Global Compliance Minimization

The total compliance minimization does design structures with maximum stiffness as is discussed at Global Compliance Minimization. An example as how to use the optimization is shown in an example optimization example.py

Density Constraints

Constraints class used to specify the density constraints of the topology optimisation problem. It contains functions for minimum and maximum element density in the upcomming iteration and the magnitude of the volume constraint function itself of the current design. This version of the code is used for the global compliance minimization.

Bram Lagerweij Aerospace Structures and Materials Department TU Delft 2018

class src_Compliance.constraints.DensityConstraint(nelx, nely, move, volume_frac, density_min=0.0, density_max=1.0)

This object relates to the constraints used in this optimization. It can be used for the MMA updatescheme to derive what the limit is for all element densities at every itteration. The class itself is not changed by the itterations.

Parameters

  • nelx (int) – Number of elements in x direction.

  • nely (int) – Number of elements in y direction.

  • move (float) – Maximum change in density of an element over 1 itteration.

  • volume_frac (float) – Maximum volume that can be filled with material.

  • volume_derivative (2D array size(1, nelx*nely)) – Sensityvity of the density constraint to the density in each element.

  • density_min (float, optional) – Minumum density, set at 0.0 if not specified.

  • density_max (float, optional) – Maximum density, set at 0.0 if not specified.

nelx

Number of elements in x direction.

Type

int

nely

Number of elements in y direction.

Type

int

move

Maximum change in density of an element over 1 itteration.

Type

float

volume_frac

Maximum volume that can be filled with material.

Type

float

volume_derivative

Sensityvity of the density constraint to the density in each element.

Type

2D array size(1, nelx*nely)

density_min

Minumum density, set at 0.0 if not specified.

Type

float, optional

density_max

Maximum density, set at 0.0 if not specified.

Type

float, optional

current_volconstrain(x)

Calculates the current magnitude of the volume constraint funcion:

\[V_{\text{constraint}} = \frac{\sum v_e X_e}{ V_{\max}}-1\]
Parameters

x (2D array size(nely, nelx)) – Density distribution of this itteration.

Returns

curvol – Curent value of the density constraint function.

Return type

float

xmax(x)

This function calculates the maximum density value of all ellements of this itteration.

Parameters

x (2D array size(nely, nelx)) – Density distribution of this itteration.

Returns

xmax – Maximum density values of this itteration after updating.

Return type

2D array size(nely, nelx)

xmin(x)

This function calculates the minimum density value of all ellements of this itteration.

Parameters

x (2D array size(nely, nelx)) – Density distribution of this itteration.

Returns

xmin – Minimum density values of this itteration for the update scheme.

Return type

2D array size(nely, nelx)

Load Cases

This file containts the Load class that allows the generation of an object that contains geometric, mesh, loads and boundary conditions that belong to the load case. This version of the code is meant for global compliance minimization.

Bram Lagerweij Aerospace Structures and Materials Department TU Delft 2018

Parent Load Case

class src_Compliance.loads.Load(nelx, nely, young, Emin, poisson)

Load parent class that contains the basic functions used in all load cases. This class and its children do cantain information about the load case conciderd in the optimisation. The load case consists of the mesh, the loads, and the boundaries conditions. The class is constructed such that new load cases can be generated simply by adding a child and changing the function related to the geometry, loads and boundaries.

Parameters

  • nelx (int) – Number of elements in x direction.

  • nely (int) – Number of elements in y direction.

  • young (float) – Youngs modulus of the materias.

  • Emin (float) – Artifical Youngs modulus of the material to ensure a stable FEA. It is used in the SIMP based material model.

  • poisson (float) – Poisson ration of the material.

nelx

Number of elements in x direction.

Type

int

nely

Number of elements in y direction.

Type

int

young

Youngs modulus of the materias.

Type

float

Emin

Artifical Youngs modulus of the material to ensure a stable FEA. It is used in the SIMP based material model.

Type

float

poisson

Poisson ration of the material.

Type

float

dim

Amount of dimensions conciderd in the problem, set at 2.

