simulations

The EasyFEA/simulations/ module in EasyFEA provides essential tools for creating and managing simulations. These simulations are built using a Mesh and a _IModel (material).

With this module, you can construct:

• Linear elastic simulations with ElasticSimu.

• Nonlinear hyperelastic simulations with HyperElasticSimu.

• Euler-Bernoulli beam simulations with BeamSimu.

• PhaseField damage simulations for quasi-static brittle fracture with PhaseFieldSimu.

• Thermal simulations with ThermalSimu.

• Weak form simulations with WeakFormSimu.

How to create new simulations in EasyFEA ?

To create new simulation classes, you can take inspiration from existing implementations. Make sure to follow the _Simu interface. The ThermalSimu class is relatively simple and can serve as a good starting point. See EasyFEA/simulations/_thermal.py for more details.

Detailed simulations API

class EasyFEA.simulations.AlgoType(value)

Bases: str, Enum

static Get_Hyperbolic_Types()

Return type:

list[str]

static Get_Hyperbolic_and_Parabolic_Types()

Return type:

list[str]

elliptic = 'elliptic'

Solve K u = F

hht = 'hht'

Solve K u_np1ma + C v_np1ma + M a_np1ma = F_np1ma

midpoint = 'midpoint'

Solve K u_np1/2 + C v_np1/2 + M a_np1/2 = F_np1/2

newmark = 'newmark'

Solve K u_np1 + C v_np1 + M a_np1 = F_np1

u_np1 = u_n + dt v_n + dt^2/2 ((1 - 2 B) a_n + 2 B a_np1)

v_np1 = v_n + dt ((1 - gamma) a_n + gamma a_np1)

parabolic = 'parabolic'

Solve K u_npa + C v_npa = F_npa

EasyFEA.simulations.Load_Simu(folder, filename='simulation')

Loads the simulation from the specified folder.

Parameters:

• folder (str) – simulation’s folder.

• filename (str, optional) – The simualtion’s name, by default “simulation”.

Returns:

The loaded simulation.

Return type:

_Simu

EasyFEA.simulations.Load_pickle(folder, filename)

Returns folder/filename.pickle object.

class EasyFEA.simulations.ResolType(value)

Bases: str, Enum

r1 = '1'

xi = inv(Aii) * (bi - Aic * xc)

r2 = '2'

Lagrange multipliers

r3 = '3'

Penality

EasyFEA.simulations.Save_pickle(obj, folder, filename)

Saves the object in folder/filename.pickle.

Return type:

None

EasyFEA.simulations.Solve_simu(simu, problemType)

Solving the simulation’s problem according to the resolution type.

class EasyFEA.simulations._Simu(mesh, model, verbosity=True, useIterativeSolvers=True)

Bases: _IObserver, Updatable, ABC

The following classes inherit from the parent class _Simu:

• ElasticSimu

• HyperElasticSimu

• PhaseFieldSimu

• BeamSimu

• ThermalSimu

• WeakFormSimu

To create new simulation classes, you can take inspiration from existing implementations.

Make sure to follow this interface.

The ThermalSimuclass is relatively simple and can serve as a good starting point.

See simulations/_thermal.py for more details.

To use the interface/inheritance, 13 methods need to be defined.

General:

• def Get_problemTypes(self) -> list[ModelType]:

• def Get_unknowns(self, problemType=None) -> list[str]:

• def Get_dof_n(self, problemType=None) -> int:

These functions provides access to the available unknowns and degrees of freedom (dofs).

Solve:

• def Get_x0(self, problemType=None):

• def Construct_local_matrix_system(self, problemType):

These functions assemble the matrix system K u + C v + M a = F.

Iterations:

• def Save_Iter(self) -> None:

• def Set_Iter(self, index=-1) -> None:

These functions are used to save or load iterations.

Results:

• def Results_Available(self) -> list[str]:

• def Result(self, result: str, nodeValues=True, iter=None) -> float | _types.FloatArray:

• def Results_Iter_Summary(self) -> tuple[list[int], list[tuple[str, _types.FloatArray]]]:

• def Results_dict_Energy(self) -> dict[str, float]:

• def Results_displacement_matrix(self) -> _types.FloatArray:

• def Results_nodesField_elementsField(self, details=False) -> tuple[list[str], list[str]]:

These functions are used to process the results.

Assembly(problemType)

Assembles the matrix system K u + C v + M a = F for the given problemType.

Return type:

tuple[csr_matrix, csr_matrix, csr_matrix, csr_matrix]

property Bc_Dirichlet: list[BoundaryCondition]

Returns a copy of the Dirichlet conditions.

property Bc_Display: list[BoundaryCondition | LagrangeCondition]

Returns a copy of the boundary conditions for display.

Bc_Init()

Initializes Dirichlet, Neumann and Lagrange boundary conditions

Return type:

None

property Bc_Lagrange: list[LagrangeCondition]

Returns a copy of the Lagrange conditions.

property Bc_Neuman: list[BoundaryCondition]

Returns a copy of the Neumann conditions.

