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)
= -z * κ , where κ = ∂²w/∂x² , ∂²w/∂y² , 2∂²w/∂x∂y ^T 1.3 Constitutive Equation for Laminates For a laminate with N layers, the bending stiffness matrix D (3×3) is defined as: Composite Plate Bending Analysis With Matlab Code
w = α1 + α2 ξ + α3 η + α4 ξ² + α5 ξη + α6 η² + α7 ξ³ + α8 ξ²η + α9 ξ η² + α10 η³ + α11 ξ³η + α12 ξ η³ Where ξ = x/a, η = y/b (element coordinates). The shape functions are derived by imposing nodal DOF. [k] = ∫_-1^1∫_-1^1 [B]^T [D] [B] * det(J) * (a*b) * dξ dη Here [B] relates curvatures to nodal DOF, and [D] is the laminate bending stiffness matrix. 2.3 Equivalent Nodal Load for Uniform Pressure For uniform pressure p (N/m²): 1) nodes = elements(e
% Loop over all elements for e = 1:size(elements,1) nodes = elements(e, :); x_coords = X(nodes); y_coords = Y(nodes); x_coords = X(nodes)