Type

int

alldofs()

Returns a list with all degrees of freedom.

Returns

all – List with numbers from 0 to the maximum degree of freedom number.

Return type

1-D list

edof()

Generates an array with the position of the nodes of each element in the global stiffness matrix.

Returns

  • edof (2-D array size(nelx*nely, 8)) – The list with all elements and their degree of freedom numbers.

  • x_list (1-D array len(nelx*nely*8*8)) – The list with the x indices of all ellements to be inserted into the global stiffniss matrix.

  • y_list (1-D array len(nelx*nely*8*8)) – The list with the y indices of all ellements to be inserted into the global stiffniss matrix.

fixdofs()

Returns a list with indices that are fixed by the boundary conditions.

Returns

fix – List with all the numbers of fixed degrees of freedom. This list is empty in this parrent class.

Return type

1-D list

force()

Returns an 1D array, the force vector of the loading condition.

Returns

f – Empy force vector.

Return type

1-D array length covering all degrees of freedom

freedofs()

Returns a list of arr indices that are not fixed

Returns

free – List containing all elemens of alldogs except those that appear in the freedofs list.

Return type

1-D list

lk(E, nu)

Calculates the local siffness matrix depending on E and nu.

Parameters

  • E (float) – Youngs modulus of the material.

  • nu (float) – Poisson ratio of the material.

Returns

ke – Local stiffness matrix.

Return type

2-D array size(8, 8)

node(elx, ely)

Calculates the topleft node number of the requested element

Parameters

  • elx (int) – X position of the conciderd element.

  • ely (int) – Y position of the conciderd element.

Returns

topleft – The node number of the top left node

Return type

int

nodes(elx, ely)

Calculates all node numbers of the requested element

Parameters

  • elx (int) – X position of the conciderd element.

  • ely (int) – Y position of the conciderd element.

Returns

  • n1 (int) – The node number of the top left node.

  • n2 (int) – The node number of the top right node.

  • n3 (int) – The node number of the bottom right node.

  • n4 (int) – The node number of the bottom left node.

passive()

Retuns three lists containing the location and magnitude of fixed density values

Returns

  • elx (1-D list) – X coordinates of all passive elements, empty for the parrent class.

  • ely (1-D list) – Y ccordinates of all passive elements, empty for the parrent class.

  • values (1-D list) – Density values of all passive elements, empty for the parrent class.

  • fix_ele (1-D list) – List with all element numbers that are allowed to change.

Child Load Cases

class src_Compliance.loads.HalfBeam(nelx, nely, young, Emin, poisson)

Bases: src_Compliance.loads.Load

This child of the Loads class represents the loading conditions of a half mbb-beam. Only half of the beam is considerd due to the symetry around the y axis.

No methods are added compared to the parrent class. The force and fixdofs functions are changed to output the correct force vector and boundary condition used in this specific load case. See the functions themselfs for more details

fixdofs()

The boundary conditions of the half mbb-beam fix the x displacments of all the nodes at the outer left side and the y displacement of the bottom right element.

Returns

fix – List with all the numbers of fixed degrees of freedom.

Return type

1-D list

force()

The force vector containts a load in negative y direction at the top left corner.

Returns

f – A -1 is placed at the index of the y direction of the top left node.

Return type

1-D array length covering all degrees of freedom

class src_Compliance.loads.Beam(nelx, nely, young, Emin, poisson)

Bases: src_Compliance.loads.Load

This child of the Loads class represents the full mbb-beam without assuming an axis of symetry. To enforce an node in the middle nelx needs to be an even number.

No methods are added compared to the parrent class. The force and fixdofs functions are changed to output the correct force vector and boundary condition used in this specific load case. See the functions themselfs for more details

fixdofs()

The boundary conditions of the full mbb-beam fix the x and y displacment of the bottom left node ande the y displacement of the bottom right node.

Returns

fix – List with all the numbers of fixed degrees of freedom.

Return type

1-D list

force()

The force vector containts a load in negative y direction at the mid top node.

