A novel detailed analytical approach for determining the optimal design of FRP pressure vessels subjected to hydrostatic loading: Analytical model with experimental validation

Abstract

A new practical analytical approach has been developed in order to reach the optimal fiber orientation in design of fiber reinforced polymer pressure vessels (FRPPVs) subjected to hydrostatic pressure. The method consists of analytical solutions along with optimizing process in which different decisive factors such as buckling pressure, weight, failure of fiber and matrix, thickness, number and angle of layers are considered as problem constraints. In analytical part, besides the buckling analysis, Tsai-Wu and Hashin failure criteria are employed to analyze the failure of the structure. Then, the genetic algorithm (GA), as a robust optimization method, is applied to achieve the optimal orientation pattern with minimum weight and maximum buckling load. In addition, the impact of mapped fitness function in optimization process is exclusively analyzed. Next, to validate the reliability and effectiveness of the proposed approach, two different experimental methods, including the strain gauge and volume control methods, are performed and measured buckling pressure is compared with the analytical results. The results indicated that using the proposed approach, critical buckling load increases by 40% while the weight is reduced by 15%, simultaneously.

Introduction

Composites are an innovative group of materials that have a wide range of application from aerospace components, military vehicles and building constructions to dentistry, orthopedic surgery and storage vessels etc. [[1], [2], [3], [4], [5], [6], [7], [8], [9], [10]]. Available researches suggest that structural elastic stability is one of the most practical issues in design and analysis of composite structures. This area of study includes buckling, wrinkling, snapping and cavitation [[11], [12], [13], [14], [15], [16]]. Accordingly, buckling optimization analysis of composite elements has drawn a wide attention in recent decade. In a recent study by Grande et al. [17], the role of global buckling in the optimization process of grid shell structures was examined. In this study, authors underlined and compared the effectiveness of some optimization strategies in which the buckling constraint is a crucial factor. Kolahchi et al. [18] used Grey Wolf algorithm to evaluate the optimal design of a sandwich nanocomposite plate with sensor and actuator layers. The motion equations were derived based on the sinusoidal shear piezo elasticity theory and dynamic buckling was estimated. The results suggest that increase of nanoparticle volume fraction results in higher optimal dimensionless frequency due to increase in the structural stiffness. Ghahfarokhi and Rahimi [19] presented an analytical approach for global buckling of composite cylindrical shells with lattice cores. The critical buckling load was calculated by Rayleigh-Ritz method. Comparison of the obtained results with finite element methods (FEM) revealed that the proposed approach is able to estimate global buckling load of stiffened composite cylindrical shells accurately. In an effort by Lou et al. [20], post-buckling of hybrid piezoelectric microplates under thermo-electro-mechanical loads was analyzed by employing the modified couple stress theory. The results demonstrated that the use of a positive electric field declines the critical mechanical/thermal buckling load. Bessa and Pellegrino [21] developed a computational framework for design of structures with uncertain responses. The proposed approach was proved to be able to increase the ultimate buckling limit in structures with complex non-linear behavior. The scale of the computations carried out in this framework was much larger than previous design/optimization studies of a deployable structure. In a research by Taheri-Behrooz et al. [22], the influence of initial geometric imperfection on the buckling response of composite cylinders was characterized through the numerical and experimental investigations. The estimated buckling loads by the nonlinear method, without considering initial imperfection effect, were virtually higher than the ones measured experimentally. This could be due to the lack of damage consideration around the cutout during the growing cutout size in numerical simulations.

In addition to buckling constraint [23], the mass, thickness [[24], [25], [26]] and stacking sequence [27,28] are other important parameters to reach the optimized design of laminated composite structures. In a multi-objective optimization study by Ghasemi and Hajmohammad [29] the evolutionary algorithm of NASG-II was developed to obtain the least and highest possible weight and buckling pressure in fiber reinforced polymer (FRP) composite shells, respectively. It was signified that application of the multi-objective optimized model can reduce the cost of specimen up to 12% where the weight to buckling pressure ratio was at minimum state. In Ref. [30] the laminate stacking sequence was considered as a variable in multi-objective optimization of composite stiffened panels. A two-level approximation method was represented and genetic algorithm (GA) was then adopted. Next, different initial designs of laminate arrangements were investigated and reasonable optimization results, which are tradeoffs between conflicting objectives and feasible designs satisfying all considered constraints, were obtained. Albanesi et al. [31] proposed a new method to simultaneously determine the optimized ply arrangement, ply number and ply drop configuration of laminated wind turbine blades. The method consisted of GA and inverse FEM. The results indicated that the proposed method is a robust redesign tool for precisely determining the optimized design of layer arrangement in laminated wind turbine blades, reducing the weight by 15% compared to initial arrangement.

In this research, a new practical approach consisting of analytical solutions coupled with optimization process is presented. At first, buckling analysis of a fiber reinforced polymer pressure vessel (FRPPV) under external hydrostatic pressure is carried out. The failure of the FRPPV is then examined employing Tsai-Wu and Hashin failure criteria. In addition to these constraints, the weight of FRPPV, thickness, number and angle of the laminates are also considered in optimization analysis. The GA is employed as optimization method and different mapped fitness functions are investigated. Finally, optimal layer arrangement for design and manufacturing of FRPPV is proposed. Moreover, two distinct experimental tests are performed to validate the reliability of present approach. The innovative outcomes of this research can be practically used in design of cylindrical composite structures and help to achieve cost-effective manufacturing in composite-based industries.