i am trying to get the value of u_E using the equation, but matlab says it has error in that line which has the equation.

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kaixi gu 2022-9-10

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评论： Torsten 2022-9-10

%creat symbol for axial force, length, thickness, displacemnent and width
syms f l t d w
%define governing equations for parameter
stress = f./(t*w)
strain = d./l
%measurement resolution and uncertainty
u_f = (f./100)./2./12;
u_l = 1/32/12/2;
u_t = 0.001/2/12;
u_d = (d./100)./2./12;
u_w = 0.001/12/2;
%zeroth order uncertainty
E = (f.*l)./(d.*w*t);
u_E = sqrt((diff(E,u_f).*u_f).^2 + (diff(E,u_d).*u_d).^2 + ...
    (diff(E,u_l).*u_l).^2+(diff(E,u_t).*u_t).^2+(diff(E,u_w).*u_w).^2)
%define symbolic data
T = readtable('Intro_specimen 2.txt');
f = T{:,2};
l = 6.125;
t = 0.057;
d = (T{:,1})./12;
w = 0.414;
%substitute value into equation
stress = eval(stress);
strain = eval(strain);
%plot with errorbar
plot(strain,stress)
hold on
title('strain vs. stress')
xlabel('strain (ft^3)')
ylabel('stress (slug/ft^3)')

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Answer 1

Paul 2022-9-10

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Hi kaixi

%creat symbol for axial force, length, thickness, displacemnent and width
syms f l t d w
%define governing equations for parameter
stress = f./(t*w);
strain = d./l;
%measurement resolution and uncertainty
u_f = (f./100)./2./12;
u_l = 1/32/12/2;
u_t = 0.001/2/12;
u_d = (d./100)./2./12;
u_w = 0.001/12/2;
%zeroth order uncertainty
E = (f.*l)./(d.*w*t);
u_E = sqrt((diff(E,u_f).*u_f).^2 + (diff(E,u_d).*u_d).^2 + ...
    (diff(E,u_l).*u_l).^2+(diff(E,u_t).*u_t).^2+(diff(E,u_w).*u_w).^2)

In the Symbolic Math Toolbox, the function diff is used to diffentiate an expression with respect to a variable. So

diff(E,u_f)

means take the derivative of E wrt u_f, but u_f is an expression, not a variable. Similarly, u_l is a number, not a variable.

What exactly is the math that we're trying to implement?

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kaixi gu 2022-9-10

i am trying to calculate the zeroth order of uncertainty using that equation, then i am trying to plot the graph with error bar. f is the force and d is the displacement, and they are a set of data from the txt file. l, t, w are constant value.