%% Function name
%        principalstrains

%% Revised: 
%       16 January 2014

%% Author
%       Adam Wolfe, Trey Moore, & Autar Kaw
%       Section: All
%       Semester: Fall 2012

%% Purpose
%       Given the global strains acting on the lamina, output the 
%       longitudinal, transverse and in plane principal strains of a lamina

%% Usage
%       function [pe1,pe2,gmax,thetap,thetas] = principalstrains(strain_glo)
% Input variables
%       strain_glo=vector of global strain applied to unidirectional lamina
%       [strain_glo]=[epsx;epsy;epsxy]
%       epsx=longitudinal global strain
%       epsy=transverse global strain
%       epsxy=in-plane global strain
% Output variables
%       pe1=principal strain in direction 1
%       pe2=principal strain in direction 2
%       gmax=maximum shear strain
%       thetape=angle at which principal strain occurs
%       thetase=angle at which maximum shear strain occurs
% Keyword
%       global strains
%       principal strains

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

%% Code
function [pe1,pe2,gmax,thetape,thetase] = principalstrains(strain_glo)
% Strain in the x-direction
epsx=strain_glo(1);
% Strain in the y-direction
epsy=strain_glo(2);
% Strain in the x-y plane
epsxy=strain_glo(3);
% Longitudinal and Transverse Stresses
pe_1=((epsx+epsy)/2)+sqrt((((epsx-epsy)/2)^2)+((epsxy)^2));
pe_2=((epsx+epsy)/2)-sqrt((((epsx-epsy)/2)^2)+((epsxy)^2));
thetape=atand((2*epsxy)/(epsx-epsy))/2;
if pe_1 > pe_2
    pe1=pe_1;
    pe2=pe_2;
else
    pe1=pe_2;
    pe2=pe_1;
end
% Shear Stresses
gmax=sqrt((((epsx-epsy)/2)^2)+(epsxy^2));
thetase=atand(-(epsx-epsy)/(2*epsxy))/2;
end