Bc_dofs_Dirichlet(problemType=None)

Returns dofs related to Dirichlet conditions.

Return type:

ndarray[tuple[Any, ...], dtype[TypeVar(IntType, bound= Union[integer, int])]]

Bc_dofs_Neumann(problemType=None)

Returns dofs related to Neumann conditions.

Return type:

ndarray[tuple[Any, ...], dtype[TypeVar(IntType, bound= Union[integer, int])]]

Bc_dofs_known_unknown(problemType)

Returns known and unknown dofs.

Return type:

tuple[ndarray[tuple[Any, ...], dtype[TypeVar(IntType, bound= Union[integer, int])]], ndarray[tuple[Any, ...], dtype[TypeVar(IntType, bound= Union[integer, int])]]]

Bc_dofs_nodes(nodes, unknowns, problemType=None)

Returns degrees of freedom associated with the nodes, based on the problem type and unknowns.

Parameters:

• nodes (_types.IntArray) – nodes.

• unknowns (list) – unknowns (e.g [“x”,”y”,”rz”])

• problemType (str) – Problem type.

Returns:

Degrees of freedom.

Return type:

_types.IntArray

Bc_values_Dirichlet(problemType=None)

Returns dofs values related to Dirichlet conditions.

Return type:

ndarray[tuple[Any, ...], dtype[floating]]

Bc_values_Neumann(problemType=None)

Returns dofs values related to Neumann conditions.

Return type:

ndarray[tuple[Any, ...], dtype[floating]]

Bc_vector_Dirichlet(problemType=None)

Returns a vector filled with Dirichlet boundary conditions values.

Return type:

ndarray[tuple[Any, ...], dtype[floating]]

Bc_vector_Neumann(problemType=None)

Returns a vector filled with Neuman boundary conditions values.

Return type:

ndarray[tuple[Any, ...], dtype[floating]]

abstractmethod Construct_local_matrix_system(problemType)

Construct the local matrix system K u + C v + M a = F for the given problem.

Return type:

tuple[Optional[FeArray], Optional[FeArray], Optional[FeArray], Optional[FeArray]]

Get_K_C_M_F(problemType=None)

Returns the assembled matrices of K u + C v + M a = F for the given problem.

Return type:

tuple[csr_matrix, csr_matrix, csr_matrix, csr_matrix]

Get_contact(masterMesh, slaveNodes=None, masterNodes=None)

Returns the simulation nodes detected in the master mesh with the associated displacement matrix to the interface.

Parameters:

• masterMesh (Mesh) – master mesh

• slavenodes (_types.IntArray, optional) – slave nodes, by default None

• masternodes (_types.IntArray, optional) – master nodes, by default None

Returns:

nodes, displacementMatrix

Return type:

tuple[_types.IntArray, _types.FloatArray]

abstractmethod Get_dof_n(problemType=None)

Returns the number of degrees of freedom per node.

Return type:

int

Get_lb_ub(problemType)

Returns the lower bound and upper bound.

Return type:

tuple[ndarray[tuple[Any, ...], dtype[floating]], ndarray[tuple[Any, ...], dtype[floating]]]

abstractmethod Get_problemTypes()

Returns the problem types available through the simulation.

Return type:

list[ModelType]

abstractmethod Get_unknowns(problemType=None)

Returns a list of unknowns available in the simulation.

Return type:

list[str]

abstractmethod Get_x0(problemType=None)

Returns the solution from the previous iteration.

Return type:

ndarray[tuple[Any, ...], dtype[floating]]

Need_Update(value=True)

Sets whether the simulation needs to reconstruct matrices K, C, M and F.

property Niter: int

Number of iterations

abstractmethod Result(option, nodeValues=True, iter=None)

Returns the result. Use Results_Available() to know the available results.

Return type:

Union[ndarray[tuple[Any, ...], dtype[floating]], float]

abstractmethod Results_Available()

Returns a list of available results in the simulation.

Return type:

list[str]

Results_Get_Bc_Summary()

Returns the simulation loading summary.

Return type:

str

Results_Get_Iteration_Summary()

Returns the iteration’s summary.

Return type:

str

abstractmethod Results_Iter_Summary()

Returns the values to be displayed in Plot_Iter_Summary.

Return type:

tuple[list[int], list[tuple[str, ndarray[tuple[Any, ...], dtype[floating]]]]]

Results_Reshape_values(values, nodeValues)

Reshapes input values based on whether they are stored at nodes or elements.

Parameters:

• values (_types.FloatArray) – Input values to reshape.

• nodeValues (bool) – If True, the output will represent values at nodes; if False, values on elements will be derived.

Returns:

Reshaped values on nodes or elements.

Return type:

_types.FloatArray

Raises:

Exception – Raised if unexpected conditions occur during the calculation.

Results_Set_Bc_Summary()

Sets the simulation loading summary.

