Compute ABD matrices, in-plane strains and curvatures, ply stresses, and Tsai-Wu/Tsai-Hill failure criteria based on Classical Lamination Theory in real time. Ideal for CFRP and GFRP laminate design.
Laminate force-strain relationship (ABD matrix):
$$\begin{bmatrix}N \\ M \end{bmatrix}= \begin{bmatrix}A & B \\ B & D \end{bmatrix}\begin{bmatrix}\varepsilon^0 \\ \kappa \end{bmatrix}$$Ply stress in material axes: $\{\sigma\}_k = [Q]_k [T]_k \{\varepsilon\}(z_k)$
$A_{ij}= \sum_k \bar{Q}_{ij}^{(k)}(z_k - z_{k-1})$, $D_{ij}= \frac{1}{3}\sum_k \bar{Q}_{ij}^{(k)}(z_k^3 - z_{k-1}^3)$
| Ply # | Angle [°] | σ₁ [MPa] | σ₂ [MPa] | τ₁₂ [MPa] | Tsai-Wu FI | Tsai-Hill FI | Status |
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The core of CLT is the constitutive relation that links the applied forces and moments (N, M) to the mid-plane strains and curvatures (ε⁰, κ) of the laminate. This is done through the combined ABD stiffness matrix.
$$ \begin{bmatrix}N \\ M \end{bmatrix}= \begin{bmatrix}A & B \\ B & D \end{bmatrix}\begin{bmatrix}\varepsilon^0 \\ \kappa \end{bmatrix}$$N: In-plane force resultant [N/mm]. M: Moment resultant [N·mm/mm]. A: Extensional stiffness matrix. B: Coupling stiffness matrix. D: Bending stiffness matrix. ε⁰: Mid-plane strain. κ: Plate curvature.
To assess the safety of each individual ply, we calculate its stress in the material direction and evaluate it against a failure criterion. The Tsai-Wu criterion is a common interactive tensor polynomial.
$$ F_i \sigma_i + F_{ij}\sigma_i \sigma_j \geq 1 \quad \text{(Failure when ≥ 1)}$$Here, σ_i are the ply stresses (σ₁, σ₂, τ₁₂). The coefficients F_i and F_{ij} are derived from the ply strengths you input: tensile/compressive strength in fiber direction (F₁t, F₁c), transverse strength (F₂t, F₂c), and shear strength (F₁₂). An index below 1 means the ply is safe.
Aerospace Wing & Fuselage Skins: Composite laminates are designed to be lightweight yet withstand complex aerodynamic loads and pressurization. Engineers use CLT to optimize ply angles (e.g., [0/±45/90]s) to achieve the right balance of stiffness, strength, and buckling resistance, exactly as you can experiment with in this simulator.
Wind Turbine Blades: These massive structures experience extreme bending and torsional loads. CLT analysis is critical for placing unidirectional plies (high E₁) along the spar caps for bending strength and ±45° plies in the shear webs to handle torsional forces, ensuring a 20+ year lifespan.
Automotive Chassis & Body Panels: In high-performance or electric vehicles, carbon fiber panels reduce weight to increase range or speed. CAE engineers use CLT to simulate crashworthiness, where the coupling effects (B matrix) and progressive ply failure (Tsai-Wu) are analyzed to manage energy absorption.
Sports Equipment (Racquets, Bikes): The feel and performance of a tennis racket or bicycle frame are finely tuned by layering plies at specific angles. CLT helps designers tailor the bending stiffness (D matrix) and torsional rigidity by adjusting the sequence, much like changing parameters here to see the immediate effect on deformation.
First, the misconception that "you can input any material constant and still get a result." For example, CFRP's E₁ (longitudinal Young's modulus) is around 120 GPa, but are you inadvertently using a value for GFRP (about 40 GPa)? This changes the order of magnitude of the results, rendering them useless. Initially, it's safest to copy and use the default values in the tool or values from a material database as-is. Next, the assumption that "a failure criterion value below 1.0 guarantees absolute safety." Even with a Tsai-Wu ratio of 0.95, failure can still occur in reality due to delamination, manufacturing defects, or cyclic loading. Simulation results are merely a "guideline for comparison." Finally, the pitfall of thinking "only 0° and 90° ply angles need to be considered." While symmetric laminates like [0/90]s are fundamental, ±45° plies are essential if you want to increase shear stiffness. For instance, incorporating diverse angles like in a [0/±45/90]s laminate makes it stronger against complex loads.