4. i-SAS_iFEM

4.1. base

class ifem.base.Base(input_names, output_names, structural_model_name, cfg)

Bases: object

Abstract class for FEM and iFEM

ANALYSIS_TYPE

the analysys type.

Type

str

REQUIRED_INPUTS

the required inputs name.

Type

list[str]

MERGE_TYPE

the type of matrix to be merged

Type

list[str]

structural_model_name

structural model name.

Type

str

input

inputs.

Type

dict[str, DataFrame]

cfg

config.

Type

dict[str]

elems

list of elem(solid_1, shell_iqs4 and so on) instance.

Type

list[elem]

node_dof

node degrees of freedom (dof) per node. 1-D array of shape (node_num)

Type

ndarray[np.int64]

node_dof_elem

node degrees of freedom (dof) per element. 1-D array of shape (elem_num)

Type

ndarray[np.int64]

total_node_dof

the sum of all node degrees of freedom (dof).

Type

int

node_id2node_idx

a dictionary that maps the node_id to the index after reordering the node.

Type

dict[int, int]

node_idx2dof_idx

a dictionary that maps the index after reordering the node to an index that has a dof value of the node.

Type

dict[int, list[int]]

elem_id2elem_idx

a dictionary that maps the elem_id to the index after reordering the elements.

Type

dict[int, int]

shell_idx

## to be written

k_matrix

merged Kmatrix.

Type

csr_matrix

u_vector

the value of the node degrees of freedom (dof). 2-D array of shape (total_node_dof, 1)

Type

csc_matrix

bound

the value of constraint.

Type

nddarray

bound_idx

bound_idx[i] is True if i-th node degrees of freedom (dof) is bound, False otherwise.

Type

nddarray[bool]

postprocess_matrix

dict of postprocessed matrix.

Type

dict

ANALYSIS_TYPE = None
MERGE_TYPE = ['node_dof', 'node_dim', 'elem_dim']
REQUIRED_INPUTS = ['fe_node', 'fe_elem', 'fe_connection', 'fe_constraint']
CONNECTION_MAGIC_NUMBER = [0]
__init__(input_names, output_names, structural_model_name, cfg)

constructor

Parameters

  • input_names (dict) – dict whose keys are names of input quantity and values are names of input data.

  • output_names (dict) – dict whose keys are names of output quantity and values are names of output data.

  • structural_model_name (str, optional) – structural model name.

  • cfg (dict) – config.

static set_elems(structural_model, gcs_rotation=True)

Initialize elems and set variables. :param structural_model: structural model data in i-SAS format. :type structural_model: dict :param gcs_rotation: use gcs rotation or not. :type gcs_rotation: bool

Returns

list of elem(solid_1, shell_iqs4 and so on) instance.

Return type

elems (list[elem])

static calc_node_dof(elems, node_num, node_id)

Calculate node degrees of freedom (dof) per node and element. :param elems: list of elem(solid_1, shell_iqs4 and so on) instance. :type elems: list[elem] :param node_num: the number of node. :type node_num: int :param node_id: the list of node_id :type node_id: list[int]

Returns

node degrees of freedom (dof) per node. 1-D array of shape (node_num) node_dof_elem (ndarray[np.int64]): node degrees of freedom (dof) per element.

1-D array of shape (elem_num)

Return type

node_dof (ndarray[np.int64])

static calc_node_idx2dof_idx(node_dof)

Make a dictionary that maps the index after reordering the node to an index that has a dof value of the node. :param node_dof: node degrees of freedom (dof) per node. 1-D array of shape (node_num) :type node_dof: ndarray[np.int64]

Returns

a dictionary that maps the index after reordering the node to an

index that has a dof value of the node.

Return type

node_idx2dof_idx (dict[int, list[int]])

merge_matrix(matrices, type_row, type_col, dim=None, valid_idx=None)

Merge each element’s matrices according to type_name. :param matrices: list of matrix. matrices[i] contains the i-th element matrix. :type matrices: list[ndarray] :param type_row: type_name of row. Type is one of ‘node_dof’, ‘node_dim’, ‘elem_dim’. :type type_row: str :param type_col: type_name of colomn. Type is one of ‘node_dof’, ‘node_dim’, ‘elem_dim’. :type type_col: str :param dim: the dimension of each element or node.