Returns

f – Where at the inndex relating to the y direction of the top mid node a -1 is placed.

Return type

1-D array length covering all degrees of freedom

class src_Compliance.loads.Canti(nelx, nely, young, Emin, poisson)

Bases: src_Compliance.loads.Load

This child of the Loads class represents the loading conditions of a cantilever beam. The beam is encasted on the left an the load is applied at the middel of the right side. To do this an even number for nely is required.

No methods are added compared to the parrent class. The force and fixdofs functions are changed to output the correct force vector and boundary condition used in this specific load case. See the functions themselfs for more details

fixdofs()

The boundary conditions of the cantileverbeam fix the x and y displacment of all nodes on the left side.

Returns

fix – List with all the numbers of fixed degrees of freedom.

Return type

1-D list

force()

The force vector containts a load in negative y direction at the mid most rigth node.

Returns

f – Where at the inndex relating to the y direction of the mid right node a -1 is placed.

Return type

1-D array length covering all degrees of freedom

class src_Compliance.loads.Michell(nelx, nely, young, Emin, poisson)

Bases: src_Compliance.loads.Load

This child of the Loads class represents the loading conditions of a half a Michell structure. A load is applied in the mid left of the design space and the boundary conditions fixes the x and y direction of the middle right node. Due to symetry all nodes at the left side are constraint in x direction. This class requires nely to be even.

No methods are added compared to the parrent class. The force and fixdofs functions are changed to output the correct force vector and boundary condition used in this specific load case. See the functions themselfs for more details

fixdofs()

The boundary conditions of the half mbb-beam fix the x displacments of all the nodes at the outer left side and the y displacement of the mid right element.

Returns

fix – List with all the numbers of fixed degrees of freedom.

Return type

1-D list

force()

The force vector containts a load in negative y direction at the mid most left node.

Returns

f – Where at the inndex relating to the y direction of the mid left node a -1 is placed.

Return type

1-D array length covering all degrees of freedom

class src_Compliance.loads.BiAxial(nelx, nely, young, Emin, poisson)

Bases: src_Compliance.loads.Load

This child of the Loads class represents the loading conditions of a bi-axial loaded plate. All outer nodes have a load applied that goes outward. This class is made to show the checkerboard problem that generaly occeurs with topology optimisation.

No methods are added compared to the parrent class. The force, fixdofs and passive functions are changed to output the correct force vector, boundary condition and passive elements used in this specific load case. See the functions themselfs for more details

fixdofs()

The boundary conditions fix the top left node in x direction, the bottom left node in x and y direction and the bottom right node in y direction only.

Returns

fix – List with all the numbers of fixed degrees of freedom.

Return type

1-D list

force()

The force vector containing loads that act outward from the edge.

Returns

f – Where at the indices related to the outside nodes an outward force of 1 is inserted.

Return type

1-D array length covering all degrees of freedom

passive()

The Bi-Axial load case requires fully dense elements around the border. This is done to enforce propper load introduction.

Returns

  • elx (1-D list) – X coordinates of all passive elements, empty for the parrent class.

  • ely (1-D list) – Y ccordinates of all passive elements, empty for the parrent class.

  • values (1-D list) – Density values of all passive elements, empty for the parrent class.

Finite Element Solvers

Finite element solvers for the displacement from stiffness matrix and force vector. This version of the code is meant for global compliance minimization.

Bram Lagerweij Aerospace Structures and Materials Department TU Delft 2018

Parent Solver

class src_Compliance.fesolvers.FESolver(verbose=False)

This parent FEA class can only assemble the global stiffness matrix and exclude all fixed degrees of freedom from it. This stiffenss csc-sparse stiffness matrix is assebled in the gk_freedof method. This class solves the FE problem with a sparse LU-solver based upon umfpack. This solver is slow and inefficient. It is however more robust.

Parameters

verbose (bool, optional) – False if the FEA should not print updates

verbose

False if the FEA does not print updates.

Type

bool

displace(load, x, ke, kmin, penal)

FE solver based upon the sparse SciPy solver that uses umfpack.

