Calculating Axial Deformation of bar in MATLAB | Finite Element Analysis (FEA) Method

[@ananthuv9843]

Where is the code?

[@themechanicalengineer]

% Parameters
L = 1.0; % Length of the bar (meters)
Nx = 100; % Number of elements
E = 2.1e11; % Young's Modulus (Pa)
A = 0.001; % Cross-sectional Area (m^2)
F = 1000; % Applied axial force (Nm)
% Element properties
elementLength = L / Nx; % Length of each element
elementNodes = 2; % Number of nodes per element (2 for linear elements)
% Node coordinatesx = linspace(0, L, Nx + 1);
% Initialize stiffness matrix and force vector
K_global = zeros(Nx + 1, Nx + 1);
F_global = zeros(Nx + 1, 1);
% Assembly of stiffness matrix and force vector
for e = 1:Nx
% Element stiffness matrix
ke = (E * A / elementLength) * [1, -1; -1, 1];
% Element force vector
fe = (F * elementLength / 2) * [1; 1];
% Add element contributions to global matrix
nodes = [e, e+1];
K_global(nodes, nodes) = K_global(nodes, nodes) + ke;
F_global(nodes) = F_global(nodes) + fe;
end
% Apply boundary conditions (fixed ends)
K_global(1, :) = 0;
K_global(1, 1) = 1;
F_global(1) = 0;
K_global(end, :) = 0;
K_global(end, end) = 1;
F_global(end) = 0;
% Solve for displacements
u = K_global \ F_global;
% Plot the deformation
plot(x, u)
xlabel('Position (m)')
ylabel('Deformation (m)')
title('Deformation')
grid on

[@mukundpurohit2637]

What changes should be made if the beam is cantilever with force at free end?

[@themechanicalengineer]

Use the stiffness matrix and force vector of beam elements. The procedure is same.

[@askandmishra4811]

How to derive axial deformations for a column in matlab using fem and also for buckling condition

[@themechanicalengineer]

To derive axial deformations for a column using the Finite Element Method (FEM) in MATLAB:
Define the geometry and material properties of the column.
Create a mesh with finite elements (e.g., 1D beam elements).
Specify boundary conditions (e.g., supports and applied loads).
Assemble the stiffness matrix for the system.
Apply loads to the column.
Solve for the displacements using a solver like the backslash operator ().
Calculate axial deformations at different points along the column by analyzing the displacement results.