This is used if the type_name contains ‘node_dim’ or ‘elem_dim’.

Parameters

valid_idx (list[int]) – the index of matrices that are used to merge.

Returns

merged matrix. Row and column lengths are calculated based on type_name.

Return type

merged_matrix (csr_matrix)

get_rc_num(type_name, dim=None)

Get row or colomn lengths of merged matrix according to type_name. :param type_name: type_name. Type is one of ‘node_dof’, ‘node_dim’, and ‘elem_dim’. :type type_name: str :param dim: the dimension of each element or node.

This is used if the type_name contains ‘node_dim’ or ‘elem_dim’.

Returns

row or colomn lengths of merged matrix.

Return type

rc_num (int)

get_el_num(type_row, type_col, dim=None)

Get the number of elements in the matrix for each element :param type_row: type_name of row. Type is one of ‘node_dof’, ‘node_dim’, ‘elem_dim’. :type type_row: str :param type_col: type_name of colomn. Type is one of ‘node_dof’, ‘node_dim’, ‘elem_dim’. :type type_col: str :param dim: the dimension of each element or node.

This is used if the type_name contains ‘node_dim’ or ‘elem_dim’.

Returns

the number of elements in the matrix for each element.

Return type

el_num (ndarray)

get_rc(type_name, i, idx=None, dim=3)

Get the index of row or colomn of self.elements[i]. :param type_name: type_name. Type is one of ‘node_dof’, ‘node_dim’, and ‘elem_dim’. :type type_name: str :param i: index of self.elements. :type i: int :param idx: index when type_name is ‘node_dof’ :type idx: ndarray[int] :param dim: the dimension of each element or node.

This is used if the type_name contains ‘node_dim’ or ‘elem_dim’.

Returns

the index of row or colomn of self.elements[i].

Return type

rc (ndarray[int])

merge_vector(matrices, dim, valid_idx=None)

Merge each element’s matrices according to type_name. :param matrices: list of matrix. matrices[i] contains the i-th element matrix. :type matrices: list[ndarray] :param dim: the dimension of each element or node. :type dim: int :param valid_idx: the index of matrices that are used to merge. :type valid_idx: list[int]

Returns

merged vector. 2-D array of shape (node_num*dim, 1)

Return type

merged_vector (csr_matrix)

load_structural_model(structural_model)

Load structural model.

check_structural_model(structural_model)

Check that the required input is included.

set_bound()

Set the element’s constraints to the instance.

calc_d_matrix_elem()

Calculate the Dmatrix of each element.

calc_postprocess_matrix(result_fields=None, update=True)

Compute the matrix needed to obtain the result. :param result_fields: the field of results wanted to be obtained. :type result_fields: set :param update: True if self.postprocess_matrix is needed to update, False otherwise. :type update: bool

postprocess(u_vector, result_fields=None)

Compute the result. :param result_fields: the field of results wanted to be obtained. :type result_fields: set

set_coord_sys()

To create the output_metadata, set the appropriate coordinate system corresponding to the key in output_names.

make_structural_model_connections()

Make analysis_structural_model_connections.

load_input_info(output_metadata, structural_model_connections)

Load information about the data to process the data :param output_metadata: output metadata. :type output_metadata: pd.DataFrame :param structural_model_connections: connections between data and structural model. :type structural_model_connections: dict

get_data_name_dim()

Createa a dict in which the data_name is a key and the dimension is value. :returns: a dict in which the data_name is a key and the dimension is value. :rtype: data_name_dim (dict)

get_data_name_data_type()

Createa a dict in which the data_name is a key and the data type. :returns: a dict in which the data_name is a key and the data type. :rtype: data_name_data_type (dict)

load_info(data_name_dim, data_name_data_type, output_metadata, structural_model_connections)

Load information about input data. :param data_name_dim: a dict in which the data_name is a key and the dimension is value. :type data_name_dim: dict :param data_name_data_type: a dict in which the data_name is a key and the data type. :type data_name_data_type: dict :param output_metadata: output metadata. :type output_metadata: pd.DataFrame :param structural_model_connections: connections between data and structural model. :type structural_model_connections: dict

Returns

a dict in which the data_name is a key and the information about the data.

