⚡ electrical engineering

Sensitivity Analysis and Optimization of Burst Pressure in Composite Cylindrical Pressure Vessels

This paper presents a multivariable optimization study using analytical sensitivity analysis and failure criteria to determine optimal fiber angles and layer thickness distributions that significantly maximize the burst pressure of laminated composite cylindrical pressure vessels.

Original authors: Saeed Abolghasemi

Published 2026-07-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Saeed Abolghasemi

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are building a giant, high-tech water balloon, but instead of rubber, you are wrapping it in layers of super-strong fabric. This isn't just any balloon; it's a pressure vessel designed to hold gases at pressures so high they would make a soda can explode instantly. In the world of engineering, these vessels are the heavy lifters of industry, carrying everything from natural gas to rocket fuel. The secret sauce? They are made of "composites," which are like a sandwich of strong fibers (think tiny, stiff threads) glued together with a sticky matrix (like epoxy resin). The magic happens when you twist these fibers at different angles as you wrap them around the cylinder. Just like how a woven basket is stronger if you weave the reeds in a specific pattern, the way you angle these fibers determines how much pressure the tank can take before it pops. Engineers have long known that if you get the angle just right, the tank becomes incredibly tough. But there's a catch: usually, they assume every single layer of that fabric sandwich is exactly the same thickness. It's like assuming every layer of a lasagna must be the same size, even though maybe the middle layers need to be thicker to handle the heat, or the outer layers need to be thinner to save weight. The big question is: if we could tweak not just the angle of the fibers, but also the thickness of each individual layer, could we make these tanks even stronger?

This paper, written by Saeed Abolghasemi from Golestan University, dives deep into that very question. The author treats the pressure vessel like a complex puzzle where the goal is to find the "perfect" combination of fiber angles and layer thicknesses to make the tank withstand the highest possible pressure before it bursts. To solve this, the paper uses a mathematical "stress test" based on two famous rulebooks for predicting failure: the Tsai-Hill and Tsai-Wu criteria. You can think of these as two different ways of checking if a bridge is about to collapse; one is a bit more conservative, while the other looks at how different forces interact with each other. The author didn't just guess; they built a sophisticated computer model that calculates exactly how the stress moves through the layers of the tank. Then, they used a clever mathematical trick called "sensitivity analysis." Imagine you are tuning a radio; you turn the dial slightly to see if the signal gets clearer or fuzzier. In this case, the author mathematically "turned the dial" on the fiber angles and layer thicknesses to see exactly how much the burst pressure would change. This allowed them to find the precise settings that maximize strength, rather than just stumbling upon a good guess.

The results of this digital experiment are quite revealing. The study found that by optimizing both the angle and the thickness of the layers, you can significantly boost the pressure the vessel can hold. For a specific type of strong material called graphite/epoxy, the best design found in these simulations could withstand a burst pressure of about 8.68 MPa using the Tsai-Hill rulebook, or up to 8.92 MPa using the Tsai-Wu rulebook. For a slightly less stiff material called glass/epoxy, the numbers were lower, reaching about 2.37 MPa and 2.72 MPa respectively. One of the most interesting discoveries was about the "stacking sequence," or the order in which the layers are wrapped. The paper suggests that a symmetric pattern, where the layers mirror each other (like a sandwich with the same filling on top and bottom), often performs the best. In fact, for the best-performing design, the simulation showed that all the layers reached their breaking point at the exact same time. This is the engineering equivalent of a choir where every singer hits the high note perfectly together, rather than one person screaming while the others are still warming up. It means the material is being used with maximum efficiency.

However, the paper also points out that there isn't always just one single "perfect" answer. For some designs, the computer found multiple different ways to arrange the layer thicknesses that resulted in the same maximum strength. It's like finding that you can make a perfect cake with either two cups of flour and one cup of sugar, or one and a half cups of flour and one and a half cups of sugar; both recipes work, but they are different. The study also noted that if you include a layer of fibers wrapped straight along the length of the cylinder (a 0° layer), the maximum pressure the tank can hold tends to drop slightly, because that specific layer can't adjust as easily to the twisting forces as the angled layers can. Ultimately, this research suggests that the old way of making these tanks—where every layer is the same thickness—is leaving potential strength on the table. By carefully tailoring the thickness of each layer to match the stress it feels, engineers can build pressure vessels that are safer and stronger, provided they use the right mathematical tools to figure out the recipe. The findings are based entirely on these analytical simulations, offering a clear roadmap for how to design better vessels, even if the real-world manufacturing challenges of making layers of varying thickness are a separate story.

