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Solving Classical Laminate Stiffness & Weibull Distribution

Composite Mechanics & Optimizer

Classical Laminate Theory & Weibull Statistical Reliability Solver

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Total Thickness
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Plies Count
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Structural Status
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Min Strength Ratio

Laminate Stack Editor

Ply # Thickness (mm) Angle (°) Material Selection Actions

CLT Stiffness Matrices [A], [B], [D]

A Matrix (In-Plane Stiffness)
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B Matrix (Extension-Bending Coupling)
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D Matrix (Bending Stiffness)
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Homogenized 2D Engineering Constants

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Longitudinal Modulus Ex (GPa)
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Transverse Modulus Ey (GPa)
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Shear Modulus Gxy (GPa)
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Poisson's Ratio νxy
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Influence Coeff. ηxy,x
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Influence Coeff. ηxy,y

Ply-by-Ply Analysis

Ply Material Angle (°) Thickness (mm) Midplane Z (mm) σ₁ (MPa) σ₂ (MPa) τ₁₂ (MPa) Tsai-Wu Index Strength Ratio Status
No analysis run yet. Set inputs and click "Solve Current Laminate" or "Optimize".

Laminate Stacking View

No stack loaded

Stress/Strain Distribution

Directional Elastic Properties (Polar Moduli)

This polar plot shows the variation of equivalent Young's Moduli (Ex, Ey) and Shear Modulus (Gxy) in GPa as a function of orientation angle θ (0° to 360°). The plot updates dynamically as you modify the laminate stacking sequence in the editor or the material properties.

Optimizer Constraints

Lamination-parameter mode requires exactly one candidate material.

Requires strength ratios to be greater than SF (i.e. Failure Index ≤ 1/SF).

Requires "Direct Stacking GA" strategy. Material/thickness selection still comes from the candidates below; only the angle becomes a free variable. The 10% Rule is skipped in this mode.

Weibull Statistical Parameters

Indicates scatter of strength. Typical value for carbon/glass fibers: 8.0 - 15.0.

Allowed failure risk (e.g. 0.01 = 1% chance of FPF).

Optimization Results

Configure options above and click "Optimize Configuration" in the sidebar to run the optimizer.

Weibull Fit Outputs

Calibration Source: Synthetic Monte Carlo
Weibull Modulus (Input): -
Weibull Modulus (Fitted): -
Failure Coefficient (Nominal): -
Failure Coefficient (Fitted scale): -
Failure Probability at load (1.0): -

Laminate Strength Probability Distribution

Linearized Weibull Plot & Goodness of Fit

MLE & Goodness-of-Fit
MLE Shape Parameter (mMLE): -
MLE Scale Parameter (σ0,MLE): -
AD Statistic (Adjusted): -
Fit Verification Status: -
Design Allowables (A & B-Basis)
Method B-Basis (T90) A-Basis (T99)
Normal Dist - -
Weibull Dist - -
Non-Parametric - -

The Failure Coefficient (Scale parameter) represents the load factor multiplier at which the probability of laminate failure reaches 63.2%. The algorithm calculates the exact strength limit of the laminate system (using a Monte Carlo simulation or evaluating directly against the loaded experimental coupon data).

Experimental Test Data Fit

Upload a CSV or TXT file with experimental failure/strength measurements (one value per line or comma-separated) to fit a Weibull distribution and overlay it on the chart.

No file selected

Plate Buckling Parameters

Results

Critical Load Factor (λcr): -
Dominant Mode (m, n): -

3D Buckling Mode Shape Visualizer

Run buckling analysis to display 3D mode shape

Plate Bending Parameters

Results

Max Deflection (wmax): -
Deflection Location (x, y): -

3D Deflection Visualizer

Run bending analysis to display 3D deformation grid

Plate Vibration Parameters

Natural Frequencies

Mode (m, n) Frequency (Hz)
No vibration data yet

3D Fundamental Mode Shape Visualizer

Run vibration analysis to display 3D fundamental mode
[SYSTEM] Engine online and ready for calculations.
For solver assumptions, theories, and engineering verification details, see the Solver Capabilities & Technical Methodology Guide.