, the series converges quickly. Limiting the calculation to MaxTerms = 49 ensures accuracy within a fraction of a percent while keeping computational demands low.
[Ke] = ∫ [B_m]^T [A] [B_m] dA + ∫ [B_b]^T [D] [B_b] dA + ∫ [B_s]^T [As] [B_s] dA
For a laminate of N layers, we compute:
fprintf('Layer %d (%.0f deg):\n', k, layers(k)); fprintf(' Top (z=%.4f): Sx=%.2f MPa\n', z_top_k, stress_top(1)/1e6); end Composite Plate Bending Analysis With Matlab Code
The current code can be extended to:
for thicker ones. The central goal is to determine the laminate stiffness matrices (
For an orthotropic lamina (e.g., fiber-reinforced composite) oriented at an angle θ, the stress-strain relationship in the lamina's principal coordinates (1,2) is: , the series converges quickly
due to the symmetric boundary conditions and symmetric load profile. Stress and Strain Recovery Once the deflection field
%% Composite Plate Bending Analysis using FSDT % Rectangular laminated composite plate with various boundary conditions % Author: FEA for Composites % Units: SI (N, m, Pa)
w(x,y)=∑m=1∞∑n=1∞Wmnsin(mπxa)sin(nπyb)w open paren x comma y close paren equals sum from m equals 1 to infinity of sum from n equals 1 to infinity of cap W sub m n end-sub sine open paren the fraction with numerator m pi x and denominator a end-fraction close paren sine open paren the fraction with numerator n pi y and denominator b end-fraction close paren 2. Step-by-Step MATLAB Implementation The MATLAB code is structured into three parts: The central goal is to determine the laminate
are the reduced stiffness components derived from engineering constants ( 2.2. Laminate Level (Force-Deformation) The overall bending behavior is captured by the matrix (Extensional, Coupling, and Bending stiffness):
Computes the stiffness matrices A, B, D by iterating through layers, transforming the Q-matrix, and integrating through the thickness.
matrix and calculates the maximum deflection of a under uniform load (
E1 = 100e9; % Young's modulus in the 1-direction (Pa) E2 = 50e9; % Young's modulus in the 2-direction (Pa) nu12 = 0.3; % Poisson's ratio G12 = 20e9; % Shear modulus (Pa) t = [0.001; 0.002]; % layer thicknesses (m) Lx = 1; % plate length in the x-direction (m) Ly = 1; % plate length in the y-direction (m) q = 1000; % uniform load (Pa)
% Mid-plane strains and curvatures ex0 = 0; ey0 = 0; gxy0 = 0; kx = -q / (24 * D); ky = -q / (24 * D); kxy = 0;