Technical Summary: Sensitivity Analysis and Optimization of Burst Pressure in Composite Cylindrical Pressure Vessels

Problem Statement
Composite cylindrical pressure vessels are critical for storing and transporting industrial gases at elevated pressures, offering significant weight reduction compared to metallic alternatives. However, ensuring structural integrity is paramount, as failure can lead to severe safety and economic consequences. The burst pressure—the maximum internal pressure a vessel can withstand before losing structural integrity—depends on complex variables including fiber orientation (winding angle), layer thickness, stacking sequence, and material properties. While previous studies have optimized fiber angles or assumed uniform layer thicknesses, the influence of non-uniform thickness distribution on burst pressure and its optimization potential has received limited attention. This paper addresses the multivariable optimization of burst pressure by treating both fiber angle and individual layer thickness as design variables.

Methodology
The study employs a theoretical framework based on the membrane theory of shells for stress analysis and the First-Ply Failure (FPF) method for estimating burst pressure. The core of the methodology involves:

Analytical Modeling: The stress-strain relations for orthotropic laminae are established using Classical Laminate Theory (CLT). The global stress components are transformed into local coordinates to evaluate failure.
Failure Criteria: Two failure criteria are utilized to predict burst pressure: the Tsai–Hill criterion (based on distortion energy) and the Tsai–Wu criterion (accounting for stress component interactions).
Sensitivity Analysis: A key methodological contribution is the derivation of analytical sensitivity expressions. The paper calculates the derivatives of the burst pressure with respect to the fiber angle ( $\theta$ ) and the thickness of the $i$ -th layer ( $t_i$ ). This involves differentiating the stiffness matrices ( $A, B, D$ ) and the resulting stress/strain distributions.
Optimization Procedure: A gradient-based optimization algorithm (implemented in MATLAB) utilizes these analytical sensitivities to maximize the burst pressure. The objective is to find the optimal vector of design variables $X = [\theta, t_1, t_2, \dots, t_n]$ subject to a constant total wall thickness constraint.

Key Results
The study presents numerical results for Graphite/Epoxy and Glass/Epoxy laminates across various symmetric and antisymmetric stacking sequences:

Validation: The proposed analytical approach was validated against results from Adali et al. [9], showing good agreement in predicted critical pressures.
Fiber Angle Optimization: When only fiber angle was optimized (assuming uniform thickness), the Tsai–Wu criterion generally predicted higher burst pressures than Tsai–Hill. The symmetric four-layer laminate $[\theta/-\theta]_s$ consistently yielded the highest burst pressure for both materials and criteria. For Graphite/Epoxy, the optimal angle was approximately $53^\circ$ – $54^\circ$ , while Glass/Epoxy showed similar trends.
Thickness Distribution Optimization: When layer thickness was included as a variable, the study found that for many stacking sequences, multiple thickness distributions could achieve the same maximum burst pressure (indicating local extrema).
- Maximum Performance: The maximum attainable burst pressure for Graphite/Epoxy was found to be 8.68 MPa (Tsai–Hill) and 8.92 MPa (Tsai–Wu). For Glass/Epoxy, the values were 2.37 MPa and 2.72 MPa, respectively.
- Simultaneous Failure: For the optimal $[\theta/-\theta]_s$ configuration, the analysis revealed that the critical pressure was constant through the laminate thickness. This implies that all layers reach their failure limit simultaneously, representing an ideal utilization of the material's load-carrying capacity.
- Impact of 0° Layers: Stacking sequences containing a $0^\circ$ layer generally resulted in slightly lower maximum burst pressures, as the $0^\circ$ layer could not adapt its orientation to the optimal state.

Significance and Claims
The paper claims that the pressure-carrying capacity of composite pressure vessels can be significantly enhanced through the appropriate selection of both fiber orientation and laminate thickness distribution. The primary significance of this work lies in:

Analytical Sensitivity: Providing explicit analytical expressions for the sensitivity of burst pressure to design variables, which facilitates efficient gradient-based optimization without relying solely on computationally expensive finite element simulations for every iteration.
Thickness Optimization: Demonstrating that relaxing the assumption of uniform layer thickness allows for further improvements in burst pressure beyond what is achievable by optimizing fiber angles alone.
Design Efficiency: Identifying that specific symmetric layups (specifically $[\theta/-\theta]_s$ ) allow for simultaneous failure of all plies, thereby ensuring the full structural potential of the composite is utilized.

The authors conclude that their approach offers a robust method for designing composite pressure vessels with maximized burst pressure, highlighting the importance of considering thickness distribution as a critical design variable alongside fiber orientation.

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