%% Function name
%       midplane

%% Revised:
%       28 January 2014

%% Author
%       Swamy Rakesh Adapa, Trey Moore, & Autar Kaw
%       Section: All
%       Semester: Fall 2013

%% Purpose
%       Given the midplane extensional, coupling and bending stiffness 
%       matrices of the laminate, mechanical and fictitious hygrothermal 
%       force & moment vectors, output the midplene 
%       strains and curvatures

%% Usage
%       function [eps0,kappa] = midplane(A,B,D,NM,MM,NT,MT,NC,MC)
% Input variables
%       A=extensional stiffness matrix 
%       B=coupling stiffness matrix
%       D=bending stiffness matrix
%       NM=vector of mechanical forces
%       MM=vector of mechanical moments
%       NT=vector of fictitious thermal forces
%       MT=vector of fictitious thermal moments
%       NC=vector of fictitious moisture forces
%       MC=vector of fictitious moisture moments
% Output variables
%       eps0=midplane strains
%       kappa=midplane curvatures 
% Keyword
%       stiffness matrix
%       mechanical load
%       hygrothermal load
%       midplane strains
%       midplane curvatures

%% License Agreement
%       http://www.eng.usf.edu/~kaw/OCW/composites/license/limiteduse.pdf

%% Code
function [eps0,kappa] = midplane(A,B,D,NM,MM,NT,MT,NC,MC)
% Midplane strains and curvature
[midplane] = inv([A B; B D])*([NM; MM]+[NT; MT]+[NC; MC]);
[eps0] = [midplane(1); midplane(2);midplane(3)];
[kappa] = [midplane(4); midplane(5); midplane(6)];
end