Parameters

  • load (object, child of the Loads class) – The loadcase(s) considerd for this optimisation problem.

  • x (2-D array size(nely, nelx)) – Current density distribution.

  • ke (2-D array size(8, 8)) – Local fully dense stiffnes matrix.

  • kmin (2-D array size(8, 8)) – Local stiffness matrix for an empty element.

  • penal (float) – Material model penalisation (SIMP).

Returns

u – Displacement of all degrees of freedom

Return type

1-D array len(max(edof)+1)

gk_freedofs(load, x, ke, kmin, penal)

Generates the global stiffness matrix with deleted fixed degrees of freedom. It generates a list with stiffness values and their x and y indices in the global stiffness matrix. Some combination of x and y appear multiple times as the degree of freedom might apear in multiple elements of the FEA. The SciPy coo_matrix function adds them up at the background.

Parameters

  • load (object, child of the Loads class) – The loadcase(s) considerd for this optimisation problem.

  • x (2-D array size(nely, nelx)) – Current density distribution.

  • ke (2-D array size(8, 8)) – Local fully dense stiffnes matrix.

  • kmin (2-D array size(8, 8)) – Local stiffness matrix for an empty element.

  • penal (float) – Material model penalisation (SIMP).

Returns

k – Global stiffness matrix without fixed degrees of freedom.

Return type

2-D sparse csc matrix

Child Solvers

class src_Compliance.fesolvers.CvxFEA(verbose=False)

Bases: src_Compliance.fesolvers.FESolver

This parent FEA class is used to assemble the global stiffness matrix while this class solves the FE problem with a Supernodal Sparse Cholesky Factorization.

verbose

False if the FEA should not print updates.

Type

bool

displace(load, x, ke, kmin, penal)

FE solver based upon a Supernodal Sparse Cholesky Factorization. It requires the instalation of the cvx module. 1

Parameters

  • load (object, child of the Loads class) – The loadcase(s) considerd for this optimisation problem.

  • x (2-D array size(nely, nelx)) – Current density distribution.

  • ke (2-D array size(8, 8)) – Local fully dense stiffnes matrix.

  • kmin (2-D array size(8, 8)) – Local stiffness matrix for an empty element.

  • penal (float) – Material model penalisation (SIMP).

Returns

u – Displacement of all degrees of freedom

Return type

1-D array len(max(edof))

References

1

Y. Chen, T. A. Davis, W. W. Hager, S. Rajamanickam, “Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate”, ACM Transactions on Mathematical Software, 35(3), 22:1-22:14, 2008.

class src_Compliance.fesolvers.CGFEA(verbose=False)

Bases: src_Compliance.fesolvers.FESolver

This parent FEA class can assemble the global stiffness matrix and this class solves the FE problem with a sparse solver based upon a preconditioned conjugate gradient solver. The preconditioning is based upon the inverse of the diagonal of the stiffness matrix.

verbose

False if the FEA should not print updates.

Type

bool

ufree_old

Displacement field of previous CG iteration

Type

array len(freedofs)

displace(load, x, ke, kmin, penal)

FE solver based upon the sparse SciPy solver that uses a preconditioned conjugate gradient solver, preconditioning is based upon the inverse of the diagonal of the stiffness matrix. Currently the relative tolerance is hardcoded as 1e-3.

Recomendations

  • Make the tolerance change over the iterations, low accuracy is required for first itteration, more accuracy for the later ones.

  • Add more advanced preconditioner.

  • Add gpu accerelation.

Parameters

  • load (object, child of the Loads class) – The loadcase(s) considerd for this optimisation problem.

  • x (2-D array size(nely, nelx)) – Current density distribution.

  • ke (2-D array size(8, 8)) – Local fully dense stiffnes matrix.

  • kmin (2-D array size(8, 8)) – Local stiffness matrix for an empty element.

  • penal (float) – Material model penalisation (SIMP).

