MATLAB: How to give input to function

function u=heat(nx,hx,nt,ht,init,lowb,hib,K)
% Solves parabolic equ'n.
% e.g. heat flow equation.
% Example call: u=heat(nx,hx,nt,ht,init,lowb,hib,K)
% nx, hx are number and size of x panels
% nt, ht are number and size of t panels
% init is a row vector of nx+1 initial values of the function.
% lowb & hib are boundaries at low and hi values of x.
% Note that lowb and hib are scalar values.
% K is a constant in the parabolic equation.
alpha=K*ht/hx^2;
A=zeros(nx-1,nx-1); u=zeros(nt+1,nx+1);
u(:,1)=lowb*ones(nt+1,1);
u(:,nx+1)=hib*ones(nt+1,1);
u(1,:)=init;
A(1,1)=1+2*alpha; A(1,2)=-alpha;
for i=2:nx-2
  A(i,i)=1+2*alpha;
  A(i,i-1)=-alpha; A(i,i+1)=-alpha;
end
A(nx-1,nx-2)=-alpha; A(nx-1,nx-1)=1+2*alpha;
b(1,1)=init(2)+init(1)*alpha;
for i=2:nx-2, b(i,1)=init(i+1); end
b(nx-1,1)=init(nx)+init(nx+1)*alpha;
[L,U]=lu(A);
for j=2:nt+1
  y=L\b; x=U\y;
  u(j,2:nx)=x'; b=x;
  b(1,1)=b(1,1)+lowb*alpha;
  b(nx-1,1)=b(nx-1,1)+hib*alpha;
end

How can I use this function and what parameter I have to give for Input? Thanks

Best Answer

You should introduce the below constants

nx=
hx=
nt=
ht=
init=
lowb
hub=
k=

Then type

output=heat(nx,hx,nt,ht,init,lowb,hib,K)

