Imperfection Sensitivity Research Articles

8-MW wind turbine tower computational shell buckling benchmark. Part 2: Detailed reference solution

An assessment of the elastic–plastic buckling limit state for multi-strake wind turbine support towers poses a particular challenge for the modern finite element analyst, who must competently navigate numerous modelling choices related to the tug-of-war between meshing and computational cost, the use of solvers that are robust to highly nonlinear behaviour, the potential for multiple near-simultaneously critical failure locations, the complex issue of imperfection sensitivity and finally the interpretation of the data into a safe and economic design.This paper presents a detailed reference solution to the computational buckling analysis of a standardised benchmark problem of an 8-MW multi-strake wind turbine support tower. Both linear and nonlinear analyses are performed, including advanced GMNIA with several different models of geometric imperfections. The crucial issue of interpreting the imperfection amplitude in a way that is compliant with the new prEN 1993-1-6 is discussed in detail. The solution presented herein is intended for use by analysts in both industry and academia for training, verification and calibration of finite element models and is intended to initiate a public repository of such computational solutions for metal civil engineering shell structures.This paper is the second of a pair. The first paper [37] presents a synthesis of 29 submissions to an international round-robin exercise performed on the same benchmark problem.

Buckling behaviour of dual-thickness dished shells under uniform pressure

The dual thickness dished shells are made of conical frustum with a closed stiff top at the smaller diameter end of the frustum. The dished shells are categorized as dual-thickness because of higher thickness of the top circular region than that of the conical region. The higher thickness of top flat circular portion makes this more stiffer. The buckling behaviour of these shells is similar to that of arches, spherical caps and shallow conical frustums. The variation in curvature of these shells and different stiffnesses of the conical and top circular region makes them very interesting and innovative. Making the top circular region stiffer avoids the need for stiff support in the top circular region for practical applications under uniform pressure. In the present study, a nonlinear finite element analysis on metallic dished shells of dual-thickness is attempted by varying different geometrical parameters such as thickness of conical region, height and top flat region radius of the shell under uniform pressure. This parametric analysis is carried out to find out the effect of elastic and elastic-perfectly-plastic material properties, boundary conditions and imperfection sensitivity of Eigen-mode type axisymmetric imperfections on the critical buckling pressure. It is found that material plasticity has a significant effect on the critical buckling pressure of dual-thickness dished shells. The effect of the axisymmetric Eigen-mode imperfections on critical buckling pressure is significant for the elastic material model and very small with elastic-perfectly-plastic material models. The information collected from the current study can be used for the detailed design of dual thickness dished shells.

Increasing reliability of axially compressed cylinders through stiffness tailoring and optimization.

The capabilities of the rapid tow shearing (RTS) process are explored to reduce the well-known imperfection sensitivity of axially compressed cylindrical shells. RTS deposits curvilinear carbon fibre tapes with a fibre-angle-thickness coupling that enables the in situ manufacturing of embedded rings and stringers. By blending the material's elastic modulus and wall thickness smoothly across the cylindrical surface, the load paths can be redistributed favourably with a minimal-design approach that contains part count and weight while ameliorating imperfection sensitivity. A genetic algorithm that incorporates realistic manufacturing imperfections and axial stiffness penalty is used to maximize the 99.9% reliability load of straight fibre (SF) and RTS cylinders. The axial stiffness penalty ensures that reliability does not come at the expense of stiffness. The first-order second-moment method is used to calculate statistical moments that enable an estimate of the 99.9% reliability load. Due to the fibre-angle-thickness coupling of RTS, buckling data are normalized by mass and thickness. Compared to a quasi-isotropic laminate, which corresponds to the optimal eight-layer design for a perfect cylinder, the optimized SF and RTS laminates have a 6% and 8% greater 99.9% normalized reliability load. By relaxing the axial stiffness penalty, the performance benefit can be increased such that SF and RTS cylinders exceed the 99.9% normalized reliability load of an eight-layer quasi-isotropic laminate by 23% and 37%, respectively. Both improvements (with and without penalty functions) stem largely from a reduction in the variance of the buckling-load distribution, thereby demonstrating the potential of fibre-steered cylinders in reducing the imperfection sensitivity of cylindrical shells. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.

Probing the stability landscape of cylindrical shells for buckling knockdown factors.