Return type:

None

Results_Set_Iteration_Summary()

Sets the iteration’s summary.

Return type:

None

abstractmethod Results_dict_Energy()

Returns a dictionary containing the names and values of the calculated energies.

Return type:

dict[str, float]

abstractmethod Results_displacement_matrix()

Returns displacements as a matrix [dx, dy, dz] (Nn,3).

Return type:

ndarray[tuple[Any, ...], dtype[floating]]

abstractmethod Results_nodeFields_elementFields(details=False)

Returns lists of nodesFields and elementsFields displayed in paraview.

Return type:

tuple[list[str], list[str]]

Save(folder, filename='simulation', additionalInfos='')

Saves the simulation and its summary in the folder. Saves the simulation as ‘filename.pickle’.

Return type:

None

abstractmethod Save_Iter()

Saves iteration results in _results.

Return type:

dict[str, Any]

abstractmethod Set_Iter(iter=-1, resetAll=False)

Sets the simulation to the specified iteration (usually the last one) and then reset the required variables if necessary (resetAll).

Returns the simulation results dictionary.

Return type:

dict

Solve()

Computes the solution field for the current boundary conditions.

Returns:

The solution of the simulation.

Return type:

_types.FloatArray

Solver_Set_Elliptic_Algorithm()

Sets the algorithm’s resolution properties for an elliptic problem.

Used to solve K u = F.

Return type:

None

Solver_Set_Hyperbolic_Algorithm(dt, beta=0.25, gamma=0.5, algo=AlgoType.newmark, alpha=0.5)

Sets the algorithm’s resolution properties for a Hyperbolic problem.

Used to solve K u + C v + M a = F.

Parameters:

• dt (float) – The time increment.

• beta (float, optional) – The coefficient beta, by default 1/4.

• gamma (float, optional) – The coefficient gamma, by default 1/2.

• algo (AlgoType, optional) –

  Algo used to solve K u + C v + M a = F, by default AlgoType.newmark

  K u_np1 + C v_np1 + M a_np1 = F_np1.

• alpha (float, optional) – The coefficient alpha, by default 1/2.

Return type:

None

Solver_Set_Parabolic_Algorithm(dt, alpha=0.5)

Sets the algorithm’s resolution properties for a parabolic problem.

Used to solve K u_np1 + C v_np1 = F_np1 with:

u_np1 = u_n + dt v_npa

Parameters:

• dt (float) – The time increment.

• alpha (float, optional) –

  The alpha criterion, by default 1/2

  • 0 -> Forward Euler

  • 1 -> Backward Euler

  • 1/2 -> midpoint

Return type:

None

add_dirichlet(nodes, values, unknowns, problemType=None, description='')

Adds Dirichlet’s boundary conditions.

Parameters:

• nodes (_types.IntArray) – nodes

• values (list) –

  list of values that can contains floats, arrays or functions or functions.

  e.g [10, lambda x,y,z: 10*x - 20*y + x*z, _types.FloatArray]

  The functions use the x, y and z nodes coordinates.

  Please note that the functions must take 3 input parameters in the order x, y, z, whether the problem is 1D, 2D or 3D.

• unknowns (list[str]) – unknowns where values will be applied (e.g [‘y’, ‘x’])

• problemType (ModelType, optional) – problem type, if not specified, we take the basic problem of the problem

• description (str, optional) – Description of the condition, by default “”.

Return type:

None

add_lineLoad(nodes, values, unknowns, problemType=None, description='')

Adds a linear load.

Parameters:

• nodes (_types.IntArray) – nodes

• values (list) –

  list of values that can contain floats, arrays or functions or lambda functions.

  e.g = [10, lambda x,y,z: 10*x - 20*y + x*z, _types.FloatArray]

  functions use x, y and z integration points coordinates (x,y,z are in this case arrays of dim (e,p))

  Please note that the functions must take 3 input parameters in the order x, y, z, whether the problem is 1D, 2D or 3D.

• unknowns (list[str]) – unknowns where values will be applied (e.g [‘y’, ‘x’])

• problemType (ModelType, optional) – problem type, if not specified, we take the basic problem of the problem

• description (str, optional) – Description of the condition, by default “”.

Return type:

None

add_neumann(nodes, values, unknowns, problemType=None, description='')

Adds Neumann’s boundary conditions.

Parameters:

• nodes (_types.IntArray) – nodes

• values (list) –

  list of values that can contains floats, arrays or functions or functions.

  e.g [10, lambda x,y,z: 10*x - 20*y + x*z, _types.FloatArray]

  The functions use the x, y and z nodes coordinates.

  Please note that the functions must take 3 input parameters in the order x, y, z, whether the problem is 1D, 2D or 3D.

• unknowns (list[str]) – unknowns where values will be applied (e.g [‘y’, ‘x’])

• problemType (ModelType, optional) – problem type, if not specified, we take the basic problem of the problem

• description (str, optional) – Description of the condition, by default “”.