Return type

data_name_data_info (dict)

load_output_info(model_connections, data_type)

Load output information. :param model_connections: connections between data and structural model. :type model_connections: pd.DataFrame :param data_type: data type. :type data_type: str

check_connection(self_connection, connection, data_type)

Test whether their contents are equal when given analysis_structural_model_connection for different dimensions of the same data type. :param self_connection: analysis_structural_model_connection already set. :type self_connection: pd.DataFrame :param connection: analysis_structural_model_connection given. :type connection: pd.DataFrame :param data_type: data type. :type data_type: str

solve(k_matrix, f_vector)

Solving the linear equation of Ku = F to find the value of u vector. :param k_matrix: Kmatrix or iKmatrix. 2-D array of shape (total_node_dof, total_node_dof) :type k_matrix: csr_matrix :param f_vector: force vector or iFvector. 2-D array of shape (total_node_dof, 1) :type f_vector: csc_matrix

Returns

displacement of each degree of freedom of nodes.

2-D array of shape (total_node_dof, 1)

f_vector (ndarray): force vector or iFvector. 2-D array of shape (total_node_dof, 1)

Return type

u_vector (ndarray)

arrange_data(data)

Arrange the data along the time resolution. :param data: data calculated before :type data: dict

Returns

the data along the time resolution start_time_stamps (list[int]): start time stamps used in data end_time_stamps (list[int]): end time stamps used in data

Return type

time_data (dict)

set_output_transformer()
transform_output(output)

transform coordinate system of output :param output: The value of output where the global coordinate system is expected is also the

value of the local coordinate system

Returns

transformed result.

Return type

output (dict)

4.2. fem

class ifem.fem.Fem(input_names, output_names, structural_model_name, cfg)

Bases: ifem.base.Base

ANALYSIS_TYPE = 'FEM'
__init__(input_names, output_names, structural_model_name, cfg)

constructor

Parameters

  • input_names (dict) – dict whose keys are names of input quantity and values are names of input data.

  • output_names (dict) – dict whose keys are names of output quantity and values are names of output data.

  • structural_model_name (str, optional) – structural model name.

  • cfg (dict) – config.

calc_k_matrix()

Calculate the Kmatrix of each element and merge them.

calc_k_matrix_elem()

Calculate the Kmatrix of each element.

merge_k_matrix()

Merge the Kmatrices of each element.

calc_f_coef()

Calculate the coefficients on the surface force and the coefficients on the volume force of each element and merge them.

calc_f_coef_elem()

Calculate the coefficients on the surface force and the coefficients on the volume force of each element.

merge_f_coef()

Merge the coefficients on the surface force and the coefficients on the volume force in each element.

calc_f_vector(data)

Compute a force vector with surface loads, body loads, and point loads. :param data: information about the load at a specific time. :type data: dict

Returns

force vector. 2-D array of shape (total_node_dof, 1)

Return type

f_vector (csc_matrix)

calc_ft_vector(data)

Compute a force vector with surface loads. :param data: information about the load at a specific time. :type data: dict

Returns

force vector of surface loads. 2-D array of shape (total_node_dof, 1)

Return type

ft_vector (csc_matrix)

calc_fg_vector(data)

Compute a force vector with body loads. :param data: information about the load at a specific time. :type data: dict

Returns

force vector of body loads. 2-D array of shape (total_node_dof, 1)

Return type

fg_vector (csc_matrix)

calc_fp_vector(data)

Compute a force vector with point loads. :param data: information about the load at a specific time. :type data: dict

Returns

force vector of point loads. 2-D array of shape (total_node_dof, 1)

Return type

fp_vector (csc_matrix)

calc_force_t(data)

Compute a force vector with surface loads for each surface on elems. :param data: information about the load at a specific time. :type data: dict

Returns

a force vector with surface loads for each surface on elems.

each force vector is 2-D array of shape (total_elems * 3, 1)

Return type

force_t (dict)

calc_force_g(data)

Compute a force vector with body loads on the elements. :returns: a force with body loads on the elements. 2-D array of shape (total_elems * 3, 1) :rtype: force_g (csc_matrix)

set_model(output_metadata, sensors, structural_models, structural_model_connections, streaming)

set model and calculate intermediate values

Parameters

  • output_metadata (pd.DataFrame) – output metadata.

