pymoto.DensityFilter

class pymoto.DensityFilter(*args, nonpadding=None, **kwargs)

Standard density filter for a structured mesh in topology optimization

The filtered densities are calculated as

\(y_i = \sum_j \frac{H_{ij}}{s_i}x_j\),

where \(H_{ij}=\max \left( r - \sqrt{ (x_j - x_i)^2 + (y_j - y_i)^2 + (z_j - z_i)^2 } , 0 \right)\),

and \(s_i=\sum_j H_{ij}\).

Input Signal:

Output Signal:

Parameters:

domain (pymoto.VoxelDomain) – The finite element domain

Keyword Arguments:

radius (float or int) – The filtering radius (in absolute units of elements)
nonpadding (numpy.array[int]) – An array with indices at places where \(s_i = \max(\mathbf{s}) \: \forall\: i \notin \mathcal{N}\). For a density filter this mimics having values of 0 outside of the domain, thus emulating padding of the boundaries.

References

Bruns & Tortorelli (2001). Topology optimization of non-linear elastic structures and compliant mechanisms. Computer Methods in Applied Mechanics and Engineering, 190(26–27), 3443–3459. doi: 10.1016/S0045-7825(00)00278-4
Bourdain (2001). Filters in topology optimization. International Journal for Numerical Methods in Engineering, 50, 2143-2158. doi: 10.1002/nme.116

__init__(*args, nonpadding=None, **kwargs)

Initialize abstract base-class for linear filters

Parameters:: nonpadding (numpy.array[int], optional) – An array with indices at places where \(s_i = \max(\mathbf{s}) \: \forall\: i \notin \mathcal{N}\). For a density filter this mimics having values of 0 outside of the domain, thus emulating padding of the boundaries.

Methods

`__init__`(*args[, nonpadding])	Initialize abstract base-class for linear filters
`connect`(sig_in[, sig_out])	Connect without automatic adding to a function network
`get_input_sensitivities`([as_list])
`get_input_states`([as_list])
`get_output_sensitivities`([as_list])
`get_output_states`([as_list])
`reset`()	Reset the state of the sensitivities (they are set to zero or to None)
`response`()	Calculate the response from sig_in and output this to sig_out
`sensitivity`()	Calculate sensitivities using backpropagation

Attributes

`n_in`	Get the number of input signals
`n_out`	Get the number of output signals
`sig_in`
`sig_out`

connect(sig_in: Signal | Iterable[Signal], sig_out: Signal | Iterable[Signal] = None): Connect without automatic adding to a function network

property n_out: int

Get the number of output signals

Note: Cannot be used in the initial __call__()

reset(): Reset the state of the sensitivities (they are set to zero or to None)

sensitivity()

Calculate sensitivities using backpropagation

Based on the sensitivity we get from sig_out, reverse the process and output the new sensitivities to sig_in