% Compute ply positions (z coordinates) z_coords = linspace(-h_total/2, h_total/2, n_layers+1);
fprintf('========================================\n'); fprintf('Composite Plate Bending Analysis Results\n'); fprintf('========================================\n'); fprintf('Laminate: [0/90/90/0]\n'); fprintf('Plate size: %.2f m x %.2f m\n', a, b); fprintf('Thickness: %.3f mm\n', h_total 1000); fprintf('Pressure: %.1f Pa\n', p0); fprintf('Mesh: %dx%d elements\n', Nx_elem, Ny_elem); fprintf('Center deflection (FEM) : %.6f mm\n', w_center_FEM 1000); fprintf('Center deflection (Analytical) : %.6f mm\n', w_analytical 1000); fprintf('Error: %.2f %%\n', abs(w_center_FEM - w_analytical)/w_analytical 100);
Mxx ; Myy ; Mxy = [D] * κxx ; κyy ; κxy We use a 4-node rectangular element (size 2a×2b in local coordinates). Each node has 3 DOF: w, θx = ∂w/∂y, θy = -∂w/∂x. 2.1 Shape Functions (non-conforming but widely used) The deflection w is approximated by a 12-term polynomial: Composite Plate Bending Analysis With Matlab Code
% Find center deflection center_x = floor(nx/2)+1; center_y = floor(ny/2)+1; w_center_FEM = W(center_x, center_y);
% To get correct results, replace this function with a proper % Kirchhoff plate element or use Mindlin-Reissner theory. % The current script structure is valid but needs B matrix implementation. % Compute ply positions (z coordinates) z_coords =
%% 1. Input Parameters a = 0.2; % plate length in x-direction (m) b = 0.2; % plate length in y-direction (m) h_total = 0.005; % total plate thickness (m) Nx_elem = 8; % number of elements along x Ny_elem = 8; % number of elements along y p0 = 1000; % uniform pressure (Pa)
f_e = ∫_-1^1∫_-1^1 p * [N_w]^T * det(J) * (a*b) dξ dη Only the w DOF has load; θx, θy loads are zero. The code below solves a simply supported square composite laminate [0/90/90/0] under uniform pressure. We compare center deflection with analytical series solution. 3.1 Complete MATLAB Code % ============================================================ % Composite Plate Bending Analysis using 4-node Rectangular Element % Classical Laminated Plate Theory (CLPT) % Degrees of freedom per node: w, theta_x, theta_y % ============================================================ clear; clc; close all; % The current script structure is valid but
% At each node i, shape function for w gives 1 at node i, 0 at others. % Using bilinear shape functions for w alone would cause incompatibility. % For a working element, we use the ACM element (12 DOF). Simplified here: