program matlab

1. 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,mu,l,lamda); z0 = linspace(a,b,11); yinit = [0 0 0 0]; initial_values = bvpinit(z0, yinit); solutn = bvp4c(deq,@bcdnts,initial_values); soln = deval(solutn,z0); z0' soln'

2. Function specifying boundary conditions function bdry = bcdnts( u0,u1 ) global po global pin bdry = [ u0(4)-pin ; u1(4)+po ; u0(3) ; u1(3) ]; end
Differential equation function function f = D2_diffeqtn( r,u,m,l,lmda ) f = zeros(4,1); f(1) = u(4)/(2*m+lmda)-lmda/(2*m+lmda)*u(1)/r + lmda/l*pi*u(2)/(2*m+lmda); f(2) = u(3)/m - pi/l*u(1); f(3) = -lmda/(2*m+lmda)*pi/l*u(4) - 2*m*lmda/(2*m+lmda)*pi/l*u(1) - (lmda^2/(2*m+lmda)- (2*m+lmda))*pi^2/l^2*u(2) - u(3)/r; f(4) = 2*m/r*u(4)/(2*m+lmda) + pi/l*u(3) - 2*m*lmda/r*pi/(2*m+lmda)*u(2)/l + ((2*m+lmda)/r^2- lmda^2/(2*m+lmda)*1/r^r)*u(1); end

3. EXECUTION
E = 2.000000000000000e+11 ans = 1.0e+02 * 0.050000000000000 0.145000000000000 0.240000000000000 0.335000000000000 0.430000000000000 0.525000000000000 0.620000000000000 0.715000000000000 0.810000000000000 0.905000000000000 1.000000000000000