  • sensors (dict) – sensors.

  • structural_models (dict) – structural models.

  • structural_model_connections (dict) – connections between data and structural model.

  • streaming (bool) – if true, run as structural_analysis.

__call__(data)

Calculate various values based on the data. :param data: data calculated before :type data: dict

Returns

calculated result. used_timestamp (dict):

used timestamp for each input data. Dict has two keys, ‘s’ as strating timestamp and ‘e’ as end time stamp, and the value is 1d-array of the timestamp used to caclulate output, whose length is the same as the length of output.

Return type

results (dict)

4.3. ifem

class ifem.ifem.IFem(input_names, output_names, structural_model_name, cfg)

Bases: ifem.base.Base

ANALYSIS_TYPE = 'iFEM'
__init__(input_names, output_names, structural_model_name, cfg)

constructor

Parameters

  • input_names (dict) – dict whose keys are names of input quantity and values are names of input data.

  • output_names (dict) – dict whose keys are names of output quantity and values are names of output data.

  • structural_model_name (str, optional) – structural model name.

  • cfg (dict) – config.

calc_i_k_matrix()

Calculate the iKmatrix of each element and merge them.

calc_i_k_matrix_elem()

Calculate the iKmatrix of each element.

merge_i_k_matrix()

Merge the iKmatrices of each element.

calc_i_f_coef()

Calculate the iFcoef of each element and merge them.

calc_i_f_coef_elem()

Calculate the iFcoef of each element.

merge_i_f_coef()

Merge the the iFcoef of each element.

calc_i_f_vector(data)

Compute iFvector. :param data: information about the strain at a specific time. :type data: dict

Returns

iFvector. 2-D array of shape (total_node_dof, 1)

Return type

i_f_vector (csr_matrix)

calc_strain(data)

Compute strain. :param data: information about the strain at a specific time. :type data: dict

Returns

strain values on elems. 2-D array of shape (total_elems * 6, 1)

Return type

strain (csc_matrix)

calc_strain_sep(data)

Compute strain. :param data: information about the strain at a specific time. :type data: dict

Returns

separated strain values on elems. 1-D array of shape (total_elems * 3) strain_sep_k (ndarray): separated strain values on elems. 1-D array of shape (total_elems * 3) strain_sep_g (ndarray): separated strain values on elems. 1-D array of shape (total_elems * 2)

Return type

strain_sep_e (ndarray)

load_strain_sep(data, strain_key)

Load strain information. :param data: information about the strain at a specific time. :type data: dict :param strain_key: the name of the key of the strain. :type strain_key: str

Returns

strain values on elems. 2-D array of shape (6, total_elems) r3 (ndarray): r3 values of elems. 2-D array of shape (total_elems)

Return type

strain_sep (ndarray)

set_model(output_metadata, sensors, structural_models, structural_model_connections, streaming)

set model and calculate intermediate values

Parameters

  • output_metadata (pd.DataFrame) – output metadata.

  • sensors (dict) – sensors.

  • structural_models (dict) – structural models.

  • structural_model_connections (dict) – connections between data and structural model.

  • streaming (bool) – if true, run as structural_analysis.

set_input_transformer(data_type, elem_ids, coord_sys)

Set coordinate system transformer of input strain :param data_type: data type. :type data_type: str :param elem_ids: id of elements. :type elem_ids: list :param coord_sys: coordinate system. :type coord_sys: str

transform_input(data)
__call__(data)

Calculate various values based on the data. :param data: data calculated before :type data: dict

Returns

calculated result. used_timestamp (dict):

used timestamp for each input data. Dict has two keys, ‘s’ as strating timestamp and ‘e’ as end time stamp, and the value is 1d-array of the timestamp used to caclulate output, whose length is the same as the length of output.

