An Optimum Design for Composite Cylindrical Pressure Vessels

Abstract

Composite materials have found wide applications in different engineering fields; mechanical, aeronautical, civil and chemical. This is due to the attractive properties which these materials possess as the high strength, high modules, low density, high corrosion resistance and well-tailored as needed through fabrication. One of these mechanical applications is composite pressure vessels of different shapes; cylindrical, spherical, toroidal and elliptical. In this paper, cylindrical pressure vessels fabricated from an inside liner (aluminum or polymeric material) reinforced with different composite overwrapped; glass, carbon and Kevlar mixed with epoxy resin have been considered. Generally, the composite pressure vessels containthe inside liner to prevent the leakage of the inside fluid, where the compositefibers cannot prevent that leakage due to the presence of voids and gaps between the fibers. The fibrous materials are used to give a reinforcement to the liner for sustaining the resulting hoop and longitudinal stresses in the vessel wall. A design optimization has been performed to get the optimal parameters (outer radius, fiber volume fraction and fiber orientation angle) governing the design objective which is minimizing the vessel weight. After formulation of the optimization problem, as objective and constraints functions, Kuhn-Tucker method has been used to declare the main conditions of optimum design. This technique is used since the problem isnonlinear with inequality constraints. Then, the optimum solution is obtained using MATLAB program and checked with Kuhn Tucker conditions.

Introduction

Pressure vessels are leak-proof containers used in many mechanical and aerospace applications as: hydraulic cylinders, boilers, gas containers, oil pipelines and much more.

These vessels can take many configurations; cylindrical, spherical, elliptical, and toroidal manufactured from different engineering materials as: carbon steel, aluminum, stainless steel and recently from fibrous composite materials.

Although cylindrical pressure vessels are less durable than spherical ones (due to the high stress induced in their walls compared to spherical pressure vessels), but they are less expensive in production.

The design of these vessels depends on many different parameters. Some of these parameters are related to material such as:material strength, modulus and density. Some parameters are related to functionslike pressure loading, temperature and type of fluid to be stored. Whereas, the other parameters are related to geometry as diameter, thickness and length.The most common material used for manufacturing pressure vessels is carbon steel. This is due to its excellent durability, versatility, and cost-effectiveness. Carbon steel can withstand high pressures and temperatures, making it ideal for a wide range of industrial applications

Recently, pressure vessels are made from composite materials due to the attractive properties of these materials as; low density, high strength/weight ratio, high modulus/weight ratio and high corrosion resistance [1].

The pressure vessels fabricated from composite materials generally comprise an inside polymeric liner reinforced by fibers wound around it to give the vessel the high strength and high modules [2]. Advanced fibers as:glass, Kevlar, carbon or hybrid fibers may be used for this purpose.

In this paper, the design of cylindrical pressure vessels subjected to internal pressures and fabricated from different composite fibrous materials has been optimized.This optimum design is based on the failure criteria of composite materials, and the simple formulae for determining the cylinder shapes by using mathematical optimization techniques.

Conclusion

Throughout the optimization work performed in this paper, the following conclusions can be withdrawn: 1) Composite pressure vessels can carry fluids with higher internal pressures than steel ones of the same dimensions with light weights. 2) These types of pressure vessels must use an inside liner (polymeric or aluminum) to sustain the radial stresses and thus prevent the fluid leakage through the gaps between fibers. 3) The failure analysis performed in this paper is based on the Maximum stress theory and verified by the Tsai-Wu theory. 4) Three different advanced fibrous materials; GRP, CRP and KRP mixed with epoxy as matrix are used in the study to reinforce the pressure vessels. 5) Composite pressure vessels overwrapped by Kevlar fibrous material have shown the lowest weight among the threeconsidered fibrous materials (carbon or glass). 6) The failure of the composite pressure vessels passes by three stages: • The first stage is the interface failure due to the bond failure between the fibers and the matrix, the second failure stage is the matrix failure. These two stages of failure cause the initial failure of vessels. • The third stageis the failure due to the fiber breakage and leads to final failure of thevessel. 7) The more predominant factor affects the design of these composite vessels is the fiber strength. 8) The optimum winding angle of the fibers around the vessel is 35o with the circumference direction (i.e., 55o with the longitudinal direction) for all the types of fibrous materials. 9) The optimum fiber volume fraction is found as 60% for all the types of fibrous materials. 10) For the studied design case, the optimum outer radius of the vessel is found as 10% more than the inside radius, i.e. the wall thickness is around 10% of the vessel radius. 11) Depending on the thickness of the composite layer (which compromise the matrix and theimmersed fibers thickness), one can get the optimum number of layers. 12) As a final conclusion, in the studied case, if the thickness of the composite layers is 1mm, the optimum number of composite layers will be 10 layers with stacking laminationcode as: 5 [±35o].

References

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Copyright

Copyright © 2025 Badr Bedairi, Sultan Alqash, Badr Azzam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.