Constraints#
Built-in boundary condition implementationss
Description#
Constraints are equivalent to displacement boundary condition.
Available Constraint
Base class for constraint and displacement boundary condition implementation. |
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Boundary condition template. |
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This boundary condition class fixes one end of the rod. |
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This boundary condition class allows the specified node/link to have a configurable constraint. |
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This boundary condition class fixes the specified node or orientations. |
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This is the boundary condition class for Helical Buckling case in Gazzola et. |
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Deprecated 0.2.1: Same implementation as FreeBC |
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Deprecated 0.2.1: Same implementation as OneEndFixedBC |
Compatibility#
Constraint / Boundary Condition |
Rod |
Rigid Body |
---|---|---|
FreeBC |
✅ |
✅ |
OneEndFixedBC |
✅ |
✅ |
GeneralConstraint |
✅ |
✅ |
FixedConstraint |
✅ |
✅ |
HelicalBucklingBC |
✅ |
❌ |
Examples#
Note
PyElastica package provides basic built-in constraints, and we expect use to adapt their own boundary condition from our examples.
Customizing boundary condition examples:
Built-in Constraints#
- class elastica.boundary_conditions.ConstraintBase(*args, **kwargs)[source]#
Bases:
ABC
Base class for constraint and displacement boundary condition implementation.
Notes
Constraint class must inherit BaseConstraint class.
- Attributes:
system
RodBase or RigidBodyBaseget system (rod or rigid body) reference
- node_indicesNone or numpy.ndarray
- element_indicesNone or numpy.ndarray
- property system: Type[RodBase] | Type[RigidBodyBase]#
get system (rod or rigid body) reference
- property constrained_position_idx: ndarray | None#
get position-indices passed to “using”
- property constrained_director_idx: ndarray | None#
get director-indices passed to “using”
- class elastica.boundary_conditions.OneEndFixedBC(fixed_position, fixed_directors, **kwargs)[source]#
This boundary condition class fixes one end of the rod. Currently, this boundary condition fixes position and directors at the first node and first element of the rod.
Examples
How to fix one ends of the rod:
>>> simulator.constrain(rod).using( ... OneEndFixedBC, ... constrained_position_idx=(0,), ... constrained_director_idx=(0,) ... )
- __init__(fixed_position, fixed_directors, **kwargs)[source]#
Initialization of the constraint. Any parameter passed to ‘using’ will be available in kwargs.
- Parameters:
- constrained_position_idxtuple
Tuple of position-indices that will be constrained
- constrained_director_idxtuple
Tuple of director-indices that will be constrained
- class elastica.boundary_conditions.GeneralConstraint(*fixed_data, translational_constraint_selector=None, rotational_constraint_selector=None, **kwargs)[source]#
This boundary condition class allows the specified node/link to have a configurable constraint. Index can be passed to fix either or both the position or the director. Constraining position is equivalent to setting 0 translational DOF. Constraining director is equivalent to setting 0 rotational DOF.
Examples
How to fix all translational and rotational dof except allowing twisting around the z-axis in an inertial frame:
>>> simulator.constrain(system).using( ... GeneralConstraint, ... constrained_position_idx=(0,), ... constrained_director_idx=(0,), ... translational_constraint_selector=np.array([True, True, True]), ... rotational_constraint_selector=np.array([True, True, False]), ... )
How to allow the end of the rod to move in the XY plane and allow all rotational dof:
>>> simulator.constrain(rod).using( ... GeneralConstraint, ... constrained_position_idx=(-1,), ... translational_constraint_selector=np.array([True, True, False]), ... )
- __init__(*fixed_data, translational_constraint_selector=None, rotational_constraint_selector=None, **kwargs)[source]#
Initialization of the constraint. Any parameter passed to ‘using’ will be available in kwargs.
- Parameters:
- constrained_position_idxtuple
Tuple of position-indices that will be constrained
- constrained_director_idxtuple
Tuple of director-indices that will be constrained
- translational_constraint_selector: Optional[np.ndarray]
np.array of type bool indicating which translational degrees of freedom (dof) to constrain. If entry is True, the corresponding dof will be constrained. If None, we constrain all dofs.
- rotational_constraint_selector: Optional[np.ndarray]
np.array of type bool indicating which translational degrees of freedom (dof) to constrain. If entry is True, the corresponding dof will be constrained.
- class elastica.boundary_conditions.FixedConstraint(*args, **kwargs)[source]#
This boundary condition class fixes the specified node or orientations. Index can be passed to fix either or both the position or the director. Constraining position is equivalent to setting 0 translational DOF. Constraining director is equivalent to setting 0 rotational DOF.
See also
GeneralConstraint
Generalized constraint with configurable DOF.
Examples
How to fix two ends of the rod:
>>> simulator.constrain(rod).using( ... FixedConstraint, ... constrained_position_idx=(0,-1), ... constrained_director_idx=(0,-1) ... )
How to pin the middle of the rod (10th node), without constraining the rotational DOF.
>>> simulator.constrain(rod).using( ... FixedConstraint, ... constrained_position_idx=(10,) ... )
- __init__(*args, **kwargs)[source]#
Initialization of the constraint. Any parameter passed to ‘using’ will be available in kwargs.
- Parameters:
- constrained_position_idxtuple
Tuple of position-indices that will be constrained
- constrained_director_idxtuple
Tuple of director-indices that will be constrained
- class elastica.boundary_conditions.HelicalBucklingBC(position_start, position_end, director_start, director_end, twisting_time, slack, number_of_rotations, **kwargs)[source]#
This is the boundary condition class for Helical Buckling case in Gazzola et. al. RSoS (2018). The applied boundary condition is twist and slack on to the first and last nodes and elements of the rod.
Example case (helical buckling)
- Attributes:
- twisting_time: float
Time to complete twist.
- final_start_position: numpy.ndarray
2D (dim, 1) array containing data with ‘float’ type. Position of first node of rod after twist completed.
- final_end_position: numpy.ndarray
2D (dim, 1) array containing data with ‘float’ type. Position of last node of rod after twist completed.
- ang_vel: numpy.ndarray
2D (dim, 1) array containing data with ‘float’ type. Angular velocity of rod during twisting time.
- shrink_vel: numpy.ndarray
2D (dim, 1) array containing data with ‘float’ type. Shrink velocity of rod during twisting time.
- final_start_directors: numpy.ndarray
3D (dim, dim, 1) array containing data with ‘float’ type. Directors of first element of rod after twist completed.
- final_end_directors: numpy.ndarray
3D (dim, dim, 1) array containing data with ‘float’ type. Directors of last element of rod after twist completed.
- __init__(position_start, position_end, director_start, director_end, twisting_time, slack, number_of_rotations, **kwargs)[source]#
Helical Buckling initializer
- Parameters:
- position_startnumpy.ndarray
2D (dim, 1) array containing data with ‘float’ type. Initial position of first node.
- position_endnumpy.ndarray
2D (dim, 1) array containing data with ‘float’ type. Initial position of last node.
- director_startnumpy.ndarray
3D (dim, dim, blocksize) array containing data with ‘float’ type. Initial director of first element.
- director_endnumpy.ndarray
3D (dim, dim, blocksize) array containing data with ‘float’ type. Initial director of last element.
- twisting_timefloat
Time to complete twist.
- slackfloat
Slack applied to rod.
- number_of_rotationsfloat
Number of rotations applied to rod.