# How can I put multiple values of lbar[0.2 0.3 0.4] and sigma[0.1 0.15 0.20] to obtain the subsequent multiple values of W, F,f,deltaT and Xbar.

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AVINASH SAHU on 6 Jun 2022
Commented: AVINASH SAHU on 6 Jun 2022
% For plane slider: H = Ho + a(1-x)
Ho = 1;
alpha = 0.1;
eps = 0.1;
a = 1.0;
lbar = 0.2;
sigma = 0.10;
H = @(x) Ho + a*(1 - x);
G1 = @(x) H(x).^3 + 3 .* H(x).^2 .* alpha + 3 .* H(x) .* alpha^2 + 3 .* H(x) .* sigma^2 + eps + 3*sigma^2*alpha + alpha^3 - 12*lbar^2 .* (H(x) + alpha);
G2 = @(x) 24 * lbar^3 .* tanh(H(x)./(2*lbar));
G3 = @(x) (12*lbar^2*alpha - eps - alpha^3 - 3*sigma^2*alpha) .* (1 - (tanh(H(x)./(2*lbar))).^2);
G = @(x) G1(x) + G2(x) + G3(x);
Hm1 = @(x) H(x).* (1 ./ G(x));
Hm2 = @(x) (1 ./ G(x));
IntHm1 = integral(Hm1,0,1);
IntHm2 = integral(Hm2,0,1);
Hm = IntHm1 / IntHm2;
% Calculating dimensionless load carrying capacity
P1 = @(x) 6 .* (1 ./ G(x)) .* (H(x) - Hm);
P = @(x) integral(P1,0,x);
W = integral(P,0,1, 'ArrayValued', true)
% Calculating non dimensional Frictional Force(F):
F1 = @(x) (H(x).* P1(x)) ./2 + (1 ./ H(x));
F = integral(F1,0,1)
% Calculating coefficient of friction:
f = F/W
% Calculating non dimensional temperature rise
deltaT = F/Hm
% Calculating the center of pressure
Xbar1 = @(x) P(x) .* x;
Xbar2 = integral(Xbar1, 0, 1, 'ArrayValued', true);
Xbar = Xbar2/W
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AVINASH SAHU on 6 Jun 2022
Yes, now it is clear.