A physics-driven COPV solver that evaluates laminate behaviour at the ply level, models progressive failure,
and optimises mass against a target factor of safety — built for rapid design iteration, not black-box guesswork.
Overview
High-pressure propulsion systems occupy a uniquely difficult design space: they must safely contain extreme internal
pressures while meeting aggressive mass targets, surviving thermal and mechanical cycling, and remaining manufacturable
within real-world constraints. In rocketry, structural mass directly reduces performance — yet conservative margins are
often applied because composite failure behaviour is complex and difficult to predict.
Composite Overwrapped Pressure Vessels (COPVs) offer exceptional pressure-to-weight performance, but they introduce a level
of structural complexity that can’t be captured with thin-wall pressure vessel theory or a single “burst pressure” calculation.
Laminates are anisotropic, non-homogeneous, and fail progressively rather than catastrophically. In practice this often leads to
overbuilt designs, or reliance on high-fidelity FEA that is expensive to iterate and provides limited physical intuition early in the design process.
This project was undertaken to address that gap: I expanded an in-house layup analysis script originally written by
Thomas Russell into a transparent, computationally efficient
COPV solver capable of evaluating composite layups at the ply level, modelling progressive failure,
and optimising mass vs. target factor of safety. It is not intended to replace high-fidelity FEA — it is a
design-stage decision engine that enables rapid exploration of the design space while keeping a clear link between assumptions,
physics, and results.
Core Objective
The solver is built to answer one deceptively simple engineering question:
What is the lightest composite pressure vessel that can safely survive a specified internal pressure with a defined margin against failure?
Achieving this requires more than a single stress calculation. It demands an understanding of how loads are distributed through a
laminate, how individual plies contribute to stiffness and strength, how failure initiates, and how damage propagates as pressure increases.
The solver explicitly addresses each of these aspects and outputs not only an “answer”, but the reasoning behind it.
PHYSICS-DRIVEN
Transparent modelling built around ply-level behaviour and failure progression — not opaque burst-margin rules.
MASS-OPTIMISED
Finds the minimum-mass layup meeting a target factor of safety, with constraints aligned to real manufacturing.
DESIGN INSIGHT
Outputs failure initiation pressure, failure order, and redundancy — not just a single pass/fail number.
Structural & Material Modelling Approach
At the heart of the solver is a through-thickness representation of the vessel wall. The vessel is modelled as a cylindrical pressure
structure consisting of an optional inner liner and an externally wrapped composite laminate. Each ply is defined by its material system,
thickness, and fibre orientation angle, allowing arbitrary stacking sequences to be constructed programmatically.
The inner liner is treated as a first-class structural component rather than a simplifying assumption. Depending on material
choice and thickness, the liner may carry a meaningful fraction of axial and hoop load — particularly at lower pressures before the composite
plies fully engage. This is especially relevant for combustion chambers, where a liner may also serve thermal and sealing functions.
By modelling the liner explicitly, the solver captures evolving load-sharing behaviour between liner and overwrap as pressure increases.
Material behaviour is parameterised using elastic properties and strength limits appropriate to each system. While the solver remains intentionally
efficient, it preserves enough fidelity to distinguish fibre-dominated and matrix-dominated behaviour through orientation-dependent stress evaluation.
Below is a Block Flow Diagram (BFD) depicting how the solver runs and its internal processes:
Stress Evaluation & Load Distribution
For a given internal pressure, the solver computes global hoop and axial loading and resolves these into ply-level stress states based on each
ply’s orientation and material properties. This explicitly captures the structural reality that:
0° plies primarily contribute axial stiffness and axial load capacity
90° plies dominate hoop resistance
±45° plies are critical for shear transfer, load redistribution, and damage tolerance
Rather than averaging stresses across the laminate, each ply is evaluated individually. This is a critical distinction: COPV failure is almost
always initiated by the overstressing of a specific subset of plies, not uniform material failure through the entire thickness.
