SPACAR Wiki

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).

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:

run_sim.m

function cost = 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
    Silent = true; %run in silent mode when called by optimizer
end 
 
% DESIGN PARAMETERS
H = P(1);
B = P(2);
w = P(3);
t = P(4);
 
% Optimization parameters
stressmax = 300e6; %Max stress [MPa]
Mmax = 2.5; %Max actuation moment [Nm]
Stroke = 0.5; %Max stroke
 
 
%% NODE POSITIONS
%           x y z
nodes = [   0 0 0;      %node 1  
            0 H 0;    %node 2  
            B H 0;  %node 3
            B 0 0];   %node 4
 
 
%% ELEMENT CONNECTIVITY
%               p   q
elements = [    1   3;  %element 1
                2   3;  %element 2
                2   4]; %element 3
 
%% NODE PROPERTIES  
%node 1
nprops(1).fix               = true;         %Fix node 1
 
%node 3
nprops(3).rot_z           = Stroke;
nprops(3).mass            = 1;
nprops(3).mominertia      = [1e-3 0 0 1e-3 0 1e-3];
 
%node 4
nprops(4).fix               = true;         %Fix node 4
 
 
%% ELEMENT PROPERTIES
%Property set 1
eprops(1).elems    = [1 3];            %Add this set of properties to elements 1 and 3
eprops(1).emod     = 210e9;            %E-modulus [Pa]
eprops(1).smod     = 70e9;             %G-modulus [Pa]
eprops(1).dens     = 7800;             %Density [kg/m^3]
eprops(1).cshape   = 'rect';           %Rectangular cross-section
eprops(1).dim      = [w t];   %Width: 50 mm, thickness: 0.2 mm
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).flex     = 1:6;        	   %Model out-of-plane bending (modes 3 and 4) as flexible
eprops(1).color    = 'grey';           %Color
eprops(1).opacity  = 0.7;              %Opacity
eprops(1).cw       = true;             %Constrain warping at nodes (typical condition for flexure clamped at both ends). For a "free" end, warping is typically not constrained
 
%Property set 2
eprops(2).elems    = 2;                %Add this set of properties to element 2
eprops(2).dens     = 3000;             %Density [kg/m^3]
eprops(2).cshape   = 'rect';           %Rectangular cross-section
eprops(2).dim      = [w 10e-3];    %Width: 50 mm, thickness: 10 mm
eprops(2).orien    = [0 0 1];          %Orientation of the cross-section as a vector pointing along "width-direction"
eprops(2).nbeams   = 1;                %1 beam for simulating this element (as it is rigid an no more elements are required)
eprops(2).color    = 'darkblue';
 
 
%% OPTIONAL ARGUMENTS
opt.filename    = 'crosshinge';     %Filename
opt.calccompl   = false;            %Disable calculation of compliance matrices (can reduce computation time for large simulations)
opt.silent      = Silent;            %Run in silent mode
 
%% CALL SPACAR_LIGHT AND COMPUTE COST FUNCTION
try
    out = spacarlight(nodes, elements, nprops, eprops, opt);
    cost = 1/min(out.freq(1,:)); %cost function (inverse of first frequency )
    stress = max(out.stressmax); %max stress
    Mact = max(out.node(3).Mreac(3,:));%max actuation moment
 
    %add penalty if limits are exceeded
    if stress > stressmax
        cost = cost * (1 + (stress-stressmax)/stressmax)^5;
    end
    if Mact > Mmax
        cost = cost * (1 + (Mact-Mmax)/Mmax)^5;
    end
catch %if sumulation fails, cost is inf
    cost = inf;
end