Return type:

None

add_pressureLoad(nodes, magnitude, problemType=None, description='')

Adds a pressure.

Parameters:

• nodes (_types.IntArray) – nodes. (must belong to the edge of the mesh.)

• magnitude (float) – pressure magnitude

• problemType (str, optional) – problem type, if not specified, we take the basic problem of the problem

• description (str, optional) – Description of the condition, by default “”.

Return type:

None

add_surfLoad(nodes, values, unknowns, problemType=None, description='')

Adds a surface load.

Parameters:

• nodes (_types.IntArray) – nodes

• values (list) –

  list of values that can contain floats, arrays or functions or lambda functions.

  e.g = [10, lambda x,y,z: 10*x - 20*y + x*z, _types.FloatArray]

  functions use x, y and z integration points coordinates (x,y,z are in this case arrays of dim (e,p))

  Please note that the functions must take 3 input parameters in the order x, y, z, whether the problem is 1D, 2D or 3D.

• unknowns (list[str]) – unknowns where values will be applied (e.g [‘y’, ‘x’])

• problemType (ModelType, optional) – problem type, if not specified, we take the basic problem of the problem

• description (str, optional) – Description of the condition, by default “”.

Return type:

None

add_volumeLoad(nodes, values, unknowns, problemType=None, description='')

Adds a volumetric load.

Parameters:

• nodes (_types.IntArray) – nodes

• values (list) –

  list of values that can contain floats, arrays or functions or lambda functions.

  e.g = [10, lambda x,y,z: 10*x - 20*y + x*z, _types.FloatArray]

  functions use x, y and z integration points coordinates (x,y,z are in this case arrays of dim (e,p))

  Please note that the functions must take 3 input parameters in the order x, y, z, whether the problem is 1D, 2D or 3D.

• unknowns (list[str]) – unknowns where values will be applied (e.g [‘y’, ‘x’])

• problemType (ModelType, optional) – problem type, if not specified, we take the basic problem of the problem

• description (str, optional) – Description of the condition, by default “”.

Return type:

None

property algo: AlgoType

The algorithm used to solve the problem.

(elliptic, parabolic, hyperbolic) see:

• Solver_Set_Elliptic_Algorithm()

K u = F - Solver_Set_Parabolic_Algorithm()

K u + C v = F - Solver_Set_Hyperbolic_Algorithm()

K u + C v + M a = F

property center: ndarray[tuple[Any, ...], dtype[floating]]

Center of mass / barycenter / inertia center

property dim: int

simulation’s dimension

property isNonLinear

Returns whether the simulation is non linear.

property mass: float

property mesh: Mesh

simulation’s mesh.

property model: _IModel

model used

property problemType: ModelType

Get the simulation problem type.

property results: list[dict]

Returns a copy of the list of dictionary containing the results from each iteration.

rho

mass density

property solver: str

Solver used to solve the simulation.

property useIterativeSolvers: bool

Iterative solvers can be used.

This module contains all available simulation classes.

class EasyFEA.Simulations.BeamSimu(mesh, model, verbosity=False, useIterativeSolvers=True)

Construct_local_matrix_system(problemType)

Construct the local matrix system K u + C v + M a = F for the given problem.

Get_dof_n(problemType=None)

Returns the number of degrees of freedom per node.

Return type:

int

Get_problemTypes()

Returns the problem types available through the simulation.

Return type:

list[ModelType]

Get_unknowns(problemType=None)

Returns a list of unknowns available in the simulation.

Return type:

list[str]

Get_x0(problemType=None)

Returns the solution from the previous iteration.

Result(result, nodeValues=True, iter=None)

Returns the result. Use Results_Available() to know the available results.

Return type:

Union[ndarray[tuple[Any, ...], dtype[floating]], float]

Results_Available()

Returns a list of available results in the simulation.

Return type:

list[str]

Results_Get_Iteration_Summary()

Returns the iteration’s summary.

Return type:

str

Results_Iter_Summary()

Returns the values to be displayed in Plot_Iter_Summary.

Return type:

tuple[list[int], list[tuple[str, ndarray[tuple[Any, ...], dtype[floating]]]]]

Results_dict_Energy()

Returns a dictionary containing the names and values of the calculated energies.

Return type:

dict[str, float]

Results_displacement_matrix()

Returns displacements as a matrix [dx, dy, dz] (Nn,3).

Return type:

ndarray[tuple[Any, ...], dtype[floating]]

Results_nodeFields_elementFields(details=False)

Returns lists of nodesFields and elementsFields displayed in paraview.

Return type:

tuple[list[str], list[str]]

Save_Iter()

Saves iteration results in _results.

Set_Iter(iter=-1, resetAll=False)

Sets the simulation to the specified iteration (usually the last one) and then reset the required variables if necessary (resetAll).

Returns the simulation results dictionary.

Return type:

dict

add_connection(nodes, unknowns, description)

Connects beams together in the specified unknowns.

