Finite Element Analysis

FiniteElementAnalysis

class feastruct.fea.fea.FiniteElementAnalysis(nodes, elements, nfa)

Parent class for a finite element analysis.

Establishes a template for each different type of finite element analysis, e.g. frame, membrane, plate etc. and provides a number of generic methods which are useful for all types of analyses.

Variables:

• nodes (list[Node]) – Nodes used in the finite element analysis
• elements (list[FiniteElement]) – Elements used in the finite element analysis
• nfa (list[bool]) – Node freedom arrangement

__init__(nodes, elements, nfa)

Inits the FiniteElementAnalysis class.

Parameters:

• nodes (list[Node]) – List of nodes with which to initialise the class
• elements (list[FiniteElement]) – List of elements with which to initialise the class
• nfa (list[bool]) – Node freedom arrangement

create_element(element)

Creates a finite element and adds it to the Fea object.

Creates and returns a FiniteElement object ands adds it to the Fea object.

Parameters:element (FiniteElement) – Element to be added to the analysis object Returns:Element object Return type:FiniteElement

create_node(coords)

Creates a node and adds it to the Fea object.

Creates and returns a Node object and adds it to the Fea object.

Parameters:coords (list[float]) – Cartesian coordinates of the node ([x], [x, y] or [x, y, z]) Returns:Node object Return type:Node

get_node_lims()

Finds and returns the minimum and maximum x, y and z values within the current analysis.

Returns:(xmin, xmax, ymin, ymax, zmin, zmax) Return type:tuple(float)

FiniteElement

class feastruct.fea.fea.FiniteElement(nodes, material, efs)

Parent class for a finite element.

Establishes a template for each different type of finite element, e.g. frame element, membrane element, plate element etc. and provides a number of generic methods which are useful for all types of elements.

Variables:

• nodes (list[Node]) – List of node objects that define the geometry of the finite element
• material (Material) – Material object for the element
• efs (list[bool]) – Element freedom signature
• f_int (list[ForceVector]) – List of internal force vector results stored for each analysis case

__init__(nodes, material, efs)

Inits the FiniteElement class.

Parameters:

• nodes (list[Node]) – List of node objects that define the geometry of the finite element
• material (Material) – Material object for the element
• efs (list[bool]) – Element freedom signature

apply_nfa()

Applies the element freedom signature to all nodes in the element to generate a node freedom allocation.

get_buckling_results(analysis_case, buckling_mode=0)

Returns the eigenvalue corresponding to the buckling analysis defined by the analysis_case and the buckling_mode. Also returns an array of eigenvector values corresponding to each degree of freedom in the finite element.

Parameters:

• analysis_case (AnalysisCase) – Analysis case relating to the buckling analysis
• buckling_mode (int) – Buckling mode number

Returns:

Eigenvalue and eigenvectors (w, v). A tuple containing the eigenvalue w and an (n_nodes x n_dof) array of eigenvector values v.

Return type:

tuple(float, numpy.ndarray)

get_dofs()

Finds and returns a list of DoF objects corresponding to the degrees of freedom of the finite element.

Returns:A list of DoF objects, with a length of (n_nodes x n_dof) Return type:list[list[DoF]]

get_fint(analysis_case)

Returns the internal force vector relating to an AnalysisCase.

Parameters:analysis_case (AnalysisCase) – Analysis case relating to the internal force vector Returns:Internal force vector Return type:numpy.ndarray Raises:Exception – If the force vector cannot be found for the analysis_case

get_frequency_results(analysis_case, frequency_mode=0)

Returns the eigenvalue corresponding to the frequency analysis defined by the analysis_case and the frequency_mode. Also returns an array of eigenvector values corresponding to each degree of freedom in the finite element.

Parameters:

• analysis_case (AnalysisCase) – Analysis case relating to the frequency analysis
• frequency_mode (int) – Frequency mode number

Returns:

Eigenvalue and eigenvectors (w, v). A tuple containing the eigenvalue w and an (n_nodes x n_dof) array of eigenvector values v.

Return type:

tuple(float, numpy.ndarray)

get_gdof_nums()

Returns an array of global degree of freedom numbers corresponding to the degrees of freedom of the finite element.

Returns:A integer array of global degrees of freedom, with a length of (1 x n), where n is n_nodes x n_dof Return type:numpy.ndarray

get_geometric_stiff_matrix(analysis_case)

Placeholder for the get_geometric_stiff_matrix method.

Gets the geometric stiffness matrix for a FiniteElement.

Parameters:analysis_case (AnalysisCase) – Analysis case from which to extract the axial force Returns:Element geometric stiffness matrix Return type:numpy.ndarray

get_internal_actions(analysis_case)

Returns the internal actions for a FiniteElement.

Parameters:analysis_case (AnalysisCase) – Analysis case Returns:An array containing the internal actions for the element Return type:numpy.ndarray

get_mass_matrix()

Placeholder for the get_mass_matrix method.

Gets the mass matrix for a for a FiniteElement.

Returns:Element mass matrix Return type:numpy.ndarray

get_ndof()

Returns the number of active degrees of freedom for the element.

Returns:Number of active degrees of freedom for the element Return type:int

get_nodal_displacements(analysis_case)

Returns an array of the nodal displacements for each degree of freedom in the finite element for the analysis_case.

Parameters:analysis_case (AnalysisCase) – Analysis case relating to the displacement Returns:An (n_nodes x n_dof) array of degree of freedom displacements Return type:numpy.ndarray

get_node_coords()

Returns a NumPy array of the cartesian coordinates defining the geometry of the finite element.

Returns:An (n x 3) array of node coordinates, where n is the number of nodes for the given finite element Return type:numpy.ndarray

get_shape_function(xi)

Placeholder for the get_shape_function method.

Returns the value of the shape functions at xi.

Parameters:xi (float) – Position along the element Returns:Value of the shape functions at xi Return type:numpy.ndarray

get_stiffness_matrix()

Placeholder for the get_stiffness_matrix method.

Gets the stiffness matrix for a FiniteElement.

Returns:6 x 6 element stiffness matrix Return type:numpy.ndarray

save_fint(f, analysis_case)

Adds an internal force vector result to the FiniteElement.

Parameters:

• f (numpy.ndarray) – Internal force vector
• analysis_case (AnalysisCase) – Analysis case relating to the internal force vector

ForceVector

class feastruct.fea.fea.ForceVector(f, analysis_case)

Class for storing a force vector for a finite element.

Variables:

• f – Force vector (n x 1), where n is the number of dofs within the element
• analysis_case (AnalysisCase) – Analysis case relating to the displacement

Vartype:

numpy.ndarray

__init__(f, analysis_case)

Inits the ForceVector class.

Variables:f – Force vector (n x 1), where n is the number of dofs within the element Vartype:numpy.ndarray Parameters:analysis_case (AnalysisCase) – Analysis case relating to the displacement