CubeSat Satellite
CubeSat satellites, measuring only 10×10×10 cm, are widely used for low-cost space exploration but face extreme loading conditions during launch into Low Earth Orbit (LEO). Designing lightweight yet durable composite panels for these spacecraft requires optimizing the ply orientation and stacking sequence of fiber-reinforced laminates. Using Classical Laminated Plate Theory (CLPT), our objective was to analyze stresses, strains, and failure indices for potential layups and determine the most reliable configuration under realistic launch loads.
Project Overview
CubeSats must endure accelerations of up to 10g during ascent to Low Earth Orbit, making laminate optimization critical to prevent premature failure.
We selected a Carbon/Epoxy IM6G/3501-6 composite system. Compared to E-glass/epoxy, it offered a 312% higher longitudinal modulus (169 GPa vs. 41 GPa) and nearly double the tensile strength (2240 MPa vs. 1140 MPa). Against Kevlar/epoxy, it showed a 19% improvement in tensile strength (2240 MPa vs. 1400 MPa) while also maintaining superior stiffness, which Kevlar often sacrifices. Even within carbon systems, IM6G outperformed common alternatives such as AS4, offering about a 15% higher longitudinal modulus (169 GPa vs. 147 GPa).
For our design, the laminate was constrained to a 2.1 mm total thickness, consisting of 14 plies at 0.15 mm each, which aligned with CubeSat industry standards while maintaining the thin-laminate assumptions of Classical Laminated Plate Theory.
While the project originally required analyzing any two layup sequences, we went beyond the assignment and set out to evaluate the entire design space. By assuming symmetry about the mid-plane, the problem reduced to 7 unique plies, each with 8 possible orientations (0°, ±30°, ±45°, ±60°, 90°), leading to 2,097,152 possible stacking sequences (8^7) to evaluate. I personally developed a MATLAB algorithm to systematically analyze all combinations under both Tsai-Wu and Maximum Strain failure criteria.
Figure 1. Material comparison of longitudinal modulus (GPa).
Figure 2. Material comparison of longitudinal tensile strength (MPa).
MATLAB Analysis
The purpose of the MATLAB code was to identify laminate layups that could survive CubeSat launch loads while minimizing the Failure Index (FI) as measured by two criteria: Tsai-Wu and Maximum Strain. In both cases, an FI value of 1 corresponds to the onset of failure. While lower FI values at baseline loads indicate greater safety margin, the goal of this optimization was to scale the applied loads upward and determine which laminate could withstand the highest multiplier before its FI reached 1. In this way, the “best” layup was not the one with the lowest FI under initial conditions, but the one that failed last when pushed to its structural limit.
To achieve this, the script first generated all 2,097,152 symmetric stacking sequences in a 2,097,152 by 14 matrix. For each candidate layup (rows), the program calculated the reduced stiffness matrices (S and Q) at the lamina level, then assembled the laminate stiffness matrices (A, B, D). Using these, it computed both global stresses and strains as well as local ply-level responses under the applied Nx, Ny, Mx, and My loads. These loads represented the distributed in-plane forces and bending moments generated by 5g (x-direction) and 10g (y-direction) launch accelerations acting on the CubeSat panels. Each sequence was then evaluated with the Tsai-Wu quadratic failure theory, which accounts for multiaxial stress interactions, and the Maximum Strain criterion, which flags failure when principal strains exceed material limits.
Any stacking sequence with FI ≥ 1 was discarded, as this indicated ply failure, while those that remained were compared to identify the layup with the lowest maximum FI across all plies. This approach systematically eliminated weak designs while converging on sequences that delayed failure as much as possible. Ultimately, the algorithm transformed what would have been a subjective, trial-and-error task into a quantitative optimization problem.
Figure 3. MATLAB workflow for evaluating symmetric laminate stacking sequences (SS). The process calculates stresses, applies failure criteria, and selects the optimal stacking sequence.
Figure 4. MATLAB implementation of the Tsai-Wu failure criterion, looping through all stacking sequences to compute ply-level stresses, evaluate failure indices, and identify the layup with the lowest maximum failure index.
Results & Conclusion
The MATLAB optimization identified two optimal stacking sequences, one based on the Tsai-Wu criterion and another based on the Maximum Strain criterion, and compared them against a user-defined layup ([0/±45/90]s). This provided a direct benchmark between automated optimization and traditional hand-selected designs.​
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Optimized Tsai-Wu Layup: [60/–60/–45/–30/30/–30/60]s
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Maximum FI = 1.00 (ply 14) under baseline launch loads.
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Baseline Loads: Nx = 18.15 N, Ny = 36.3 N, Mx = 453.75 N·mm, My = 907.5 N·mm.
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Optimized Max Strain Layup: [45/–60/–60/45/–45/–45/30]s
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FI = 1.504 (ply 14) at the same baseline loads, meaning it “failed” under Tsai-Wu but was still valid under Max Strain.
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Sustained higher scaled loads before failing in the outermost ply (ply 14).
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User-Defined Layup: [90/45/0/90/45/0/90]s
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Maximum FI = 2.178 at baseline loads, with first-ply failure occurring in the outermost ply (ply 14).
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Failed twice as fast as the optimized sequences.
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Demonstrated how intuitive, hand-selected orientations can leave hidden weaknesses, particularly when heavily biased toward 0° and 90° plies.
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Stiffness Considerations:
The ABD matrices revealed that the user-defined layup actually produced the highest stiffness values, particularly in the A and D matrices. However, this came at the expense of strength and durability. While stiffness helps resist deformation, overly stiff laminates concentrate stresses, making them more prone to ply-level failure and delamination. The optimized sequences struck a better balance, providing sufficient stiffness for structural stability while also maximizing failure resistance under multi-axial loads.
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Comparison of Criteria:
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Tsai-Wu Criterion: Conservative, accounting for multiaxial stress interactions. It predicted failure earlier (FI ≈ 1 at baseline), but gave a more realistic safety margin critical for aerospace.
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Maximum Strain Criterion: Allowed higher load predictions, suggesting more capacity, but neglected stress interactions, making it less reliable for complex CubeSat loading conditions.
Figure 5. Comparison of three stacking sequences: the best layup identified using the Tsai-Wu criterion for maximum loading (shown in the two figures below).
Figure 6. Failure load cases for the three stacking sequences under both Tsai-Wu and Maximum Strain criteria. Maximum Strain allowed higher predicted loads but neglected stress coupling.
Figure 7. Final laminate design selected under the Tsai-Wu criterion.
Figure 8. Stiffness matrices (A, B, D) and local stress/strain results for the optimized [60/–60/–45/–30/30/–30/60]s laminate. The nearly zero B-matrix confirms symmetry with no bending-extension coupling, and the highest stresses occur in the outermost ply (ply 14), where first-ply failure was observed (red box).
Conclusion
The results showed that while stiffness could be maximized by certain hand-selected layups, true reliability required algorithmic optimization. The Tsai-Wu optimized layup [60/–60/–45/–30/30/–30/60]s achieved the most efficient balance of strength, stiffness, and weight while avoiding unnecessary overdesign. This comparison reinforced the importance of conservative failure theories such as Tsai-Wu in aerospace applications, where reliability takes precedence over theoretical maximum capacity.