central_diff20P.m

%3c) The function solves for the system of equations using CDM when P>0 and
%w=0 for twenty segments in terms of P and q. 
function central_diff20P(P,q) 
b=0.1; %width of beam
E=70E9; %Modulus of Elasticity 
h=0.01;%height of beam 
I=(b*(h^3))/12; %Second MOI
n=20; %Number of segments 
x=1/n; %segment equivalent 
z=((x.^4)*q)/(E*I); %differentiation used to solve for displacement

Off_Diag=-4-(((P*(1/(n^2)))/(E*I))); %Off Diagonal value 
Diag=6+((P*(2*(1/(n^2))))/(E*I)); %Diagonal value
ODV = ones((n-2),1)*Off_Diag; %Off Diagonal vector
DV = ones(n-1,1)*Diag; %Diagonal vector
OOD = ones((n-3),1); %Off off diagonal vector 

%Generate Matrix X
X=diag(ODV,-1)+ diag(DV)+diag(ODV,1)+diag(OOD,2)+diag(OOD,-2);
X(1,1)= 5+((P*(2*(1/(n^2))))/(E*I));
X((n-1),(n-1))=5+((P*(2*(1/(n^2))))/(E*I));

%Generate  Matrix Y
Y=[z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z;z];
%Solve for deflection Matrix 
W=X\Y;
end