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optimization [2018/09/18 10:28]
mark.naves 		optimization [2022/01/12 13:41] (current)
jan.dejong
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 ===== Example: Shape optimization of cross-hinge ===== ===== Example: Shape optimization of cross-hinge =====
  
-This example provides a shape optimization of a single cross flexure by using matlab's ''fmincon'' function. For this optimization a crosshinge is considered with a mass and inertia connected to node 3. Furthermore, the optimization objective is to maximize the first parasitic frequency of the system (note: rotation of the cross-hinge is prescribed to de desired rotation angle. Therefore, the first parasitic frequency of the system is given by the first eigenfrequency).+This example provides a shape optimization of a single cross flexure by using matlab's ''fmincon'' function. For this optimization a crosshinge is considered with a mass and inertia connected to node 3. Furthermore, the optimization objective is to maximize the first parasitic frequency of the system (note: rotation of the cross-hinge is prescribed to de desired rotation angle. Therefore, the first parasitic frequency of the system is given by the first eigenfrequency). A rotation of 0.5rad, a maximum stress of 300MPa and and a maximum actuation force of 2.5Nm is considered.
  
 The cost function of the optimization is defined by the inverse of the first eigenfrequency. Additionally, a limit on the maximum stress and actuation force is implemented by applying a penalty on the value of the cost function. The matlab function which calls spacarlight and computes the cost function is defined by: The cost function of the optimization is defined by the inverse of the first eigenfrequency. Additionally, a limit on the maximum stress and actuation force is implemented by applying a penalty on the value of the cost function. The matlab function which calls spacarlight and computes the cost function is defined by:
  
 <code matlab run_sim.m> <code matlab run_sim.m>
-function cost = run_sim(P, Silent)% EXAMPLE SCRIPT FOR RUNNING SPACAR LIGHT +function [cost, out] = run_sim(P, Silent)% EXAMPLE SCRIPT FOR RUNNING SPACAR LIGHT
-% This example simulates a simple cross flexure rotating due to an applied moment+
 if nargin == 1 if nargin == 1
     Silent = true; %run in silent mode when called by optimizer     Silent = true; %run in silent mode when called by optimizer
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 stressmax = 300e6; %Max stress [MPa] stressmax = 300e6; %Max stress [MPa]
 Mmax = 2.5; %Max actuation moment [Nm] Mmax = 2.5; %Max actuation moment [Nm]
-Stroke = 0.5; %Max stroke+Stroke = 0.5; %Max stroke [Rad]
  
  
 %% NODE POSITIONS %% NODE POSITIONS
 %           x y z %           x y z
-nodes = [   0 0 0;      %node 1  +nodes = [   0 0 0;    %node 1  
             0 H 0;    %node 2               0 H 0;    %node 2  
-            B H 0;  %node 3+            B H 0;    %node 3
             B 0 0];   %node 4             B 0 0];   %node 4
  
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 eprops(1).orien    = [0 0 1];          %Orientation of the cross-section as a vector pointing along "width-direction" eprops(1).orien    = [0 0 1];          %Orientation of the cross-section as a vector pointing along "width-direction"
 eprops(1).nbeams   = 2;                %Number of beams used to model this element  eprops(1).nbeams   = 2;                %Number of beams used to model this element 
-eprops(1).flex     = 1:6;            %Model out-of-plane bending (modes 3 and 4) as flexible+eprops(1).flex     = 1:6;              %Consider all deformation modes (1 to 6) as flexible
 eprops(1).color    = 'grey';           %Color eprops(1).color    = 'grey';           %Color
 eprops(1).opacity  = 0.7;              %Opacity eprops(1).opacity  = 0.7;              %Opacity
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 end end
 </code> </code>
 +
 +An example to conduct the optimization is provided below, taking into account additional boundary conditions on the design parameters of the cross-hinge. See matlab's documentation on ''fmincon'' for more information.
 +
 +<code matlab optimization.m>
 +%filename
 +simulation = @run_sim;
 +
 +%starting point
 +x0 = [0.1;  0.1;  50e-3; 0.2e-3];
 +
 +%constraints
 +b1 = [0.05; 0.05; 25e-3; 0.1e-3];   % Lower bound (b1 < x)
 +b2 = [0.2;  0.2;  75e-3; 1e-3  ];       % Upper bound (x < b2)
 +
 +A = [-eye(4); eye(4)];
 +b = [-b1;b2];
 +
 +%optimization
 +x_opt = fmincon(simulation, x0, A, b);
 +
 +%show results
 +[cost, out] = run_sim(x_opt,false);
 +</code>
 +//Note: prescribing input rotation is only supported for SPACAR light version 1.27 or higher.//
optimization.1537259300.txt.gz · Last modified: 2018/09/18 10:28 by mark.naves

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