CLPT assumes that straight lines normal to the mid-surface remain straight and normal after deformation (no shear deformation). Displacement field:
u(x,y,z) = u0(x,y) - z * ∂w/∂x
v(x,y,z) = v0(x,y) - z * ∂w/∂y
w(x,y,z) = w0(x,y)
We use a 4-node rectangular plate element with 5 DOF per node (FSDT):
u, v, w, θx, θy
Shape functions are bilinear Lagrange interpolations. The element stiffness matrix is: Composite Plate Bending Analysis With Matlab Code
[Ke] = ∫ [B_m]^T [A] [B_m] dA + ∫ [B_b]^T [D] [B_b] dA + ∫ [B_s]^T [As] [B_s] dA
where:
For validation, replace the laminate with a single isotropic layer (set E1=E2, G12=E/(2(1+nu)), same thickness). Compare to analytical formula: CLPT assumes that straight lines normal to the
[ w_max = 0.00406 \fracq a^4E h^3 \quad \text(square, simply supported) ]
Your MATLAB result should match closely. We use a 4-node rectangular plate element with
Unlike isotropic materials (like steel or aluminum), composite laminates have directional properties that vary based on fiber orientation and stacking sequence. Analyzing the bending of these plates requires calculating the ABD matrices (stiffness) and solving for curvatures and stresses.
We will focus on Classical Lamination Theory (CLT), which is the standard engineering approach for thin to moderately thick plates.
| Tool | Best For | Complexity | Cost | | :--- | :--- | :--- | :--- | | MATLAB (this code) | Learning, academic research, small parametric studies | Medium | License cost | | Python with FEniCS / scikit-fem | Open-source, similar transparency | Higher | Free | | ANSYS / Abaqus UMAT | Industrial design, large models, nonlinearity | Very High | Expensive | | LAP (Laminate Analysis Program) | Quick laminate property calc (no FEA) | Low | Free / Shareware |
If the fibers are oriented at an angle $\theta$ relative to the plate axis ($x-y$), we transform the stiffness matrix: $$ [\barQ] = [T]^-1 [Q] [T]^-T $$ (This is handled via transformation matrices involving $\sin\theta$ and $\cos\theta$).