Topology Optimization

namedtuple sigmaepsilon.topopt.oc.oc.OptRes(x: Iterable, obj: float, vol: float, pen: float, n: int)[source]

A tuple collecting information about an iteration block.

Fields

  1.  x (Iterable) – Alias for field number 0

  2.  obj (float) – Alias for field number 1

  3.  vol (float) – Alias for field number 2

  4.  pen (float) – Alias for field number 3

  5.  n (int) – Alias for field number 4

sigmaepsilon.topopt.oc.oc.maximize_stiffness(structure: Structure, *args, miniter: int = 50, maxiter: int = 100, p_start: float = 1.0, p_stop: float = 3.0, p_inc: float = 0.2, p_step: int = 5, q: float = 0.5, vfrac: float = 0.6, dtol: float = 0.1, r_max: Optional[float] = None, penalty: Optional[float] = None, nostop: bool = True, neighbours: Optional[Iterable] = None, guess: Optional[Iterable] = None, i_start: int = 0, **kwargs) → OptRes[source]

Performs topology optimization using an Optimality Criteria Method to maximize the stiffness of a structure, given a design space and a certain amount of material to distribute.

\begin{equation} \begin{array}{rrclcl} \displaystyle \min_{\boldsymbol{\rho}} & \mathbf{u(\boldsymbol{\rho})}^T \mathbf{f} \\ \textrm{s. t.} \\ & \mathbf{K}(\boldsymbol{\rho}) \mathbf{u(\boldsymbol{\rho})} & = & \mathbf{f} \\ & V(\boldsymbol{\rho}) - \eta V_0 & \leq & 0 & & \\ & \rho_i \in \{0, 1\} & & & & \forall i \in N \end{array} \end{equation}
Parameters

  • structure (Structure) – An instance of sigmaepsilon.solid.fem.Structure.

  • miniter (int, Optional) – The minimum number of iterations to perform. Default is 50.

  • maxiter (int, Optional) – The maximum number of iterations to perform. Default is 100.

  • p_start (float, Optional) – Initial value of the penalty on intermediate densities. Default is 1.

  • p_stop (float, Optional) – Final value of the penalty on intermediate densities. Default is 3.

  • p_inc (float, Optional) – Increment of the penalty on intermediate densities. Default is 0.2

  • p_step (int, Optional) – The number of interations it takes to increment the penalty on intermediate density values. Default is 5.

  • q (float, Optional) – Smoothing factor. Defaul is 0.5.

  • vfrac (float, Optional) – The fraction of available volume and the volume of the virgin structure. Default is 0.6.

  • dtol (float, Optional) – This controls the maximum change in the value of a design variable. Default is 0.1.

  • r_max (float, Optional) – Radius for filtering. Default is None.

  • neighbours (float, Optional) – The neighbours of the cells for filtering. Default is None.

  • guess (numpy.ndarray, Optional) – A guess on the solution. This parameter can be used to contiue a workflow. Default is None.

  • i_start (int, Optional) – Starting index for iterations. This parameter can be used to contiue a workflow. Default is 0.

  • summary (bool, Optional) – If True, a short summary about execution time and the number of iterations is available after execution as structure.summary[‘topopt’]. Default is False.

  • nostop (bool, Optional) – If True, iterations neglect all stopping criteria, those govern by mniniter and maxiter included. Default is False.

Yields

OptRes – The results of the actual iteration.

Notes

  • The function returns a generator expression.

  • This function can be used for both size and topology optimization, depending on the inputs.