%% Function name
%       beta_gtol
    
%% Revised
%       15 January 2014

%% Author
%       Younes Benkabbou, Trey Moore, & Autar Kaw
%       Section: All
%       Semester: Fall 2012

%% Purpose
%       Given the longitudinal and transverse coefficients of moisture 
%       expansion of a unidirectional lamina, and the angle of the ply, 
%       this function outputs the coefficients of moisture expansion for 
%       an angle lamina.

%% Usage 
%       function [betaxy] = beta_gtol(beta12, angle)
% Input variables
%       beta12=vector of moisture expansion of unidirectional lamina 
%               in 1,2 direction 
%       [beta12]=[beta1;beta2;zero]
%       beta1=longitudinal coefficient of moisture expansion.
%       beta2=transverse coefficient of moisture expansion.
%       beta12=in-plane coefficient of moisture expansion.
%       angle=angle of ply given in degrees.
% Output variables
%       betaxy=vector of coefficients of moisture expansion for angle
%               in x,y direction
%       [betax,betay,betaxy]

% Keyword
%       coefficient of moisture expansion
%       angle ply

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

%% Code
function[betaxy]= beta_gtol(beta12,angle)
% Sine of the angle of the lamina
s=sind(angle);
% Cosine of the angle of the lamina
c=cosd(angle);
% Inverse Transformation Matrix
T=[c^2 s^2 2*s*c; s^2 c^2 -2*s*c; -s*c s*c c^2-s^2];
% Reuter Matrix
R=[1 0 0; 0 1 0; 0 0 2];
% Calculating the coefficients of moisture expansion for angle lamina
betaxy=((R*inv(T))*inv(R))*beta12;
end