Program for axisymmetric problem matlab
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This document describes solving an axisymmetric problem for a plate using boundary value problems and finite element analysis. It defines material properties, dimensions, and boundary conditions for the plate. It then sets up and solves a second order differential equation to find the displacement values at nodes along the plate using a boundary value problem solver and evaluates the solution.
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![PROGRAM FOR AXISYMMETRIC PROBLEM format long; %Entering the properties of the material of the plate fprintf('Properties of the material:n') E=input('Modulus of Elasticity, E(N/m^2): '); nu=input('Poisson Ratio: '); mu=E/(2*(1+nu)); lambda=0.5*((((2*nu+1)/(1-2*nu))*mu)-mu); %Entering the dimensions of the plate fprintf('nDimensions:n'); r=input('a = '); l=input('h = '); %Entering the boundary conditions of the plate fprintf('nBoundary conditions:n'); po=input('Enter the Top load(kN/m^2): '); sigmaz_a=input('Enter the Bottom load(kN/m^2): '); sigmaz_b=input('Enter the Bottom load(kN/m^2): '); global po po = 10000; global pin pin = 5000; deq = @(r,u) D2_diffeqtn(r,u,nust,Est); r0 = linspace(a,b,11); uinit = [0 0]; initial_values = bvpinit(r0, uinit); solutn = bvp4c(deq,@bcdnts,initial_values); soln = deval(solutn,r0); r0' soln'](https://image.slidesharecdn.com/programforaxisymmetricproblem-141104134151-conversion-gate01/85/Program-for-axisymmetric-problem-matlab-1-320.jpg)
![Function specifying boundary conditions function bdry = bcdnts( u0,u1 ) global po global pin bdry = [ u0(2)-pin ; u1(2) + po ]; end
Differential equation function function f = D2_diffeqtn( r,u,nu_st,Est ) f = zeros(2,1); f(1) = -nu_st/r*u(1) + u(2)*(1-nu_st^2)/Est; f(2) = Est*u(1)/r^2 + u(2)*(nu_st-1)/r; end](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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%%
%ratN_range = 1e-2; ratS_range = [ 0.5: 0.2: 2];
ratN_range = 1; ratS_range = 1; %This doesn’t matter for Parabolic DOS
for iN = 1 : length(ratN_range)
for iS = 1 : length(ratS_range)
u.ratN = ratN_range(iN);
u.ratS = ratS_range(iS);
u.N2 = u.ratN * u.N1;
try
% Ef_(iN,iS) = Calculate_Ef(u); %Here its calculating the f_function
Ef_(iN,iS) = -0.356324 %REMOVE-TESTING
u.Ef_ = Ef_(iN,iS); %Here Ef equals
u.Q = Calculate_El(u);%Here is calculating the charge
DiffQ(u);
catch
Ef_(iN,iS) = NaN; %If there is nothing then NaN
end
end
end
clf,
plot(u.psi_0_range, u.Q) %Its plotting the graph
u.Ef_all = Ef_;
save \'u.mat\' %It saves all the data in u.file
save \'Ef_.dat\' Ef_ -ascii %Exports the data of Ef as ascii
keyboard %This command gives the control to the user
end
%================================================
function [Ef_] = Calculate_Ef(u)
clc
time = cputime;
%rescale volumes for numerical stability
u.Nscale = u.N1 ^ 2;
Nscale = u.Nscale;
u.N1 = u.N1 / Nscale;
u.N2 = u.N2 / Nscale;
u.Z1 = u.Z1 / Nscale;
u.Z2 = u.Z2 / Nscale;
%get rid of the u.\'\'
N1 = u.N1; N2 = u.N2;
Z1 = u.Z1; Z2 = u.Z2;
Eg = u.Eg;
a = u.a;
NA = u.NA/Nscale; ND = u.ND/Nscale;
P_1 = @(E) Z1.*sqrt(-Eg-E); %This is the parabolic function(Valance band)
P_2 = @(E) Z2.*sqrt(E-Eg); %This is the parabolic function (Conduction band)
Fn = @(E,Ef) 1 ./ ( exp((E-Ef)/a) ); %This is the Fermi-dirac for electrons
Fp = @(E,Ef) 1 ./ ( exp((Ef-E)/a) ); %This is the Fermi-dirac for holes
dp = @(E,Ef) P_1(E) .* Fp(E,Ef); %the integrands
dn = @(E,Ef) P_2(E) .* Fn(E,Ef);
p = @(Ef) Nscale * (IntegrateInf_p( @(E) dp(E,Ef), u ) + ND); %define our functions p & n
(Ef)
n = @(Ef) Nscale * (IntegrateInf_n( @(E) dn(E,Ef), u ) + NA);
%%we need to make sure that multiplication/division with Nscale is consistent all the way
through to DiffQ
Ef_ = Solve_Ef(-0.5, p, n); %Ef* is obtained here
fprintf(\'The value Ef*= %f, gives equal val.
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- 3. EXECUTION