Returns

u – Displacement of all degrees of freedom

Return type

1-D array len(max(edof)+1)

Optimization Module

Topology Optimization class that handles the itterations, objective functions, filters and update scheme. It requires to call upon a constraint, load case and FE solver classes. This version of the code is meant for global compliance minimization.

Bram Lagerweij Aerospace Structures and Materials Department TU Delft 2018

class src_Compliance.topopt.Topopt(constraint, load, fesolver, verbose=False)

This is the optimisation object itself. It contains the initialisation of the density distribution.

Parameters

  • constraint (object of DensityConstraint class) – The constraints for this optimization problem.

  • load (object, child of the Loads class) – The loadcase(s) considerd for this optimisation problem.

  • fesolver (object, child of the CSCStiffnessMatrix class) – The finite element solver.

  • verbose (bool, optional) – Printing itteration results.

constraint

The constraints for this optimization problem.

Type

object of DensityConstraint class

load

The loadcase(s) considerd for this optimisation problem.

Type

object, child of the Loads class

fesolver

The finite element solver.

Type

object, child of the CSCStiffnessMatrix class

verbose

Printing itteration results.

Type

bool, optional

itr

Number of iterations performed

Type

int

x

Array containing the current densities of every element.

Type

2-D array size(nely, nelx)

xold1

Flattend density distribution one iteration ago.

Type

1D array len(nelx*nely)

xold2

Flattend density distribution two iteration ago.

Type

1D array len(nelx*nely)

low

Column vector with the lower asymptotes, calculated and used in the MMA subproblem of the previous itteration.

Type

1D array len(nelx*nely)

upp

Column vector with the lower asymptotes, calculated and used in the MMA subproblem of the previous itteration.

Type

1D array len(nelx*nely)

comp(x, u, ke, penal)

This funcion calculates compliance and compliance density derivative.

Parameters

  • x (2-D array size(nely, nelx)) – Possibly filterd density distribution.

  • u (1-D array len(max(edof)+1)) – Displacement of all degrees of freedom.

  • ke (2-D array size(8, 8)) – Element stiffness matrix with full density.

  • penal (float) – Material model penalisation (SIMP).

Returns

  • c (float) – Compliance for the current design.

  • dc (2-D array size(nely, nelx)) – Compliance sensitivity to density changes.

densityfilt(rmin, filt)

Filters with a normalized convolution on the densities with a radius of rmin if:

>>> filt=='density'
Parameters

  • rmin (float) – Filter size.

  • filt (str) – The filter type that is selected, either ‘sensitivity’ or ‘density’.

Returns

xf – Filterd density distribution.

Return type

2-D array size(nely, nelx)

iter(penal, rmin, filt)

This funcion performs one itteration of the topology optimisation problem. It

  • loads the constraints,

  • calculates the stiffness matrices,

  • executes the density filter,

  • executes the FEA solver,

  • calls upon the compliance and compliance sensitivity calculation,

  • executes the sensitivity filter,

  • executes the MMA update scheme,

  • and finaly updates density distribution (design).

Parameters

  • penal (float) – Material model penalisation (SIMP).

  • rmin (float) – Filter size.

  • filt (str) – The filter type that is selected, either ‘sensitivity’ or ‘density’.

Returns

  • change (float) – Largest difference between the new and old density distribution.

  • c (float) – Compliance for the current design.

layout(penal, rmin, delta, loopy, filt, history=False)

Solves the topology optimisation problem by looping over the iter function.

Parameters

  • penal (float) – Material model penalisation (SIMP).

  • rmin (float) – Filter size.

  • delta (float) – Convergence is roached when delta > change.

  • loopy (int) – Amount of iteration allowed.

  • filt (str) – The filter type that is selected, either ‘sensitivity’ or ‘density’.

  • history (bool, optional) – Do the intermediate results need to be stored.

Returns

  • xf (array size(nely, nelx)) – Density distribution resulting from the optimisation.