The buckling response of axially compressed cylindrical shells is well known for its imperfection sensitivity. Mapping out a stability landscape by localized probing has recently been proposed as a rational means for establishing shell buckling knockdown factors. Probing using a point force directed radially inwards and perpendicular to the cylinder wall is based on the insight that a localized single dimple exists as an edge state in the basin boundary of the stable prebuckling equilibrium. Here, we extend the idea of probing to bi-directional inwards and outwards forces to trigger both single-dimple and double-dimple edge states. We identify key features of the ensuing probing stability landscape and generalize these to derive three design curves of varying conservatism that are a function of the non-dimensional Batdorf parameter only. Interestingly, the most conservative of the three knockdown curves bounds a large dataset of experimental buckling results from below, despite being derived from probing features of geometrically perfect cylinders. Overall, the three design curves permit a more nuanced design approach than legacy knockdown factors, as different levels of conservatism can be chosen based on expected manufacturing quality. For instance, the most and least conservative of the three design guidelines differ by a factor of 3 for the most slender cylinder geometries, and the associated reduction in safety factor has profound implications for efficient structural design. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.

Foreword to the special issue on new developments in structural stability.

Foreword to the special issue on new developments in structural stability.

Manufacture and Buckling Test of a Variable-Stiffness, Variable-Thickness Composite Cylinder Under Axial Compression

Variable-angle tow (VAT) manufacturing methods significantly increase the design space for elastic tailoring of composite structures by smoothly changing fiber angle and ply thickness across a component. Rapid tow shearing (RTS) is a VAT manufacturing technique that uses in-plane shearing (rather than in-plane bending) to steer tows of dry or pre-impregnated fibers. RTS offers a number of benefits over conventional bending-driven steering processes, including tessellation of adjacent tow courses; no overlaps or gaps between tows; and no fiber wrinkling or bridging. Further to this, RTS offers an additional design variable: fiber orientation to tow thickness coupling due to the volumetric relation between tow shearing and the tow’s thickness and width. Previous computational work has shown that through a judicious choice of curvilinear fiber trajectories along a cylinder’s length and across its circumference, the imperfection sensitivity of cylindrical shells under axial compression can be reduced and load-carrying capacity increased. The present work aims to verify these predictions by manufacturing and testing two cylinders: an RTS cylinder and a straight-fiber, quasi-isotropic cylinder as a benchmark. The tow-steered manufacturing process, imperfection measurements, instrumentation, and buckling tests of both cylinders are discussed herein. The experimental tests results are compared against high-fidelity geometrically nonlinear finite element models that include measured geometric and loading imperfections before and during the tests. Finally, a discussion is provided on the outstanding challenges in designing and manufacturing RTS cylinders for primary aerostructures.

Numerical and Experimental Buckling and Post-Buckling Analyses of Sphere-Segmented Toroidal Shell Subject to External Pressure

This study determined the buckling characteristics of sphere-segmented toroidal shells subjected to external pressure. The proposed toroidal vessel comprises six spheres and six rings. Two laboratory models with the same nominal dimensions were manufactured, measured, tested, and evaluated. To investigate whether sphere-segmented toroidal shells are imperfection-sensitive structures with closely spaced eigenvalues, the subspace algorithm was applied to evaluate the first 50 eigenmodes, and the modified Riks algorithm was used to obtain post-buckling characteristics. The results indicated that the deviation between the results of the experimental and numerical analyses was within a reasonable range. The proposed sphere-segmented toroidal shells were highly imperfection-sensitive structures with closely spaced eigenvalues. Subsequently, imperfection sensitivity analysis confirmed this conclusion. In numerical analyses, the first eigenmode could be considered as the worst eigenmode of sphere-segmented toroidal shells. The trend of the equilibrium path of sphere-segmented toroidal shells was consistent with spherical shells, revealing instability. In addition, ellipticity and completeness exerted a negligible effect on the buckling load of sphere-segmented toroidal shells.

Experimental-numerical study of wrinkling in rotary-draw bending of Tight Fit Pipes

The paper focuses on tight fit pipe (TFP) wrinkling in rotary-draw bending (RDB), where TFP is a double-walled pipe. To this end, a corrosion-resistant alloy liner is fitted inside an outer carbon steel pipe through a thermal-hydraulic manufacturing process. A 3D elastic–plastic finite element (FE) model (the dynamic explicit FEM code ABAQUS/Explicit) is developed in this study. This model simulates the manufacturing process in the first step of the analysis and proceeds in the rotary-draw bending analysis of the lined pipe. Then, in the third step, the springback of the two-layer pipe is analyzed. This integrated three-stage process considers geometric nonlinearities, geometric and thickness imperfections, inelastic material behavior, and contact between the two pipes. Contact pressure during the process in the presence of various imperfections is monitored by the histogram to predict wrinkling. Furthermore, the best bending angle, with minimum possibility of wrinkling in the inner pipe, is obtained by these histograms. ABAQUS scripting via the Python programming language is used to study the effect of various imperfections on RDB. Numerical results on imperfection sensitivity demonstrate the significant influence of imperfections’ amplitude on liner wrinkling. The ovality and thinning of the lined pipe via bending angle were investigated. By comparing the experimental results with those of the simulation, an appropriate agreement is observed.

