Analysis Module (compmech.analysis)

class compmech.analysis.Analysis(calc_fext=None, calc_k0=None, calc_fint=None, calc_kT=None)

Class that embodies all data required for linear/non-linear analysis

The parameters are described in the following tables:

Non-Linear Algorithm	Description
NL_method	str, 'NR' for the Newton-Raphson 'arc_length' for the Arc-Length method
line_search	bool, activate line_search (for Newton-Raphson methods only)
max_iter_line_search	int, maximum number of iteration attempts for the line-search algorithm
modified_NR	bool, activates the modified Newton-Raphson
compute_every_n	int, if modified_NR=True, the non-linear matrices will be updated at every \(n\) iterations
kT_initial_state	bool, tells if the tangent stiffness matrix should be calculated already at the initial state, which is required for example when initial imperfections take place

Incrementation	Description
initialInc	initial load increment size. In the arc-length method it will be the initial value for \(\lambda\)
minInc	minimum increment size; if achieved the analysis is terminated. The arc-length method will use this parameter to terminate when the minimum arc-length increment is smaller than minInc
maxInc	maximum increment size

Convergence Criteria	Description
absTOL	the convergence is achieved when the maximum residual force is smaller than this value
maxNumIter	maximum number of iteration; if achieved the load increment is bisected
too_slow_TOL	tolerance that tells if the convergence is too slow

Parameters:

calc_fextcallable, optional

Must return a 1-D array containing the external forces. Required for linear/non-linear static analysis.

calc_k0callable, optional

Must return a sparse matrix containing the linear stiffness matrix. Required for linear/non-linear static analysis.

calc_fintcallable, optional

Must return a 1-D array containing the internal forces. Required for non-linear analysis.

calc_kTcallable, optional

Must return a sparse matrix containing the tangent stiffness matrix. Required for non-linear analysis.

Returns:

incrementslist

Each time increment that achieved convergence.

cslist

The solution for each increment.

Attributes:

NL_method

absTOL

calc_fext

calc_fint

calc_k0

calc_kT

compute_every_n

cs

increments

initialInc

kT_initial_state

last_analysis

line_search

maxInc

maxNumIter

max_iter_line_search

minInc

modified_NR

relTOL

too_slow_TOL

Methods

static([NLgeom, silent])

General solver for static analyses

static(NLgeom=False, silent=False)

General solver for static analyses

Selects the specific solver based on the NL_method parameter.

Parameters:

NLgeombool

Flag to indicate whether a linear or a non-linear analysis is to be performed.

silentbool, optional

A boolean to tell whether the log messages should be printed.

compmech.analysis.freq(K, M, tol=0, sparse_solver=True, silent=False, sort=True, reduced_dof=False, num_eigvalues=25, num_eigvalues_print=5)

Frequency Analysis

Parameters:

Ksparse_matrix

Stiffness matrix. Should include initial stress stiffness matrix, aerodynamic matrix and so forth when applicable.

Msparse_matrix

Mass matrix.

tolfloat, optional

A tolerance value passed to scipy.sparse.linalg.eigs.

sparse_solverbool, optional

Tells if solver scipy.linalg.eig() or scipy.sparse.linalg.eigs() should be used.

Note

It is recommended sparse_solver=False, because it was verified that the sparse solver becomes unstable for some cases, though the sparse solver is faster.

silentbool, optional

A boolean to tell whether the log messages should be printed.

sortbool, optional

Sort the output eigenvalues and eigenmodes.

reduced_dofbool, optional

Considers only the contributions of \(v\) and \(w\) to the stiffness matrix and accelerates the run. Only effective when sparse_solver=False.

num_eigvaluesint, optional

Number of calculated eigenvalues.

num_eigvalues_printint, optional

Number of eigenvalues to print.

Returns:

The extracted eigenvalues are stored in the eigvals parameter and

the \(i^{th}\) eigenvector in the eigvecs[:, i-1] parameter.

compmech.analysis.lb(K, KG, tol=0, sparse_solver=True, silent=False, num_eigvalues=25, num_eigvalues_print=5)

Linear Buckling Analysis

It can also be used for more general eigenvalue analyzes if \(K\) is the tangent stiffness matrix of a given load state.

Parameters:

Ksparse_matrix

Stiffness matrix. Should include all constant terms of the initial stress stiffness matrix, aerodynamic matrix and so forth when applicable.

KGsparse_matrix

Initial stress stiffness matrix that multiplies the load multiplcator \(\lambda\) of the eigenvalue problem.

tolfloat, optional

A float tolerance passsed to the eigenvalue solver.

sparse_solverbool, optional

Tells if solver scipy.linalg.eigh() or scipy.sparse.linalg.eigsh() should be used.

silentbool, optional

A boolean to tell whether the log messages should be printed.

num_eigvaluesint, optional

Number of calculated eigenvalues.

num_eigvalues_printint, optional

Number of eigenvalues to print.

Notes

The extracted eigenvalues are stored in the eigvals parameter of the Panel object and the \(i^{th}\) eigenvector in the eigvecs[:, i-1] parameter.

compmech.analysis.static(K, fext, silent=False)

Static Analyses

Parameters:

Ksparse_matrix

Stiffness matrix. Should include initial stress stiffness matrix, aerodynamic matrix and so forth when applicable.

fextarray-like

Vector of external loads.

silentbool, optional

A boolean to tell whether the log messages should be printed.