  • xf_history (list of arrays len(itterations size(nely, nelx), float16)) – List with the density distributions of all itterations, None when history != True.

mma(m, n, itr, xval, xmin, xmax, xold1, xold2, f0val, df0dx, fval, dfdx, low, upp, a0, a, c, d)

This function mmasub performs one MMA-iteration, aimed at solving the nonlinear programming problem:

\[\begin{split}\min & f_0(x) & + a_0z + \sum_{i=1}^m \left(c_iy_i + \frac{1}{2}d_iy_i^2\right) \\ &\text{s.t. }& f_i(x) - a_iz - y_i \leq 0 \hspace{1cm} & i \in \{1,2,\dots,m \} \\ & & x_{\min} \geq x_j \geq x_{\max} & j \in \{1,2,\dots,n \} \\ & & y_i \leq 0 & i \in \{1,2,\dots,m \} \\ & & z \geq 0\end{split}\]
Parameters

  • m (int) – The number of general constraints.

  • n (int) – The number of variables \(x_j\).

  • itr (int) – Current iteration number (=1 the first time mmasub is called).

  • xval (1-D array len(n)) – Vector with the current values of the variables \(x_j\).

  • xmin (1-D array len(n)) – Vector with the lower bounds for the variables \(x_j\).

  • xmax (1-D array len(n)) – Vector with the upper bounds for the variables \(x_j\).

  • xold1 (1-D array len (n)) – xval, one iteration ago when iter>1, zero othewise.

  • xold2 (1-D array len (n)) – xval, two iteration ago when iter>2, zero othewise.

  • f0val (float) – The value of the objective function \(f_0\) at xval.

  • df0dx (1-D array len(n)) – Vector with the derivatives of the objective function \(f_0\) with respect to the variables \(x_j\), calculated at xval.

  • fval (1-D array len(m)) – Vector with the values of the constraint functions \(f_i\), calculated at xval.

  • dfdx (2-D array size(m x n)) – (m x n)-matrix with the derivatives of the constraint functions \(f_i\). with respect to the variables \(x_j\), calculated at xval.

  • low (1-D array len(n)) – Vector with the lower asymptotes from the previous iteration (provided that iter>1).

  • upp (1-D array len(n)) – Vector with the upper asymptotes from the previous iteration (provided that iter>1).

  • a0 (float) – The constants \(a_0\) in the term \(a_0 z\).

  • a (1-D array len(m)) – Vector with the constants \(a_i1 in the terms :math:\).

  • c (1-D array len(m)) – Vector with the constants \(c_i\) in the terms \(c_i*y_i\).

  • d (1-D array len(m)) – Vector with the constants \(d_i\) in the terms \(0.5d_i (y_i)^2\).

Returns

  • xmma (1-D array len(n)) – Column vector with the optimal values of the variables \(x_j\) in the current MMA subproblem.

  • low (1-D array len(n)) – Column vector with the lower asymptotes, calculated and used in the current MMA subproblem.

  • upp (1-D array len(n)) – Column vector with the upper asymptotes, calculated and used in the current MMA subproblem.

  • Version September 2007 (and a small change August 2008)

  • Krister Svanberg <krille@math.kth.se>

  • Department of Mathematics KTH, SE-10044 Stockholm, Sweden.

  • Translated to python 3 by A.J.J. Lagerweij TU Delft June 2018

sensitivityfilt(x, rmin, dc, filt)

Filters with a normalized convolution on the sensitivity with a radius of rmin if:

>>> filt=='sensitivity'
Parameters

  • x (2-D array size(nely, nelx)) – Current density ditribution.

  • dc (2-D array size(nely, nelx) – Compliance sensitivity to density changes.

  • rmin (float) – Filter size.

  • filt (str) – The filter type that is selected, either ‘sensitivity’ or ‘density’.

Returns

dcf – Filterd sensitivity distribution.