Numerical prediction and experimental analysis of the buckling loads of SMPC cylindrical shells under axial compression

The axial compressive buckling loads of shape memory polymer composite (SMPC) cylindrical shells are very sensitive to geometric imperfections and temperatures, but few studies have been conducted on this phenomenon. In this study, the buckling loads and geometric imperfection sensitivities of SMPC cylindrical shells at different temperatures are determined by means of numerical simulations and experimental analyses. The single perturbation displacement imperfection (SPDI), multiple perturbation displacement imperfection (MPDI) and linear buckling mode imperfection (LBMI) techniques are used to simulate the initial geometric imperfections and calculate the corresponding buckling loads and knock-down factors (KDFs) of SMPC cylindrical shells at different temperatures. In the experimental part, the [0/90/±45]s SMPC cylindrical shells are manufactured through the autoclave molding process. The load-bearing capacities at different temperatures are tested and compared with the numerical results. The results demonstrate that the buckling loads of the SMPC cylindrical shell obtained by numerical techniques are sensitive to temperature, while the KDFs are insensitive to temperature. Meanwhile, results indicate that brittle fracture is the main failure mode instead of buckling at low temperature, so there is a risk when using any numerical technique to design SMPC cylindrical shells in low-temperature region. At high temperatures, the SPDI method overestimates the KDFs, while the KDFs calculated by the MPDI and LBMI techniques are in good agreement with the experimental results. However, only the LBMI method can distinguish the influence of temperature on the post-buckling patterns, and the corresponding post-buckling pattern is more consistent with the experiment. In addition, the shape-recovery properties and repeatability of the SMPC cylindrical shells are good.

Buckling analyses of thin-walled cylindrical shells subjected to multi-region localized axial compression: Experimental and numerical study

Thin-walled cylindrical shell is a fundamental engineering structure which has efficient load-carrying capacity. In practical application, this structure is more easily subjected to localized axial compression loads and is prone to buckling. However, until now there is only limited studies on the buckling problems of multi-region localized axial compression loaded cylindrical shells. To elucidate the buckling behaviors of cylindrical shell under such kind of non-uniform loading condition, experimental and numerical studies are carried out in this paper. Twenty cylindrical shell test specimens with different types of localized axial compression loads are fabricated and tested. The corresponding finite element model considering the measured initial geometric imperfections is established for buckling analysis, and good agreement between the numerical and experimental results is validated. Then the buckling failure mode and axial load-carrying capacity of cylindrical shells are investigated in details. Finally, the imperfection sensitivity of thin-walled cylindrical shell under multi-region localized axial compression is discussed. It is found that the number of loading regions and the total loading area have significant effects on buckling failure mode and axial load-carrying capacity of cylindrical shells. The results obtained from experimental and numerical studies can provide some important guidance or suggestions for the design of thin-walled cylindrical shell structures in actual engineering.

Adapting Lot Quality Assurance Sampling to accommodate imperfect diagnostic tests: application to COVID-19 serosurveillance in Haiti

BackgroundLot Quality Assurance Sampling (LQAS), a tool used for monitoring health indicators in low resource settings resulting in “high” or “low” classifications, assumes that determination of the trait of interest is perfect. This is often not true for diagnostic tests, with imperfect sensitivity and specificity. Here, we develop Lot Quality Assurance Sampling for Imperfect Tests (LQAS-IMP) to address this issue and apply it to a COVID-19 serosurveillance study design in Haiti.MethodsWe first derive a modified procedure, LQAS-IMP, that accounts for the sensitivity and specificity of a diagnostic test to yield correct classification errors. We then apply the novel LQAS-IMP to design an LQAS system to classify prevalence of SARS-CoV-2 antibodies among healthcare workers at eleven Zanmia Lasante health facilities in Haiti. Finally, we show the performance of the LQAS-IMP procedure in a simulation study.ResultsWe found that when an imperfect diagnostic test is used, the classification errors in the standard LQAS procedure are larger than specified. In the modified LQAS-IMP procedure, classification errors are consistent with the specified maximum classification error. We then utilized the LQAS-IMP procedure to define valid systems for sampling at eleven hospitals in Haiti.ConclusionThe LQAS-IMP procedure accounts for imperfect sensitivity and specificity in system design; if the accuracy of a test is known, the use of LQAS-IMP extends LQAS to applications for indicators that are based on laboratory tests, such as SARS-CoV-2 antibodies.

