This directory contains number of examples of elastica. Each example cases are stored in separate subdirectories, containing case descriptions, run file, and all other data/script necessary to run. More advanced cases are stored in separate repository with its description.

In order to run examples, you will need to install additional dependencies.

make install_examples_dependencies

Some examples provide additional files or links to published paper for a complete description. Examples can serve as a starting template for customized usages.

• AxialStretchingCase
  • Purpose: Physical convergence test of simple stretching rod.
  • Features: CosseratRod, OneEndFixedRod, EndpointForces
• TimoshenkoBeamCase
  • Purpose: Physical convergence test of simple Timoshenko beam.
  • Features: CosseratRod, OneEndFixedRod, EndpointForces,
• FlexibleSwingingPendulumCase
  • Purpose: Physical convergence test of simple pendulum with flexible rod.
  • Features: CosseratRod, HingeBC, GravityForces
• ContinuumSnakeCase
  • Purpose: Demonstrate simple case of modeling biological creature using PyElastica. The example uses friction to create slithering snake, and optimize the speed using CMA.
  • Features: CosseratRod, MuscleTorques, RodPlaneContactWithAnisotropicFriction, Gravity, CMA Optimization
• ContinuumSnakeWithLiftingWaveCase
  • Purpose: Demonstrate simple case of modeling biological creature using PyElastica. The example uses friction to create slithering snake with lift.
  • Features: CosseratRod, MuscleTorquesLifting(custom implemented), SnakeRodPlaneContact(custom implemented), Gravity
• MuscularSnake
  • Purpose: Example of Parallel connection module and customized Force module to implement muscular snake.
  • Features: MuscleForces(custom implemented)
• ButterflyCase
  • Purpose: Demonstrate simple restoration with initial strain.
  • Features: CosseratRod
• CantileverDistributedLoad
  • Purpose: Demonstrate the demformation of a straight cantilever under both conservative (like water pressure) and non-conservative (like gravity) distributed load, compared with numerical solutions from Tschisgale, Silvio (2019)."Chapter 3: Numerical models of partitioned problems" Technische Univerisitat Dresden Institution of Fluid Mechanics
  • Features: CosseratRod
• CantileverTransversalLoadCase
  • Purpose: Demonstrate the demformation of a curved cantilever under transversal one-end load, and also do Physical convergence test, compared with numerical solutions from Tschisgale, Silvio (2019).
  • Features: CosseratRod
• TumblingUnconstrainedRod
  • Purpose: Demostrate the dynamics of tumbling uncontrained rod, compared with analytical solution from Hisao, Kou Hou (1998)., Computer methods in applied mechanics and engineering.
  • Features: CosseratRod
• FrictionValidationCases
  • Purpose: Physical validation of rolling and translational friction.
  • Features: CosseratRod, UniformForces, RodPlaneContactWithAnisotropicFriction
• JointCases
  • Purpose: Demonstrate various joint usage with Cosserat Rod.
  • Features: FreeJoint, FixedJoint, HingeJoint, OneEndFixedRod, EndpointForcesSinusoidal
• RigidBodyCases
  • Purpose: Demonstrate usage of rigid body on simulation.
  • Features: Cylinder, Sphere
  • RodRigidBodyContact
    • Purpose: Demonstrate contact between cylinder and rod, for different intial conditions.
    • Features: Cylinder, CosseratRods, RodCylinderContact
• HelicalBucklingCase
  • Purpose: Demonstrate helical buckling with extreme twisting boundary condition.
  • Features: HelicalBucklingBC
• ContinuumFlagellaCase
  • Purpose: Demonstrate flagella modeling using PyElastica.
  • Features: SlenderBodyTheory, MuscleTorques,
• MuscularFlagella
  • Purpose: Example of customizing Joint module and Force module to implement muscular flagella.
  • Features: MuscleForces(custom implemented)
• RodContactCase
  • RodRodContact
    • Purpose: Demonstrates contact between two rods, for different initial conditions.
    • Features: CosseratRod, RodRodContact
  • RodSelfContact
    • PlectonemesCase
      • Purpose: Demonstrates rod self contact with Plectoneme example, and how to use link-writhe-twist after simulation completed.
      • Features: CosseratRod, SelonoidsBC, RodSelfContact, Link-Writhe-Twist
    • SolenoidsCase
      • Purpose: Demonstrates rod self contact with Solenoid example, and how to use link-writhe-twist after simulation completed.
      • Features: CosseratRod, SelonoidsBC, RodSelfContact, Link-Writhe-Twist
• BoundaryConditionsCases
  • Purpose: Demonstrate the usage of boundary conditions for constraining the movement of the system.
  • Features: GeneralConstraint, CosseratRod
• DynamicCantileverCase
  • Purpose: Validation of dynamic cantilever vibration for multiple modes.
  • Features: CosseratRod, OneEndFixedRod
• RingRodCase
  • Purpose: Demonstrate simulation of ring rod.
  • Features: RingCosseratRod, OneEndFixedRod, GravityForce
• CatenaryCase
  • Purpose: Demonstrate simulation of cosserat rod under gravity with fixed ends, compared with Catenary Analytical Solution from Routh, Edward John (1891). "Chapter X: On Strings". A Treatise on Analytical Statics. University Press.
  • Features: CosseratRod, FixedConstraint, GravityForce
• KnotCase
  • Purpose: Demonstrate simulation of rod forming a knot using a tip-pose control.
  • Features: CosseratRod, KnotTheory, FixedConstraint, RodSelfContact, Custom p-controller for SO3.

• RestartExample
  • Purpose: Demonstrate the usage of restart module.
  • Features: save_state, load_state
• Visualization
  • Purpose: Include simple examples of raytrace rendering data.
  • Features: POVray

• Elastica RL control - Case presented in Elastica: A compliant mechanics environment for soft robotic control
• Gym Softrobot - Soft-robot control environment developed in OpenAI-gym format to study slender body control with reinforcement learning.

• ParallelConnectionExample
  • Purpose: Demonstrate the usage of parallel connection.
  • Features: connect two parallel rods