gemseo / problems / topo_opt

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fea_disc module

Finite element analysis (FEA) for 2D topology optimization problems.

class gemseo.problems.topo_opt.fea_disc.FininiteElementAnalysis(nu=0.3, n_x=100, n_y=100, f_node=10200, f_direction=1, f_amplitude=-1, fixed_nodes=None, fixed_dir=None, name=None)[source]

Bases: MDODiscipline

Finite Element Analysis for 2D topology optimization problems.

Take in input the Young Modulus vector E and computes in output the compliance, i.e. twice the work of external forces.

Initialize self. See help(type(self)) for accurate signature.

Parameters:

  • nu (float) –

    The material Poisson’s ratio.

    By default it is set to 0.3.

  • n_x (int) –

    The number of elements in the x-direction.

    By default it is set to 100.

  • n_y (int) –

    The number of elements in the y-direction.

    By default it is set to 100.

  • f_node (int | Sequence[int]) –

    The indices of the nodes where the forces are applied.

    By default it is set to 10200.

  • f_direction (int | Sequence[int]) –

    The force direction for each f_node, either 0 for x or 1 for y.

    By default it is set to 1.

  • f_amplitude (int | Sequence[int]) –

    The force amplitude for each pair (f_node, f_direction).

    By default it is set to -1.

  • fixed_nodes (int | Sequence[int] | None) – The indices of the nodes where the structure is clamped. If None, a default value is used.

  • fixed_dir (int | Sequence[int] | None) – The clamped direction for each node, encode 0 for x and 1 for y. If None, a default value is used.

  • name (str | None) – The name of the discipline. If None, use the class name.

compute_elementary_stiffeness_matrix()[source]

Compute the elementary stiffness matrix of 1x1 quadrilateral elements.

Return type:

None

prepare_fea()[source]

Prepare the Finite Element Analysis.

Return type:

None

cache: AbstractCache | None

The cache containing one or several executions of the discipline according to the cache policy.

data_processor: DataProcessor

A tool to pre- and post-process discipline data.

exec_for_lin: bool

Whether the last execution was due to a linearization.

input_grammar: BaseGrammar

The input grammar.

jac: MutableMapping[str, MutableMapping[str, ndarray | csr_array | JacobianOperator]]

The Jacobians of the outputs wrt inputs.

The structure is {output: {input: matrix}}.

name: str

The name of the discipline.

output_grammar: BaseGrammar

The output grammar.

re_exec_policy: ReExecutionPolicy

The policy to re-execute the same discipline.

residual_variables: dict[str, str]

The output variables mapping to their inputs, to be considered as residuals; they shall be equal to zero.

run_solves_residuals: bool

Whether the run method shall solve the residuals.