Buckling of Composite Structures with Delaminations—Laminates and Functionally Graded Materials

In the present paper, buckling problems of constructions with single delamination are examined. Structures were made of unidirectional laminates and functionally graded materials (FGM). Two types of delaminations (closed and opened) were both investigated in experiments both in rectangular plates and axi-symmetric shells. The first part of the work is devoted to the formulation of contact problems (embedded, closed delaminations) with the aid of various functional inequalities. Then, computational models are discussed. To study the influence of the variable material configuration of FGMs, the fourth-order plate/shell relations were adopted. Finally, three particular problems examined are the buckling of flat rectangular plates, spherical shells, and compressed rectangular plates with elliptical delaminations. The experiments were conducted using imperfection sensitivity analysis and post-buckling non-linear analysis. The results demonstrate that the unsymmetric configurations of FGM structures lead to the reduction of buckling loads for structures with delaminations. For FG structures, those effects are described by the simple coefficient. Linear fracture mechanics were employed to distinguish the form of unilateral boundary problems (closed or opened). In the first case, the stable variations of the strain energy release rate GI with the delamination length variations were observed, whereas in the second case the unstable variations were observed.

Imperfection sensitivity study of the thermal–mechanical buckling of laminated composite cylinders using a novel reduced-order modeling method

Laminated composite cylinders subjected to axial compression exhibit the “snap-back” response, the buckling load of which is very sensitive to initial geometric imperfections. An operating environment with high temperatures influences both the buckling behavior and imperfection sensitivity of thin-walled cylinders. This paper proposes a novel reduced-order modeling method for nonlinear buckling and imperfection sensitivity analyses, considering the effects of the initial geometric imperfections and initial temperature field. The Koiter asymptotic theory is reformulated to construct a thermal–mechanical reduced-order model with initial geometric imperfections. The initial temperature field is converted to an additional degree of freedom during the construction of the reduced-order model. An a posteriori account of geometric imperfections is achieved for the thermomechanical reduced system of the perfect structure. A predictor–corrector process is developed to trace the thermoelastic geometrically nonlinear response of an axially compressed cylinder with geometric imperfections. Various numerical examples are designed to validate the high efficiency and satisfactory accuracy of the proposed method for imperfection sensitivity analyses. The optimization process based on the proposed method is applied to determine the most imperfection-sensitive laminate and the “worst” imperfection shape.

A systematic review and meta-analysis of human and zoonotic dog soil-transmitted helminth infections in Australian Indigenous communities.

Soil-transmitted helminths (STH) infect 1.5 billion people and countless animals worldwide. In Australian Indigenous communities, STH infections have largely remained endemic despite control efforts, suggesting reservoirs of infection may exist. Dogs fulfil various important cultural, social and occupational roles in Australian Indigenous communities and are populous in these settings. Dogs may also harbour zoonotic STHs capable of producing morbidity and mortality in dogs and humans. This review provides an overview of human and zoonotic STH infections, identifies the Australian Indigenous locations affected and the parasite species and hosts involved. The meta-analysis provides estimates of individual study and pooled true prevalence of STH infections in Australian Indigenous communities and identifies knowledge gaps for further research on zoonotic or anthroponotic potential. A systematic literature search identified 45 eligible studies documenting the presence of Strongyloides stercoralis, Trichuris trichiura, Ancylostoma caninum, Ancylostoma duodenale, Ancylostoma ceylanicum, undifferentiated hookworm, and Ascaris lumbricoides. Of these studies, 26 were also eligible for inclusion in meta-analysis to establish true prevalence in the light of imperfect diagnostic test sensitivity and specificity by Rogan-Gladen and Bayesian methods. These studies revealed pooled true prevalence estimates of 18.9% (95% CI 15.8-22.1) for human and canine S. stercoralis infections and 77.3% (95% CI 63.7-91.0) for canine A. caninum infections indicating continued endemicity, but considerably more heterogenous pooled estimates for canine A. ceylanicum infections, and A. duodenale, undifferentiated hookworm and T. trichiura in humans. This review suggests that the prevalence of STHs in Australian Indigenous communities has likely been underestimated, principally based on imperfect diagnostic tests. Potential misclassification of hookworm species in humans and dogs due to outdated methodology, also obscures this picture. High-quality contemporary studies are required to establish current true prevalence of parasite species in all relevant hosts to guide future policy development and control decisions under a culturally sound One Health framework.

