%% Function name
%       laminate_moduli

%% Revised:
%       28 January 2014

%% Author:
%       Aadithya Jeyaranjan, Trey Moore, & Autar Kaw
%       Section: all
%       Semester: Fall 2013

%% Purpose:
%       Given the extensional stiffness and bending stiffness matrices, the
%       number of plies, as well as the thickness of each ply, output a
%       vector of the in-plane modulii and a vector of the flexural modulii

%% Usage
%       function [moduliplane,moduliflex] = laminate_moduli(A,D,nplies,tplies)
% Input Variables
%       A=extensional stiffness matrix
%       D=bending stiffness matrix
%       nplies=number of plies 
%       tplies=thickness of each ply
% Output Variables
%       moduliplane=vector of 4 elastic in-plane modulii of a laminate
%       moduliflex=vector of 4 elastic flexural modulii of a laminate
% Keyword
%       elastic modulus
%       shear moudulus
%       Poisson's ratio
%       Flexural elastic modulus
%       Flexural shear moudulus
%       Flexural Poisson's ratio

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

%% Code
function[moduliplane,moduliflex]=laminate_moduli(A,D,nplies,tplies)
% Extensional Compliance matrix
Astar=inv(A);
% Bending Compliance matrix
Bstar=inv(D);
% Total thickness of laminate
h=sum(tplies);
%In-Plane Longitudinal Elastic Modulus
Ex=1/(h*Astar(1,1));
%In-Plane Transverse Elastic Modulus
Ey=1/(h*Astar(2,2));
%In-Plane Poisson's ratio
nuxy=-(Astar(1,2)/Astar(1,1));
%In-Plane Shear Modulus
Gxy=1/(h*Astar(3,3));
%Row vector of the 4 In-Plane moduli
[moduliplane]=[Ex Ey nuxy Gxy];
%In-Plane Engineering constants
%Flexural Longitudinal Young's Modulus
Efx=12/(h^3*Bstar(1,1));
%Flexural Transverse Young's Modulus
Efy=12/(h^3*Bstar(2,2));
%Flexural Poison's ratio
vfxy=-(Bstar(1,2)/Bstar(1,1));
%Flexural Shear Modulus
Gfxy=12/(h^3*Bstar(3,3));
%Row vector of the 4 Flexural moduli 
[moduliflex]=[Efx Efy vfxy Gfxy];
end