%% Function name
%      AsBsDs

%% Revised
%      28 January 2014

%% Author
%      Robert Worcester, Trey Moore, & Autar Kaw
%      Section: All
%      Semester: Fall 2013

%% Purpose
%       Given the thickness of each ply and the extensional, coupling, and
%       bending matrices, output the extensional compliance, coupling
%       compliance, bending compliance, normalized extensional compliance,
%       normalized coupling compliance, and normalized bending compliance
%       matrices

%% Usage
%      function [As,Bs,Ds,Asn,Bsn,Dsn] = AsBsDs(A,B,D,tplies)
% Input variables
%       tplies=thickness of each ply
%       A=extensional stiffness matrix
%       B=coupling stiffness matrix
%       D=bending stiffness matrix
% Output variables
%       As=extensional compliance matrix
%       Bs=coupling compliance matrix
%       Ds=bending compliance matrix
%       Asn=normalized extensional compliance matriix
%       Bsn=normalized coupling compliance matrix
%       Dsn=normalized bending compliance matrix
% Keywords
%       extensional compliance matrix 
%       coupling compliance matrix
%       bending compliance matrix
%       normalized extensional compliance matrix
%       normalized coupling compliance matrix
%       normalized bending compliance matrix

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

%% Code
function [As,Bs,Ds,Asn,Bsn,Dsn] = AsBsDs(A,B,D,tplies)
% Single combined matrix comprised of the extensional stiffness matrix, coupling
% stiffness matrix, and bending stiffness matrix
[G]=[A(1,1),A(1,2),A(1,3),B(1,1),B(1,2),B(1,3);A(2,1),A(2,2),A(2,3),...
    B(2,1),B(2,2),B(2,3);A(3,1),A(3,2),A(3,3),B(3,1),B(3,2),B(3,3);...
    B(1,1),B(1,2),B(1,3),D(1,1),D(1,2),D(1,3);B(2,1),B(2,2),B(2,3),...
    D(2,1),D(2,2),D(2,3);B(3,1),B(3,2),B(3,3),D(3,1),D(3,2),D(3,3)];
% Inverse of the single combined matrix
Gs=inv(G);
% Extensional compliance matrix
As=[Gs(1,1),Gs(1,2),Gs(1,3);Gs(2,1),Gs(2,2),Gs(2,3);...
    Gs(3,1),Gs(3,2),Gs(3,3)];
% Coupling compliance matrix
Bs=[Gs(1,4),Gs(1,5),Gs(1,6);Gs(2,4),Gs(2,5),Gs(2,6);...
    Gs(3,4),Gs(3,5),Gs(3,6)];
% Bending compliance matrix
Ds=[Gs(4,4),Gs(4,5),Gs(4,6);Gs(5,4),Gs(5,5),Gs(5,6);...
    Gs(6,4),Gs(6,5),Gs(6,6)];
% Total thickness of laminate
h=sum(tplies);
% Normalized extensional compliance matrix
Asn=As*h;
% Normalized coupling compliance matrix
Bsn=Bs*(h^2/2);
% Normalized bending compliance matrix
Dsn=Ds*(h^3/12);
end