Progressive Failure Modelling
The defining feature of this project is its implementation of progressive failure analysis.
In real composite pressure vessels, failure does not occur instantaneously when the first ply reaches a strength limit.
Instead, damage initiates locally, stiffness is reduced, and load redistributes to neighbouring plies. This continues incrementally until the
remaining structure can no longer sustain the applied load.
The solver captures this behaviour explicitly. Internal pressure is increased in controlled increments. At each increment, every ply is evaluated
against its failure criterion. When a ply fails, its stiffness contribution is removed or degraded, and subsequent increments reflect physically
realistic redistribution of load.
This produces outputs that simpler approaches cannot:
Failure initiation pressure (when damage begins)
Failure sequence (which plies fail first and why)
Damage accumulation behaviour (stable progression vs brittle collapse)
Structural redundancy (how well the laminate tolerates local failure)
Two layups can appear equivalent when judged only by ultimate burst pressure, yet behave radically differently once progressive damage is considered.
This is exactly the kind of nuance that matters when trying to reduce mass safely.
Optimisation Strategy
On top of the structural solver sits an optimisation framework designed to efficiently search the design space.
Rather than brute-forcing every possible layup, the optimiser uses a binary search strategy to determine the
minimum number of plies required to meet a specified factor of safety.
For each candidate layup size, the solver evaluates whether the vessel survives the target pressure without unacceptable failure progression.
Mass is computed directly from ply count, thickness, and material density — ensuring optimisation decisions are grounded in physical reality.
This approach converges quickly while remaining robust to non-linearities introduced by progressive failure. It also enables fast parametric sweeps
across pressure, diameter, material systems, liner thickness, and angle distributions with minimal computational overhead.
Outputs & Design Insight
The solver produces structured outputs intended for both human interpretation and downstream automation. These include mass vs factor-of-safety curves,
optimal layup configurations, and detailed failure progression histories. This shifts decision-making away from simple pass/fail checks and toward
informed design trade-offs.
Importantly, the solver helps explain why a layup performs well or poorly. Poor angle distributions reveal themselves through early failures
and rapid stiffness degradation, while well-balanced laminates demonstrate gradual damage accumulation and stable load redistribution. This feedback is
invaluable when iterating under tight time constraints.
Engineering Impact
The practical impact of this project lies in reducing uncertainty early in the design process. By providing fast, physically grounded predictions of COPV
behaviour, the solver enables engineers to pursue mass reduction while maintaining confidence in structural integrity.
Rapid exploration of the design space without relying on time-intensive FEA for every iteration
Improved intuition around laminate behaviour through failure sequence and load redistribution outputs
Safer designs by highlighting brittle failure modes that might otherwise be overlooked
Better use of manufacturing resources by narrowing down to the highest-quality candidates before validation
In a propulsion context, this translates directly into performance: lower structural mass improves payload capability and propulsion efficiency,
while higher confidence in failure behaviour improves safety and reduces late-stage design churn.
Future Development
The solver architecture has been designed to support expansion as test data and requirements evolve. Planned extensions include:
More advanced failure criteria and stiffness degradation models
Thermal-structural coupling to account for elevated operating temperatures in combustion chamber applications
Geometric extensions: domes/bulkheads, thickness variation along length, and improved end-condition modelling
Experimental correlation and calibration using burst/proof test data to refine material parameters and failure thresholds
The long-term aim is a tool that bridges the gap between analytical theory and full numerical simulation — fast enough for early optimisation,
but grounded enough to earn trust when the design stakes are high.
Conclusion
This project represents a shift away from black-box structural analysis toward a transparent, physics-driven design methodology.
It treats composite pressure vessels not as monolithic components, but as evolving structures whose behaviour can be understood, predicted, and optimised.
By combining progressive failure modelling with efficient optimisation, the solver enables smarter engineering decisions at the stage where they matter most.
It stands as both a practical design tool for propulsion hardware and a demonstration of rigorous structural engineering thinking applied to real constraints.
