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Truss Design Optimization Based on Generative Algorithms

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Truss Design Optimization Based on Generative Algorithms

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Supplementary material for a WCSMO publication regarding truss design optimization.

JacobianStresscal(D, Area)
%Author: Ashish Khetan (khetan2@illinois.edu)
%Engineering System Design Lab,
%Industrial and Enterprise Systems Engineering, UIUC, IL, USA

% Copyright (c) 2013, Engineering System Design Lab (ESDL)
% All rights reserved.
% 
% Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
% 
% Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
% Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
% Neither the name of the ESDL nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY 
%AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES 
%(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, 
%STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

% Function to calculate Jacobian matrix of stress values for given Area
% values using numerical central difference method
function [JacobianStress] = JacobianStresscal(D, Area)
dArea = 0.001;
n = length(Area);
JacobianStress = zeros(n,n);
for i = 1:n
   e = zeros(size(Area));
   e(i) = 1;
   JacobianStress(:,i) = (Stresscal(D, Area+dArea*e) - Stresscal(D, Area-dArea*e))/(2*dArea);
end
end

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