Return type

2-D array size(nely, nelx)

solvemma(m, n, epsimin, low, upp, alfa, beta, p0, q0, P, Q, a0, a, b, c, d)

This function solves the MMA subproblem with a primal-dual Newton method.

\[\begin{split}\min &\sum_{j-1}^n& \left( \frac{p_{0j}^{(k)}}{U_j^{(k)} - x_j} + \frac{q_{0j}^{(k)}}{x_j - L_j^{(k)}} \right) + a_0z + \sum_{i=1}^m \left(c_iy_i + \frac{1}{2}d_iy_i^2\right) \\ &\text{s.t. }& \sum_{j-1}^n \left(\frac{p_{ij}^{(k)}}{U_j^{(k)} - x_j} + \frac{q_{ij}^{(k)}}{x_j - L_j^{(k)}} \right) - a_iz - y_i \leq b_i \\ & & \alpha_j \geq x_j \geq \beta_j\\ & & z \geq 0\end{split}\]
Returns

x – Column vector with the optimal values of the variables x_j in the current MMA subproblem.

Return type

1-D array len(n)

Plotting Module

Plotting the simulated TopOpt geometry with boundery conditions and loads.

Bram Lagerweij Aerospace Structures and Materials Department TU Delft 2018

class src_Compliance.plotting.Plot(load, title=None)

This class contains functions that allows the visualisation of the TopOpt algorithem. It can print the density distribution, the boundary conditions and the forces.

Parameters

  • load (object, child of the Loads class) – The loadcase(s) considerd for this optimisation problem.

  • title (str, optional) – Title of the plot if required.

nelx

Number of elements in x direction.

Type

int

nely

Number of elements in y direction.

Type

int

fig

An empty figure of size nelx/10 and nely/10*1.2 inch.

Type

matplotlib.pyplot figure

ax

The axis system that belongs to fig.

Type

matplotlib.pyplot axis

images

This list contains all density distributions that need to be plotted.

Type

1-D list with imshow objects

add(x, animated=False)

Adding a plot of the density distribution to the figure.

Parameters

  • x (2-D array size(nely, nelx)) – The density distribution.

  • animated (bool, optional) – An animated figure is genereted when history = True.

boundary(load)

Plotting the boundary conditions.

Parameters

load (object, child of the Loads class) – The loadcase(s) considerd for this optimisation problem.

loading(load)

Plotting the loading conditions.

Parameters

load (object, child of the Loads class) – The loadcase(s) considerd for this optimisation problem.

save(filename, fps=10)

Saving an plot in svg or mp4 format, depending on the length of the images list. The FasterFFMpegWriter is used when videos are generated. These videos are encoded with a hardware accelerated h264 codec with the .mp4 file format. Other codecs and encoders can be set within the function itself.

Parameters

  • filename (str) – Name of the file, excluding the file exstension.

  • fps (int, optional) – Amount of frames per second if the plots are animations.

show()

Showing the plot in a window.

class src_Compliance.plotting.FasterFFMpegWriter(**kwargs)

Bases: matplotlib.animation.FFMpegWriter

FFMpeg-pipe writer bypassing figure.savefig. To improofs speed with respect to the matplotlib.animation.FFMpegWriter

classmethod bin_path()

Return the binary path to the commandline tool used by a specific subclass. This is a class method so that the tool can be looked for before making a particular MovieWriter subclass available.

cleanup()

Clean-up and collect the process used to write the movie file.

finish()

Finish any processing for writing the movie.

frame_size

A tuple (width, height) in pixels of a movie frame.

grab_frame(**savefig_kwargs)

Grab the image information from the figure and save as a movie frame.

Doesn’t use savefig to be faster: savefig_kwargs will be ignored.

classmethod isAvailable()

Check to see if a MovieWriter subclass is actually available.

saving(fig, outfile, dpi, *args, **kwargs)

Context manager to facilitate writing the movie file.

*args, **kw are any parameters that should be passed to setup.

setup(fig, outfile, dpi=None)

Perform setup for writing the movie file.

Parameters

  • fig (~matplotlib.figure.Figure) – The figure object that contains the information for frames

  • outfile (str) – The filename of the resulting movie file

  • dpi (int, optional) – The DPI (or resolution) for the file. This controls the size in pixels of the resulting movie file. Default is fig.dpi.