Parameters:

• nodes (_types.IntArray) – nodes

• unknowns (list[str]) – unknowns

• description (str) – description

add_connection_fixed(nodes, description='Fixed')

Adds a fixed connection.

Parameters:

• nodes (_types.IntArray) – nodes

• description (str, optional) – description, by default “Fixed”

add_connection_hinged(nodes, unknowns=[''], description='Hinged')

Adds a hinged connection.

Parameters:

• nodes (_types.IntArray) – nodes

• unknowns (list, optional) – unknowns, by default [‘’]

• description (str, optional) – description, by default “Hinged”

add_surfLoad(nodes, values, unknowns, problemType=None, description='')

Adds a surface load.

Parameters:

• nodes (_types.IntArray) – nodes

• values (list) –

  list of values that can contain floats, arrays or functions or lambda functions.

  e.g = [10, lambda x,y,z: 10*x - 20*y + x*z, _types.FloatArray]

  functions use x, y and z integration points coordinates (x,y,z are in this case arrays of dim (e,p))

  Please note that the functions must take 3 input parameters in the order x, y, z, whether the problem is 1D, 2D or 3D.

• unknowns (list[str]) – unknowns where values will be applied (e.g [‘y’, ‘x’])

• problemType (ModelType, optional) – problem type, if not specified, we take the basic problem of the problem

• description (str, optional) – Description of the condition, by default “”.

add_volumeLoad(nodes, values, unknowns, problemType=None, description='')

Adds a volumetric load.

Parameters:

• nodes (_types.IntArray) – nodes

• values (list) –

  list of values that can contain floats, arrays or functions or lambda functions.

  e.g = [10, lambda x,y,z: 10*x - 20*y + x*z, _types.FloatArray]

  functions use x, y and z integration points coordinates (x,y,z are in this case arrays of dim (e,p))

  Please note that the functions must take 3 input parameters in the order x, y, z, whether the problem is 1D, 2D or 3D.

• unknowns (list[str]) – unknowns where values will be applied (e.g [‘y’, ‘x’])

• problemType (ModelType, optional) – problem type, if not specified, we take the basic problem of the problem

• description (str, optional) – Description of the condition, by default “”.

property center: ndarray[tuple[Any, ...], dtype[floating]]

Center of mass / barycenter / inertia center

property displacement: ndarray[tuple[Any, ...], dtype[floating]]

Displacement vector field.

1D [uxi, …]

2D [uxi, uyi, rzi, …]

3D [uxi, uyi, uzi, rxi, ryi, rzi, …]

property structure: BeamStructure

Beam structure.

class EasyFEA.Simulations.ElasticSimu(mesh, model, verbosity=False, useIterativeSolvers=True)

Construct_local_matrix_system(problemType)

Construct the local matrix system K u + C v + M a = F for the given problem.

Get_dof_n(problemType=None)

Returns the number of degrees of freedom per node.

Return type:

int

Get_problemTypes()

Returns the problem types available through the simulation.

Return type:

list[ModelType]

Get_unknowns(problemType=None)

Returns a list of unknowns available in the simulation.

Return type:

list[str]

Get_x0(problemType=None)

Returns the solution from the previous iteration.

Result(result, nodeValues=True, iter=None)

Returns the result. Use Results_Available() to know the available results.

Return type:

Union[ndarray[tuple[Any, ...], dtype[floating]], float]

Results_Available()

Returns a list of available results in the simulation.

Return type:

list[str]

Results_Get_Iteration_Summary()

Returns the iteration’s summary.

Return type:

str

Results_Iter_Summary()

Returns the values to be displayed in Plot_Iter_Summary.

Return type:

tuple[list[int], list[tuple[str, ndarray[tuple[Any, ...], dtype[floating]]]]]

Results_dict_Energy()

Returns a dictionary containing the names and values of the calculated energies.

Return type:

dict[str, float]

Results_displacement_matrix()

Returns displacements as a matrix [dx, dy, dz] (Nn,3).

Return type:

ndarray[tuple[Any, ...], dtype[floating]]

Results_nodeFields_elementFields(details=False)

Returns lists of nodesFields and elementsFields displayed in paraview.

Return type:

tuple[list[str], list[str]]

Save_Iter()

Saves iteration results in _results.

Set_Iter(iter=-1, resetAll=False)

Sets the simulation to the specified iteration (usually the last one) and then reset the required variables if necessary (resetAll).

Returns the simulation results dictionary.

Return type:

dict

Set_Rayleigh_Damping_Coefs(coefM=0.0, coefK=0.0)

Sets damping coefficients ( C = coefK * K + coefM * M ).

property accel: ndarray[tuple[Any, ...], dtype[floating]]

Acceleration vector field.

2D [axi, ayi, …]

3D [axi, ayi, azi, …]

property displacement: ndarray[tuple[Any, ...], dtype[floating]]

Displacement vector field.

2D [uxi, uyi, …]

3D [uxi, uyi, uzi, …]

property material: _Elas

elastic material

property speed: ndarray[tuple[Any, ...], dtype[floating]]

Velocity vector field.

