1D two linear 2-node element solver

Hello Everyone,

I am a beginner in matlab and trying to learn fem codding. Can someone help me to solve Problem 4.4 in "A First Course in Finite Elements: Fish, Jacob, Belytschko, Ted" book?

Thank you for your help.

[Dyuman Joshi]

Please show what you have attempted yet.

[John Adams]

% Define the number of elements

numElements = [2, 4, 8];

% Define the exact displacement function

u_ex = @(x) x.^3;

% Initialize arrays to store the errors and element sizes

errors = zeros(size(numElements));

elementSizes = zeros(size(numElements));

% Iterate over different mesh configurations

for i = 1:numel(numElements)

numElems = numElements(i);

elementSize = 1 / numElems;

% Subdivide the interval [0, 1] into elements

x = linspace(0, 1, numElems + 1);

% Initialize arrays for storing the displacements and strains

u_h = zeros(size(x)); epsilon_h = zeros(size(x));

epsilon_ex = zeros(size(x));

% Iterate over each element

for e = 1:numElems

% Define the element nodes

x1 = x(e); x2 = x(e + 1);

% Define the element shape function matrix

N_e = [(x2 - x) / (x2 - x1); (x - x1) / (x2 - x1)];

Actually, I am a bit confused about steps which one I need to do first etc. I know some theoretical aspects like when I compute displacement at 2nd node of 2nd element I should not use 1st element 1st shape function but I could not turn it into code. I need a solution of this example to better understand to topic. Please help, thank you.