% Local coordinates x = xi * a_elem; y = eta * b_elem;
% Element connectivity elements = zeros(Nx_elem * Ny_elem, 4); elem_id = 0; for iy = 1:Ny_elem for ix = 1:Nx_elem elem_id = elem_id + 1; n1 = (iy-1)*nx + ix; n2 = n1 + 1; n3 = n2 + nx; n4 = n3 - 1; elements(elem_id, :) = [n1, n2, n3, n4]; end end Composite Plate Bending Analysis With Matlab Code
% Shape functions for w (Hermitian-type, non-conforming) % We use standard Kirchhoff plate element (Zienkiewicz's non-conforming) % Define basis functions: Nw = zeros(1,4); Nwx = zeros(1,4); % dNw/dx Nwy = zeros(1,4); % dNw/dy % Local coordinates x = xi * a_elem;
function [B, detJ] = compute_B_matrix(xi, eta, a_elem, b_elem) % Computes B matrix (3x12) relating curvatures to nodal DOF % For a 4-node rectangular element with 3 DOF per node (w, thetax, thetay) % Node ordering: 1:(-1,-1), 2:(1,-1), 3:(1,1), 4:(-1,1) y = eta * b_elem
% Assemble into global matrix dof_map = zeros(1,12); for inode = 1:4 global_node = nodes(inode); dof_map(3*(inode-1)+1) = 3*(global_node-1) + 1; % w dof_map(3*(inode-1)+2) = 3*(global_node-1) + 2; % theta_x dof_map(3*(inode-1)+3) = 3*(global_node-1) + 3; % theta_y end K_global(dof_map, dof_map) = K_global(dof_map, dof_map) + Ke; F_global(dof_map) = F_global(dof_map) + Fe; end