MetaVoxels

Tools for the design and simulation of metavoxels (meta-metarial voxel lattice structures). The objective is the inverse design of metavoxels using the base voxels studied in DM3.

Demos

• Whale Simulation
• Hierarical multi-material 3*3 Base Voxel
• Precomputed 3*3 Base Voxel
• Precomputed 5*5 Base Voxel
• Precomputed 2*2 Chiral Voxel
• Precomputed 3*3 Chiral Voxel
• (Computation & visualization) 5*5 Base Voxel
• Old Demo chiral voxel (Computation & visualization)

Desired Milestones

• 3D visualization tool
• One voxel simulation
• Multi-voxel simulation
• Physical simulation/Oasis simulation comparison
• Parallel dynamic ODE solver
• Hierarchical simulation
• One voxel optimization based on desired deformation
• Inverse Design of Large Structures
• Growing and Evolving structures (Path planing + simulation)

Structural Mechanics Models

Code Structure

• 191115_NodeJsJulia: current wip folder

  • demos

    • html interactive demos of simulation results
    • contains all html and styling information

  • fea

    • folder containing the structure and physcis simulation
    • barFea.js
      • FEA of truss structures (only axial forces transfered) where each element (bar element) has 6 degrees of freedom (
        F_{x1}, F_{y1}, F_{z1}, F_{x2} ,F_{y2}, F_{z2}
        ).
      • This is used when it is assumed that the nodes are hinges (they don't transfer moments)
    • beamFea.js
      • FEA of frame structures where each element (beam element) has 12 degrees of freedom (
        F_{x1}, F_{y1}, F_{z1}, M_{x1}, M_{y1}, M_{z1}
        and
        F_{x2} ,F_{y2}, F_{z2}, M_{x2} ,M_{y2}, M_{z2}
        ).
      • To solve for the stresses and displacement the euler bernoulli equations are used.
    • parallelFea.js
      • solving for the stresses and displacement using DEM method ODE
      • it's similar to mass spring but instead of the spring equation I use euler bernouli equations were each beam has 12 degrees of freedom
      • hence I don't have to create a giant matrix to solve for stresses and displacements which make the code highly parallizable
      • Here I am able as well to accomodate for non-linear behaviour
    • flight.js
      • physcis simulation code for drone flight simulation and control

  • json

    • folder containing structures that are precomputed (either geometry or fea)
    • example of json setup:

      • {
          "nodes": [
            {
              "id": "n0", 
              "parent": "11",
              "degrees_of_freedom":[0,1,2,3,4,5] , 
              "restrained_degrees_of_freedom":[true,true,true,true,true,true],
              "position": { "x": 0, "y":0,"z":0 },
              "force":{ "x": 0, "y": 10, "z":0 },
              "displacement": { "x": 0, "y": 0,"z":0 },
              "angle": { "x": 0, "y": 0,"z":0 },
            },
          ],
          
          "edges": [
              { 
                "id": "e0", 
                "source": 0, 
                "target": 1 ,
                "area":1.0,
                "density":0.284,
                "stiffness":30.0e6,
                "stress":0,
        
             },
          ],
          "animation" :  {
            "showDisplacement" : true,
            "exageration" : 10,
            "speed":3.0
          },
          "viz" :  {
            "minStress":-500,
            "maxStress": 500,
            "colorMaps":["YlGnBu", "winter", "coolwarm","jet"],
            "colorMap":0,
          }
        }

      • useful if needed to create the geometry using python or any other software

  • julia:

    • folder containing trial code for the migration of the structure simulation to julia to do parallel computation and

  • lib

    • contains all external libraries used

  • visualization

    • Contains all 3D visualization and design code
    • draw.js
      • where i call all the high level commands for drawing voxels and simulation
    • geometry.js
      • contains low lever useful functions to create geometry (addNode, addEdge, checkAndAdd, createLattice..)
      • I am using rhino3dm library in javascript to facilitate buidling intrecate geometries
    • main.js
      • contains all three.js scene building and animation

  • app.js

    • contains code to run the simulation headless (either in javascript or julia) using nodejs

Test Cases

Whale Simulation

Using the dynamic Model, I wanted to simulate the undulatory swimming motion based on (3):

I modeled the equation in this colab notebook:

Demo:
Live Demo Link.

TODO

• One voxel simulation
  • 2D truss
  • 2D Euler-Bernoulli for one bar
  • 3D truss
  • 3D Euler-Bernoulli
• Port code to javascript
• Import geometry from stl/rhino
• intergrate tensorflow.js
• check previous nodes
• multiple voxel/lattice simulation

Demos

• different kinds of voxels
  • add chiral voxel
  • add auxetic voxel
  • add compliant voxel
  • search for one way bendy voxel
  • Demo and .gif different types of voxels beside each other
• for ARL meeting
  • compliant voxel simulation
  • dog leg simulation
  • bridge building visualization
  • more movements
    • fly? based on forces
      • (ODE version first!)
    • bend actuaton
• Fillipos 3d printed structures

Scaling

• Node js independent implementation (computation vs visualization)
• julia integration
  • julia trials
  • small example in julia
• Parallel ODE Implementation
  • re-run previous implementations
    • see performance
    • document results
  • continue implementation
    • find best dt
    • fine best number of timesteps
      • do convergence graph
    • non linear deformation
  • check javascript parallel webworkers implementation
• Hierarchical simulation
  • besise each other two
    • show blown up voxel simulation of 5*5
    • do 5*5

Interface and visualization

• feedback code/simulation running
  • check a better way
  • see way to show current timestep
• slider down for displacement instead of animation
• menu down to chose which example to upload

Differentiation and Search

• inverse matrix forward methods/parameter estimation
• adjoint linear solve
• Amanda's code

Documentation

• Explain Code Structure
• More info about simulation and physics

Code Cleaning

• create closures for threejs
• create closure for fea
• create closure for geometry
• remove double nodes

Code Structure

• create shared data structure for parallel simulation
• boudary conditions
  • create a box for loads
  • create box for restraints
  • add default material
  • add box for second material
  • when two nodes different materials use hiller method to get E
• use parent data to get hierarchy information