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Topology Optimization

Implementation of gradient and non gradient based topology optimization in Julia to compile an rich library with interchangeable objective functions and design representations (density, truss/beam, frep(level set)) for different physics (structural mechanics, heat transfer and lattice boltzmann).

Initial Notebook Link and main library/code in here.

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1. Minimum Compliance:

Equations and detailed explanation here. (adapted from here.)

2D

3D

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2. Desired Compliance:

2D

3D

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3. Multi Material:

2D

Red E=0.9, Green E=3, Blue E=1, Black(void) E=1e-9

3D

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4. Microstructure Design:

Detailed Explanation here.

2D

Maximum Bulk Modulus

Maximum Shear Modulus

Negative Negative Poisson Ratio

3D

Maximum Bulk Modulus

Maximum Shear Modulus

Negative Negative Poisson Ratio

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5. Concurrent Topology Optimization:

Detailed Explanation here.

a. One microstructure

2D

Macroscale & Microscale

3D

Macroscale & Microscale

b. Multiple microstructures

2D

Choosing the number of microstructures and their locations:

Final results:

3D

Final results:

c. Multiple microstructures with Kmeans clustering

2D

Final results:

Ex	0.32	0.27	0.187	0.321	0.298	0.15
Ey	0.102	0.103	0.255	0.093	0.088	0.098
ux	0.506	0.439	0.182	0.307	0.488	0.646
uy	0.161	0.171	0.249	0.088	0.144	0.417
S	0.055	0.058	0.047	0.036	0.049	0.071

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3D

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5. Hybrid Cellular Automata (online non-gradient based Optimization):

Detailed Explanation here.

Dynamic Optimization:

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