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

% 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

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.

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