2D [vxi, vyi, …]

3D [vxi, vyi, vzi, …]

class EasyFEA.Simulations.HyperElasticSimu(mesh, model, tolConv=1e-05, maxIter=20, verbosity=False, useIterativeSolvers=True)

Construct_local_matrix_system(problemType)

Construct the local matrix system K u + C v + M a = F for the given problem.

Get_dof_n(problemType=None)

Returns the number of degrees of freedom per node.

Return type:

int

Get_problemTypes()

Returns the problem types available through the simulation.

Get_unknowns(problemType=None)

Returns a list of unknowns available in the simulation.

Return type:

list[str]

Get_x0(problemType=None)

Returns the solution from the previous iteration.

Result(result, nodeValues=True, iter=None)

Returns the result. Use Results_Available() to know the available results.

Return type:

Union[ndarray[tuple[Any, ...], dtype[floating]], float]

Results_Available()

Returns a list of available results in the simulation.

Return type:

list[str]

Results_Iter_Summary()

Returns the values to be displayed in Plot_Iter_Summary.

Return type:

tuple[list[int], list[tuple[str, ndarray[tuple[Any, ...], dtype[floating]]]]]

Results_dict_Energy()

Returns a dictionary containing the names and values of the calculated energies.

Results_displacement_matrix()

Returns displacements as a matrix [dx, dy, dz] (Nn,3).

Return type:

ndarray[tuple[Any, ...], dtype[floating]]

Results_nodeFields_elementFields(details=False)

Returns lists of nodesFields and elementsFields displayed in paraview.

Save_Iter()

Saves iteration results in _results.

Set_Iter(iter=-1, resetAll=False)

Sets the simulation to the specified iteration (usually the last one) and then reset the required variables if necessary (resetAll).

Returns the simulation results dictionary.

property displacement: ndarray[tuple[Any, ...], dtype[floating]]

Displacement vector field.

[uxi, uyi, uzi, …]

property material: _HyperElas

hyperelastic material

class EasyFEA.Simulations.PhaseFieldSimu(mesh, model, verbosity=False, useIterativeSolvers=True)

Bc_dofs_nodes(nodes, unknowns, problemType=ModelType.elastic)

Returns degrees of freedom associated with the nodes, based on the problem type and unknowns.

Parameters:

• nodes (_types.IntArray) – nodes.

• unknowns (list) – unknowns (e.g [“x”,”y”,”rz”])

• problemType (str) – Problem type.

Returns:

Degrees of freedom.

Return type:

_types.IntArray

Construct_local_matrix_system(problemType)

Construct the local matrix system K u + C v + M a = F for the given problem.

Get_K_C_M_F(problemType=None)

Returns the assembled matrices of K u + C v + M a = F for the given problem.

Return type:

tuple[csr_matrix, csr_matrix, csr_matrix, csr_matrix]

Get_dof_n(problemType=None)

Returns the number of degrees of freedom per node.

Return type:

int

Get_lb_ub(problemType)

Returns the lower bound and upper bound.

Return type:

tuple[ndarray[tuple[Any, ...], dtype[floating]], ndarray[tuple[Any, ...], dtype[floating]]]

Get_problemTypes()

Returns the problem types available through the simulation.

Return type:

list[ModelType]

Get_unknowns(problemType=None)

Returns a list of unknowns available in the simulation.

Return type:

list[str]

Get_x0(problemType=None)

Returns the solution from the previous iteration.

Need_Update(value=True)

Sets whether the simulation needs to reconstruct matrices K, C, M and F.

Return type:

None

Result(result, nodeValues=True, iter=None)

Returns the result. Use Results_Available() to know the available results.

Return type:

Union[ndarray[tuple[Any, ...], dtype[floating]], float, None]

Results_Available()

Returns a list of available results in the simulation.

Return type:

list[str]

Results_Get_Bc_Summary()

Returns the simulation loading summary.

Return type:

str

Results_Get_Iteration_Summary()

Returns the iteration’s summary.

Return type:

str

Results_Iter_Summary()

Returns the values to be displayed in Plot_Iter_Summary.

Return type:

tuple[list[int], list[tuple[str, ndarray[tuple[Any, ...], dtype[floating]]]]]

Results_Set_Bc_Summary(config)

Sets the simulation loading summary.

Results_Set_Iteration_Summary(iter, load, unitLoad, percentage=0.0, remove=False)

Creates the iteration summary for the damage problem.

Parameters:

• iter (int) – iteration

• load (float) – loading

• unitLoad (str) – loading unit

• percentage (float, optional) – percentage of simualtion performed, by default 0.0

• remove (bool, optional) – removes line from terminal after display, by default False

Return type:

str

Results_dict_Energy()

Returns a dictionary containing the names and values of the calculated energies.

Return type:

dict[str, float]

Results_displacement_matrix()

Returns displacements as a matrix [dx, dy, dz] (Nn,3).