Return type

results (dict)

4.4. interface

class ifem.interface.Interface(instance_name, input_names, output_names, structural_model_name=None, **kwargs)

Bases: object

interface class of analysis solver

package_name = None
structural_model_required = False
__init__(instance_name, input_names, output_names, structural_model_name=None, **kwargs)

initialization of interface class of analysis solver

Parameters

  • instance_name (str) – instance name.

  • input_names (dict) – dict whose keys are names of input quantity and values are names of input data.

  • output_names (dict) – dict whose keys are names of output quantity and values are names of output data.

  • structural_model_name (str, optional) – structural model name.

  • **kwargs – Arbitrary keyword arguments.

Example

>>> input_names = {'strain': ['rosette_strain_x', 'rosette_strain_y', 'rosette_strain_xy']}
>>> output_names = {'displacement': ['analysis_displacement_z'], 'stress':['analysis_stress_x']}
>>> interface = Interface(input_names, output_names, 'beam')
abstract set_project(project_name)
Parameters

project_name (str) – project name.

set_model(output_metadata, sensors, structural_models, structural_model_connections, streaming=False)

set structural model

Parameters

  • output_metadata (pd.DataFrame) – output metadata.

  • sensors (dict) – sensors.

  • structural_models (dict) – structural models.

  • structural_model_connections (dict) – connections between data and structural model.

  • streaming (bool, optional) – if true, run as structural_analysis.

Returns

containing followings

dict: information on instance of this model. pandas.DataFrame: output metadata of this model. dict: connections between output data of this model and structural model.

Return type

tuple

__call__(input_data)

calculate quantity of state

Parameters

input_data (dict) – data calculated before

Returns

containing:

dict: analysis data. pandas.DataFrame: timestamp used. The length is the same as analysis data.

Return type

tuple

exit()

exit solver

4.5. interface_fem

class ifem.interface_fem.InterfaceFem(instance_name, input_names, output_names, structural_model_name=None, **kwargs)

Bases: ifem.interface.Interface

package_name = 'fem'
__init__(instance_name, input_names, output_names, structural_model_name=None, **kwargs)

initialization of interface class of analysis solver

Parameters

  • instance_name (str) – instance name.

  • input_names (dict) – dict whose keys are names of input quantity and values are names of input data.

  • output_names (dict) – dict whose keys are names of output quantity and values are names of output data.

  • structural_model_name (str, optional) – structural model name.

  • **kwargs – Arbitrary keyword arguments.

Example

>>> input_names = {'strain': ['rosette_strain_x', 'rosette_strain_y', 'rosette_strain_xy']}
>>> output_names = {'displacement': ['analysis_displacement_z'], 'stress':['analysis_stress_x']}
>>> interface = Interface(input_names, output_names, 'beam')
set_project(project_name)
Parameters

project_name (str) – project name.

4.6. interface_ifem

class ifem.interface_ifem.InterfaceIFem(instance_name, input_names, output_names, structural_model_name=None, **kwargs)

Bases: ifem.interface.Interface

package_name = 'ifem'
__init__(instance_name, input_names, output_names, structural_model_name=None, **kwargs)

initialization of interface class of analysis solver

Parameters

  • instance_name (str) – instance name.

  • input_names (dict) – dict whose keys are names of input quantity and values are names of input data.

  • output_names (dict) – dict whose keys are names of output quantity and values are names of output data.

  • structural_model_name (str, optional) – structural model name.

  • **kwargs – Arbitrary keyword arguments.

Example

>>> input_names = {'strain': ['rosette_strain_x', 'rosette_strain_y', 'rosette_strain_xy']}
>>> output_names = {'displacement': ['analysis_displacement_z'], 'stress':['analysis_stress_x']}
>>> interface = Interface(input_names, output_names, 'beam')
set_project(project_name)
Parameters

project_name (str) – project name.