Methods of designing inflatable shape-morphing structures with textured patterns

1. A method of designing and manufacturing an inflatable structure, the method comprising:

generating a finite element mesh defining a plurality of elements for an inflatable shape-morphing structure;

calculating a topology optimization analysis for the inflatable shape-morphing structure having a final shape in an inflated state, the topology optimization analysis determining a plurality of tensors for the plurality of elements of the finite element mesh;

converting the plurality of tensors for the plurality of elements into a plurality of diffusion coefficients for the plurality of elements;

generating a space-filling Turing pattern for the inflatable shape-morphing structure as a function of the plurality of diffusion coefficients, wherein the space-filling Turing pattern defines a simulated textured surface for the inflatable shape-morphing structure; and

3D additive manufacturing the simulated textured surface onto a sheet, configured to hold pressure within an interior thereof, such that the sheet has a textured surface mimicking the space-filling Turing pattern and the inflatable structure is manufactured.

2. The method according to claim 1 , wherein the plurality of tensors are configured to control inflation of the inflatable shape-morphing structure such that the inflatable shape-morphing structure has the final shape in the inflated state.

3. The method according to claim 1 , wherein the space-filling Turing pattern is generated with a pair of reaction-diffusion equations for a surface of the inflatable shape-morphing structure.

4. The method according to claim 1 , wherein the space-filling Turing pattern defines a simulated textured outer surface for the inflatable shape-morphing structure.

5. The method according to claim 1 , wherein the space-filling Turing pattern defines a simulated textured inner surface for the inflatable shape-morphing structure.

6. The method according to claim 1 , wherein the plurality of tensors is a plurality of orientation tensors for the plurality of elements of the finite element mesh.

7. The method according to claim 1 , wherein each of the plurality of diffusion coefficients comprises a 2 nd order tensor corresponding to a respective one of the plurality of tensors.

8. The method according to claim 1 further comprising generating CAD data for the simulated textured surface of the inflatable shape-morphing structure as a function of the space-filling Turing pattern.

9. The method according to claim 8 , wherein the CAD data defines a plurality of 3D additive manufacturing voxels corresponding for the plurality of elements for the inflatable shape-morphing structure.

10. The method according to claim 9 , wherein the 3D additive manufacturing CAD data defines at least one of a thickness for each of the plurality of 3D additive manufacturing voxels, a material for each of the plurality of 3D additive manufacturing voxels, and a manufacturing parameter for each of the plurality of 3D additive manufacturing voxels.

11. The method according to claim 9 , wherein the 3D additive manufacturing CAD data defines a thickness for each of the plurality of 3D additive manufacturing voxels as function of the space-filling Turing pattern.

12. The method according to claim 9 , wherein the 3D additive manufacturing CAD data defines a material for each of the plurality of 3D additive manufacturing voxels.

13. The method according to claim 12 , wherein the material for each of the plurality of 3D additive manufacturing voxels is as function of the space-filling Turing pattern.

14. The method according to claim 9 , wherein the 3D additive manufacturing CAD data defines a manufacturing parameter for additive manufacturing each of the plurality of 3D additive manufacturing voxels.

15. The method according to claim 14 , wherein the manufacturing parameter for each of the plurality of 3D additive manufacturing voxels is as function of the space-filling Turing pattern, and the manufacturing parameter is at least one of an illumination time, an illumination intensity, a heat input, and a cooling rate.

16. A method of designing and manufacturing an inflatable structure, the method comprising:

generating a finite element mesh for an inflatable shape-morphing structure to be formed from a sheet configured to hold pressure within an interior thereof;

calculating a topology optimization analysis for the inflatable shape-morphing structure having a final shape in an inflated state, wherein the topology optimization analysis determines a plurality of orientation tensors configured to control inflation of the inflatable shape-morphing structure such that the inflatable shape-morphing structure has the final shape;

converting the plurality of orientation tensors into a plurality of diffusion coefficients for the finite element mesh;

generating a space-filling Turing pattern for a surface of the inflatable shape-morphing structure via simulation of at least two reaction-diffusion equations as a function of the plurality of diffusion coefficients;

generating a simulated textured surface for the inflatable shape-morphing structure as a function of the generated space-filling Turing pattern; and

manufacturing the sheet with a textured surface mimicking the simulated textured surface such that the inflatable shape-morphing structure is formed.

17. The method according to claim 16 further comprising generating CAD data defining a plurality of 3D additive manufacturing voxels for the inflatable shape-morphing structure.

18. The method according to claim 17 , wherein the CAD data defines at least one of a thickness for each of the plurality of 3D additive manufacturing voxels, a material for each of the plurality of 3D additive manufacturing voxels, and a manufacturing parameter for each of the plurality of 3D additive manufacturing voxels.

19. A method of designing and manufacturing an inflatable structure with a predefined final shape, the method comprising:

generating a finite element mesh defining a plurality of elements for a surface of an inflatable shape-morphing structure;

calculating a topology optimization analysis for the inflatable shape-morphing structure such that a plurality of orientation tensors control inflation of the inflatable shape-morphing structure into the predefined final shape;

converting the plurality of orientation tensors into a plurality of diffusion coefficients for the plurality of elements;

generating a space-filling Turing pattern for the inflatable shape-morphing structure using the plurality of diffusion coefficients;

generating a textured surface for the inflatable shape-morphing structure as a function of the generated space-filling Turing pattern;

generating CAD data defining a plurality of 3D additive manufacturing voxels for additive manufacturing the inflatable structure, wherein the CAD data is generated as a function of the texture surface; and

3D additive manufacturing the 3D additive manufacturing voxels onto a sheet, configured to hold pressure within an interior thereof, such that the textured surface mimics the space-filling Turing pattern and the inflatable shape-morphing structure is manufactured.

20. The method according to claim 19 , wherein the CAD data defines at least one of a thickness for each of the plurality of 3D additive manufacturing voxels, a material for each of the plurality of 3D additive manufacturing voxels, and a manufacturing parameter for each of the plurality of 3D additive manufacturing voxels.