Return type:

ndarray[tuple[Any, ...], dtype[floating]]

Results_nodeFields_elementFields(details=False)

Returns lists of nodesFields and elementsFields displayed in paraview.

Return type:

tuple[list[str], list[str]]

Save_Iter()

Saves iteration results in _results.

Set_Iter(iter=-1, resetAll=False)

Sets the simulation to the specified iteration (usually the last one) and then reset the required variables if necessary (resetAll).

Returns the simulation results dictionary.

Return type:

dict

Solve(tolConv=1.0, maxIter=500, convOption=2)

Solves the iterative damage problem using the staggered scheme.

Parameters:

• tolConv (float, optional) – threshold used to check convergence (𝜖), by default 1.0

• maxIter (int, optional) – Maximum iterations for convergence, by default 500

• convOption (int, optional) –

  • 0 -> convergence on damage np.max(np.abs(d_np1-dk)) equivalent normInf(d_np1-dk)

  • 1 -> convergence on crack energy np.abs(psi_crack_n - psi_crack_np1)/psi_crack_np1

  • 2 -> convergence on total energy np.abs(psi_tot_n - psi_tot_np1)/psi_tot_np1

  eq (39) Ambati 2015 10.1007/s00466-014-1109-y

  • 3 -> (convD <= tolConv) and (convU <= tolConv*0.999)

  eq (25) Pech 2022 10.1016/j.engfracmech.2022.108591

Returns:

u_np1, d_np1, Ku, converged

such that:

• u_np1: displacement vector field

• d_np1: damage scalar field

• Ku: displacement stiffness matrix

• converged: the solution has converged

Return type:

_types.FloatArray, _types.FloatArray, csr_matrix, bool

add_dirichlet(nodes, values, unknowns, problemType=ModelType.elastic, description='')

Adds Dirichlet’s boundary conditions.

Parameters:

• nodes (_types.IntArray) – nodes

• values (list) –

  list of values that can contains floats, arrays or functions or functions.

  e.g [10, lambda x,y,z: 10*x - 20*y + x*z, _types.FloatArray]

  The functions use the x, y and z nodes coordinates.

  Please note that the functions must take 3 input parameters in the order x, y, z, whether the problem is 1D, 2D or 3D.

• unknowns (list[str]) – unknowns where values will be applied (e.g [‘y’, ‘x’])

• problemType (ModelType, optional) – problem type, if not specified, we take the basic problem of the problem

• description (str, optional) – Description of the condition, by default “”.

add_lineLoad(nodes, values, unknowns, problemType=ModelType.elastic, description='')

Adds a linear load.

Parameters:

• nodes (_types.IntArray) – nodes

• values (list) –

  list of values that can contain floats, arrays or functions or lambda functions.

  e.g = [10, lambda x,y,z: 10*x - 20*y + x*z, _types.FloatArray]

  functions use x, y and z integration points coordinates (x,y,z are in this case arrays of dim (e,p))

  Please note that the functions must take 3 input parameters in the order x, y, z, whether the problem is 1D, 2D or 3D.

• unknowns (list[str]) – unknowns where values will be applied (e.g [‘y’, ‘x’])

• problemType (ModelType, optional) – problem type, if not specified, we take the basic problem of the problem

• description (str, optional) – Description of the condition, by default “”.

add_neumann(nodes, values, unknowns, problemType=ModelType.elastic, description='')

Adds Neumann’s boundary conditions.

Parameters:

• nodes (_types.IntArray) – nodes

• values (list) –

  list of values that can contains floats, arrays or functions or functions.

  e.g [10, lambda x,y,z: 10*x - 20*y + x*z, _types.FloatArray]

  The functions use the x, y and z nodes coordinates.

  Please note that the functions must take 3 input parameters in the order x, y, z, whether the problem is 1D, 2D or 3D.

• unknowns (list[str]) – unknowns where values will be applied (e.g [‘y’, ‘x’])

• problemType (ModelType, optional) – problem type, if not specified, we take the basic problem of the problem

• description (str, optional) – Description of the condition, by default “”.

add_pressureLoad(nodes, magnitude, problemType=ModelType.elastic, description='')

Adds a pressure.

Parameters:

• nodes (_types.IntArray) – nodes. (must belong to the edge of the mesh.)

• magnitude (float) – pressure magnitude

• problemType (str, optional) – problem type, if not specified, we take the basic problem of the problem

• description (str, optional) – Description of the condition, by default “”.

Return type:

None

add_surfLoad(nodes, values, unknowns, problemType=ModelType.elastic, description='')

Adds a surface load.

Parameters:

• nodes (_types.IntArray) – nodes

• values (list) –

  list of values that can contain floats, arrays or functions or lambda functions.

  e.g = [10, lambda x,y,z: 10*x - 20*y + x*z, _types.FloatArray]

  functions use x, y and z integration points coordinates (x,y,z are in this case arrays of dim (e,p))

  Please note that the functions must take 3 input parameters in the order x, y, z, whether the problem is 1D, 2D or 3D.

