Composite Plate Bending Analysis With Matlab Code Link

The reduced stiffness matrix $[Q]$ relates stress and strain: $$ \beginBmatrix \sigma_1 \ \sigma_2 \ \tau_12 \endBmatrix = [Q] \beginBmatrix \epsilon_1 \ \epsilon_2 \ \gamma_12 \endBmatrix $$

Consider a square composite plate with a length and width of 10 m and a thickness of 0.1 m. The plate is made of a carbon/epoxy material with the following properties: Composite Plate Bending Analysis With Matlab Code

function [Nw, dN] = shape_functions(xi, eta) % Shape functions and derivatives for w (12-term polynomial) % xi, eta in [-1,1] for master element (size 2a x 2b) % Returns Nw (1x4) for nodal w, dN (2x4) for slopes? Actually we need 12 DOF. % Here simplified: we return shape functions for w only. % For full [B] matrix, we need derivatives of w wrt x,y. The reduced stiffness matrix $[Q]$ relates stress and

The first step is determining the , which relates mid-plane strains and curvatures to applied resultants (forces and moments). Determine Reduced Stiffness ( ): Calculate the matrix for each layer using its material properties ( Transform Stiffness ( % Here simplified: we return shape functions for w only

function As = shear_stiffness(layup, E1, E2, nu12, G12, G13, G23, k) % Transverse shear stiffness matrix (2x2) As = zeros(2,2); total_h = sum(layup(:,2)) 1e-3; z_bottom = -total_h/2; thickness = layup(:,2) 1e-3; for i = 1:size(layup,1) theta = layup(i,1); zk = z_bottom + sum(thickness(1:i)); zk_prev = zk - thickness(i); % Transform G13, G23 m = cosd(theta); n = sind(theta); Gxz = G13 m^2 + G23 n^2; Gyz = G13 n^2 + G23 m^2; Qshear = [Gxz, 0; 0, Gyz]; As = As + Qshear * (zk - zk_prev); end As = k * As; end

% w_yyyy term if j-2 >= 1, A_mat(idx, node(i,j-2)) = A_mat(idx, node(i,j-2)) + Dyy/dy^4; end A_mat(idx, node(i,j-1)) = A_mat(idx, node(i,j-1)) -4*Dyy/dy^4; A_mat(idx, node(i,j)) = A_mat(idx, node(i,j)) +6*Dyy/dy^4; A_mat(idx, node(i,j+1)) = A_mat(idx, node(i,j+1)) -4*Dyy/dy^4; if j+2 <= ny, A_mat(idx, node(i,j+2)) = A_mat(idx, node(i,j+2)) + Dyy/dy^4; end