Related Solutions

MATLAB: Can someone rearrange the code to run

%subdivisions space /time
ht=0.01; Tmax=1.2; nx=33; hx=1/(nx-1); x=[0:hx:1]';
%matrices
K=stiff2(1/pi^2,hx,nx); M=mass(1/ht,hx,nx); 
A=M+K;
%boundary conditions by deleting rows
A(nx,:)=[]; A(:,nx)=[]; A(1,:)=[]; A(:,1)=[];
%creation
R=chol(A);
%initial condition
u=cos(pi*(x-1/2));
%time step loop
k=0; 
while (k*ht<Tmax)
k=k+1;
b=M*u;
b(nx)=[];b(1)=[];
%solve
u=zeros(nx,1);
u(2:nx-1)=R\(R'\b);
end
% Set the matrices to zero
k=zeros(6,6,2); K=zeros(6,6,2); Gamma=zeros(6,6,2);
% Enter parameter values, in units: mm^2, mm^4, and MPa(10^6 N/m)
A=6000; II=200*10^6; EE=200000;
% Convert units into meters and kN
A=A/10^6; II = II/10^12; EE =EE*1000;
% Element 1
i=[0,0]; j=[7.416,3];
[k(:,:,1),K(:,:,1),Gamma(:,:,1)]=stiff(EE,II,A,i,j);
% Element 2
i=j; j=[15.416,3];
[k(:,:,2),K(:,:,2),Gamma(:,:,2)]=stiff(EE,II,A,i,j);
% Define the elementary stiffness matrix
ID=[-4 1 -7;-5 2 -8;-6 3 -9];
% Define the connection matrix
LM=[-4 -5 -6 1 2 3; 1 2 3 -7 -8 -9];
% Assemble the augmented stiffness matrix
Kaug = zeros(9); 
for elem=1:2
for r=1:6
lr=abs(LM(elem,r));
for c=1:6
lc=abs(LM(elem,c));
Kaug(lr,lc)=Kaug(lr,lc)+K(r,c,elem);
end
end
end
% Extract the stiffness matrix
Ktt=Kaug(1:3,1:3);
% Determine the reactions at the nodes in local coordinates
fea(1:6,1)=0; 
fea(1:6,2)=[0,8*4/2,4*8^2/12,0,8*4/2,-4*8^2/12]';
% Determine the reactions in the global coordinate system
FEA(1:6,1)=Gamma(:,:,1)'*fea(1:6,1);
FEA(1:6,2)=Gamma(:,:,2)'*fea(1:6,2);
% FEA_Rest for constrained nodes
FEA_Rest=[0,0,0,FEA(4:6,2)'];
% Assemble the right-hand side for non-constrained nodes
P(1)=50*3/8; P(2)=-50*7.416/8-FEA(2,2); P(3)=-FEA(3,2);
% Solve to find the displacements in meters and in radians
Displacements=inv(Ktt)*P'
% Extract Kut
Kut = Kaug(4:9,1:3);
% Compute the reactions and introduce boundary conditions
Reactions=Kut*Displacements+FEA_Rest'
% Solve to find the internal forces, excluding fixed points
dis_global(:,:,1)=[0,0,0,Displacements(1:3)'];
dis_global(:,:,2)=[Displacements(1:3)',0,0,0]; 
for elem=1:2
dis_local= Gamma(:,:,elem)*dis_global(:,:,elem)';
int_forces= k(:,:,elem)*dis_local+fea(1:6,elem)
end
%The above script calls the stiff function, which can be implemented as follows:
function [k,K,Gamma] = stiff( EE,II,A,i,j )
% Find the length
L=sqrt((j(2)-i(2))^2+(j(1)-i(1))^2);
% Compute the angle theta
if(j(1)-i(1))~=2
alpha=atan((j(2)-i(2))/(j(1)-i(1)))
else
alpha=-pi/2;
end
% Form the rotation matrix Gamma
Gamma =[cos(alpha) sin(alpha) 0 0 0 0;
-sin(alpha) cos(alpha) 0 0 0 0;
0 0 1 0 0 0;
0 0 0 cos(alpha) sin(alpha) 0;
0 0 0 -sin(alpha) cos(alpha) 0;
0 0 0 0 0 1];
% Form the elementary stiffness matrix in local coordinates
EI=EE*II; EA=EE*A; 
k=[EA/L, 0, 0, -EA/L, 0, 0; 
    0, 12*EI/L^3, 6*EI/L^2, 0, -12*EI/L^3,6*EI/L^2;
0, 6*EI/L^2, 4*EI/L, 0 -6*EI/L^2, 2*EI/L;
-EA/L, 0 ,0 , EA/L, 0, 0;
0, -12*EI/L^3, -6*EI/L^2, 0, 12*EI/L^3, -6*EI/L^2;
0, 6*EI/L^2, 2*EI/L, 0, -6*EI/L^2, 4*EI/L];
% Elementary matrix in global coordinates
K=Gamma'*k*Gamma;
end
function R=stiff2(nu,h,n)
%
[m1,m2]=size(nu);
if (length(nu)==1)
ee=nu*ones(n-1,1)/h; e1=[ee;0]; e2=[0;ee]; e=e1+e2;
else
ee=.5*(nu(1:n-1)+nu(2:n))/h; e1=[ee;0]; e2=[0;ee]; e=e1+e2;
end
R=spdiags([-e1 e -e2],-1:1,n,n);
return
end
function M=mass(alpha,h,n)
[m1,m2]=size(alpha);
if(length(alpha)==1)
ee=alpha*h*ones(n-1,1)/6;
e1=[ee;0]; e2=[0;ee]; e=e1+e2;
else
ee=h*(alpha(1:n-1)+alpha(2:n))/12;
e1=[ee;0]; e2=[0;ee]; e=e1+e2;
end
M=spdiags([e1 2*e e2],-1:1,n,n);
return
end

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