometries.
- The development of a data-driven strategy to complement designers’ creativity and knowledge would be a fascinating area of future work. The first step in establishing a data-driven approach would be to build a massive database of material models and their attributes. The physical and mechanical properties of various combinations of materials in various compositions should be tested and maintained in the database. The database could be used to generate automated suggestions pertaining to the materials to be used for different portions of the designs, the composition of materials to be used, and other topological and geometrical changes to the design using suggestive techniques developed with machine learning and probabilistic models for the CAD domain.
- To analyze and simulate the behavior of more complicated FGM objects, advanced and resilient numerical approaches as well as a representation scheme that facilitates analytical calculations must be devised. Furthermore, having a system that can optimize and recommend relevant adjustments in the design to satisfy and meet the designers’ needs would be quite advantageous. The recommended alterations could take the form of changes to the design’s geometrical characteristics, topology, or material distribution over crucial sections.
- Because the progressive and smooth changing of material constituents is a major aspect of FGMs, the most common design variable in the examined studies was the material distribution pattern. The manufacturability of the FG structure was taken into consideration in a few optimization experiments. It’s a good idea to include manufacturability in the optimization studies because it leads to more practical designs with a better chance of being mass produced.
- So far, several AM technologies have been proposed to manufacture FGMs. Real-world industrial applications, on the other hand, are still few and far between, necessitating major and thorough research efforts to address the vast array of concerns and obstacles involved. As new functional materials with complicated compositions arise, new sophisticated manufacturing technologies, including new procedures for the fabrication of FGMs, must be developed. Micro-nano additive manufacturing (sometimes referred to as micro-nano scale 3D printing) is a new processing technique for producing sophisticated micro-nano structures. High aspect ratio micro-nano structures, multi-lateral micro-nano structures, macro/micro-composite structures, and embedded hetero-structures are all possible using FGAM.
Author Contributions
Funding
Institutional Review Board Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
DED | direct energy deposition | ||
DLMD | direct laser metal deposition | ||
Symbols | DMSh | direct multi-search | |
E | Young’s modulus | DNN | deep neural network |
Et | tangent modulus | EFG | element-free Galerkin |
K | bulk modulus | FA | firefly algorithm |
k | thermal conductivity | FDM | finite difference method |
P | material properties | FEA | finite element analysis |
q | ratio of stress to strain transfer | FEM | finite element method |
sy | yield strength | FG | functionally graded |
T | temperature | FGM | functionally graded materials |
V | volume fraction | FGS | functionally graded sandwich |
FSDT | first-order shear deformation theory | ||
Greek letters | GA | genetic algorithm | |
α | coefficient of thermal expansion | HAP | hydroxyapatite |
µ | shear modulus | HSDT | higher-order shear deformation theory |
ν | Poisson’s ratio | IGA | isogeometric analysis |
ε | strain | IMD | isogeometric multi-mesh design |
σ | stress | LMD | laser metal deposition |
MAT | medial axis transform | ||
Abbreviations | mSOS | modified symbiotic organisms search | |
AEH | asymptotic expansion homogenization | NSGA | non-dominated sorting genetic algorithm |
AHEFA | adaptive hybrid evolutionary firefly algorithm | NURBS | non-uniform rational B-splines |
AM | additive manufacturing | PSO | particle swarm optimization |
ANN | artificial neural network | RVE | representative volume element |
BFG | bidirectional functionally graded | SA | simulated annealing |
CAMD | continuous approximation of material distribution | SOS | symbiotic organism search |
CPU | central processing unit | SQP | sequential quadratic programming |
CSG | constructive solid geometry | TSDT | third-order shear deformation theory |
CT | computerized tomography | X-FEM | extended finite element method |
CUF | Carrera’s unified formulation | ||
DE | differential evolution |
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Representations | Material Capability | Representational Capacity | Accuracy or Exactness | Compactness Overhead and Efficiency |
---|---|---|---|---|
Voxel model | A | ☆ ☆ ☆ ☆ | ☆ | ☆ ☆ ☆ ☆ |
Volume mesh model | A | ☆ ☆ ☆ ☆ | ☆ | ☆ ☆ ☆ |
Explicit function model | B | ☆ ☆ | ☆ ☆ ☆ ☆ | ☆ ☆ ☆ ☆ |
Control point based model | B | ☆ ☆ ☆ | ☆ ☆ ☆ ☆ | ☆ ☆ ☆ |
Implicit function model | B | ☆ ☆ ☆ | ☆ ☆ ☆ ☆ | ☆ ☆ ☆ ☆ |
Hybrid composite model | B | ☆ ☆ ☆ ☆ | / | / |
Handle Complex Geometry | Handle Complex Material Distribution | 1D,2D,3D Material Distribution | Handle Multi-Physics | Optimizing Geometry as Well | Realistic Material Model | Manufacturing Constraints | Convergence Speed | |
---|---|---|---|---|---|---|---|---|
Lieu and Lee [204] | | | 3D | | | | | Fast |
Do. et al. [148] | | | 3D | | | | | Mediocre |
Nayak and Armani [144] | | | 3D | | | | | Slow |
Das and Sutradhar [92] | | | 1D | | | | | Mediocre |
Jamshidi and Arghavani [207] | | | 2D | | | | | Fast |
Banh et al. [208] | | | 1D | | | | | Fast |
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Nayak, P.; Armani, A. Optimal Design of Functionally Graded Parts. Metals 2022, 12, 1335. https://doi.org/10.3390/met12081335
Nayak P, Armani A. Optimal Design of Functionally Graded Parts. Metals. 2022; 12(8):1335. https://doi.org/10.3390/met12081335
Chicago/Turabian StyleNayak, Priyambada, and Amir Armani. 2022. "Optimal Design of Functionally Graded Parts" Metals 12, no. 8: 1335. https://doi.org/10.3390/met12081335