• unknowns (list[str]) – unknowns where values will be applied (e.g [‘y’, ‘x’])

• problemType (ModelType, optional) – problem type, if not specified, we take the basic problem of the problem

• description (str, optional) – Description of the condition, by default “”.

property damage: ndarray[tuple[Any, ...], dtype[floating]]

Damage scalar field.

[di, …]

property displacement: ndarray[tuple[Any, ...], dtype[floating]]

Displacement vector field.

2D [uxi, uyi, …]

3D [uxi, uyi, uzi, …]

property needUpdate: bool

The object needs to be updated.

property phaseFieldModel: PhaseField

damage model

class EasyFEA.Simulations.ThermalSimu(mesh, model, verbosity=False, useIterativeSolvers=True)

Construct_local_matrix_system(problemType)

Construct the local matrix system K u + C v + M a = F for the given problem.

Get_dof_n(problemType=None)

Returns the number of degrees of freedom per node.

Return type:

int

Get_problemTypes()

Returns the problem types available through the simulation.

Return type:

list[ModelType]

Get_unknowns(problemType=None)

Returns a list of unknowns available in the simulation.

Return type:

list[str]

Get_x0(problemType=None)

Returns the solution from the previous iteration.

Result(result, nodeValues=True, iter=None)

Returns the result. Use Results_Available() to know the available results.

Return type:

Union[ndarray[tuple[Any, ...], dtype[floating]], float]

Results_Available()

Returns a list of available results in the simulation.

Return type:

list[str]

Results_Iter_Summary()

Returns the values to be displayed in Plot_Iter_Summary.

Return type:

tuple[list[int], list[tuple[str, ndarray[tuple[Any, ...], dtype[floating]]]]]

Results_dict_Energy()

Returns a dictionary containing the names and values of the calculated energies.

Return type:

dict[str, float]

Results_displacement_matrix()

Returns displacements as a matrix [dx, dy, dz] (Nn,3).

Return type:

ndarray[tuple[Any, ...], dtype[floating]]

Results_nodeFields_elementFields(details=False)

Returns lists of nodesFields and elementsFields displayed in paraview.

Return type:

tuple[list[str], list[str]]

Save_Iter()

Saves iteration results in _results.

Set_Iter(iter=-1, resetAll=False)

Sets the simulation to the specified iteration (usually the last one) and then reset the required variables if necessary (resetAll).

Returns the simulation results dictionary.

Return type:

dict

property thermal: ndarray[tuple[Any, ...], dtype[floating]]

Scalar temperature field.

[ti, ….]

property thermalDot: ndarray[tuple[Any, ...], dtype[floating]]

Time derivative of the scalar temperature field.

[d(ti)/dt, ….]

property thermalModel: Thermal

Thermal simulation model.

class EasyFEA.Simulations.WeakFormSimu(mesh, model, isNonLinear=False, tolConv=1e-05, maxIter=20, verbosity=False, useIterativeSolvers=True)

Construct_local_matrix_system(problemType)

Construct the local matrix system K u + C v + M a = F for the given problem.

Get_dof_n(problemType=None)

Returns the number of degrees of freedom per node.

Return type:

int

Get_problemTypes()

Returns the problem types available through the simulation.

Return type:

list[ModelType]

Get_unknowns(problemType=None)

Returns a list of unknowns available in the simulation.

Return type:

list[str]

Get_x0(problemType=None)

Returns the solution from the previous iteration.

Result(result, nodeValues=True, iter=None)

Returns the result. Use Results_Available() to know the available results.

Return type:

Union[ndarray[tuple[Any, ...], dtype[floating]], float]

Results_Available()

Returns a list of available results in the simulation.

Return type:

list[str]

Results_Iter_Summary()

Returns the values to be displayed in Plot_Iter_Summary.

Return type:

tuple[list[int], list[tuple[str, ndarray[tuple[Any, ...], dtype[floating]]]]]

Results_dict_Energy()

Returns a dictionary containing the names and values of the calculated energies.

Return type:

dict[str, float]

Results_displacement_matrix()

Returns displacements as a matrix [dx, dy, dz] (Nn,3).

Return type:

ndarray[tuple[Any, ...], dtype[floating]]

Results_nodeFields_elementFields(details=False)

Returns lists of nodesFields and elementsFields displayed in paraview.

Return type:

tuple[list[str], list[str]]

Save_Iter()

Saves iteration results in _results.

Set_Iter(iter=-1, resetAll=False)

Sets the simulation to the specified iteration (usually the last one) and then reset the required variables if necessary (resetAll).

Returns the simulation results dictionary.

Return type:

dict

property a: ndarray[tuple[Any, ...], dtype[floating]]

node field a = d2udt2

property u: ndarray[tuple[Any, ...], dtype[floating]]

node field u.

property v: ndarray[tuple[Any, ...], dtype[floating]]

node field v = dudt

property weakForms: WeakForms

Weak form manager.