Buckling of viscoelastic spherical shells

Viscoelastic spherical shells exhibit a wide range of time/rate-dependent buckling behaviors when subjected to pressure. For certain loadings, buckling can even occur after a significant time delay, termed creep buckling. To gain a thorough understanding of the nonlinear time-dependent buckling behavior of viscoelastic spherical shells, this work develops an analytical model employing the small-strain, moderate-rotation shell theory combined with a linearly viscoelastic material law. Numerical results are presented for axisymmetric spherical shells with geometric imperfections for two types of loading: a prescribed rate of volume change and a prescribed pressure that remains constant after it is applied. The first type reveals the rate-dependent behavior of viscoelastic buckling while the constant pressure loading is used to quantify creep buckling phenomena. The results show that viscoelasticity and loading rates play important roles in the load-carrying behavior of these shells, and the results for the constant pressure loading reveal an unexpected and important connection between the short-time elastic buckling limit and the long-time creep buckling limit. An imperfection sensitivity map is constructed for the constant pressure loading showing three regimes with qualitatively different behaviors: near-instantaneous buckling, creep buckling and no buckling.

Is diagnostic stewardship possible in solid organ transplantation?

Diagnostic stewardship in solid organ transplant (SOT) recipients has the potential to help these vulnerable patients at risk for over-testing and overtreatment. Herein, we review potential targets for diagnostic stewardship in SOT, such as Clostridioides difficile testing, urine cultures, molecular diagnostics, as well as novel areas of diagnostic stewardship. Bundled interventions focused on appropriate C. difficile testing can result in a significant decrease in testing and clinical diagnosis of C. difficile infection without any harms related to delay in diagnosis. In otherwise stable renal transplant recipients after the first month of transplant, screening urine cultures have not been shown to improve outcomes. Novel targets that require additional study in the SOT population include noninvasive fungal diagnostics and cytomegalovirus testing strategies CONCLUSIONS: Diagnostic stewardship is an innovative approach to improve diagnosis and limit unnecessary antimicrobial use. While there has been little direct exploration of diagnostic stewardship in the SOT population, there is great potential for benefit given frequent testing with diagnostics that have imperfect sensitivity and specificity, and sometimes great cost. Diagnostic stewardship in the SOT population is indeed possible but will require a multidisciplinary effort to ensure that appropriates tests and benefits are realized.

Wind-induced instability analysis of large-span single-layer lattice domes

This paper addresses the instability behaviour of single-layer lattice domes with a long span subjected to wind action. Two structural configurations with a span of 120 m and a rise-to-span ratio of 1:3 and 1:6 are analysed to compare critical dynamic loads to critical static loads. The Budiansky–Roth and phase-plane criteria are employed for estimating dynamic critical conditions. Wind fluctuation (Cpf) is simulated as a function of the average pressure coefficient (C¯p) over time, and the imperfections are set by means of the so-called “Conformable Imperfection Method”. The parameters considered in this research include the wind fluctuation, fluctuation period, geometric imperfection, and strengthening the members. It is found that the critical wind velocity reduces as the wind fluctuation increases. Furthermore, as the fluctuation period Tf increases, the difference between the static and the dynamic critical loads decreases. The use of Cpf=0.3C¯p and Tf/T1=1.0 (T1 being the fundamental period) produced the lowest amount of critical velocities of 50 and 43 m/s for D1:3 and D1:6 configurations, respectively. The corresponding critical dynamic loads were 29.27 and 15.15 kN giving the dynamic load ratio of 193%, the dynamic to static critical load ratios being 0.67 and 0.68 for these configurations. The D1:3 and D1:6 domes exhibited imperfection sensitivity by as much as about 17 and 82% load reduction, respectively, for an imperfection amplitude of Span/350. Strengthening the critical members of the D1:6 dome subjected to the wind action had the advantage of increasing the static instability load and the dynamic critical load bearing capacity by 20 and 30%, respectively. For estimating the equivalent static wind load, a reduction factor of 0.50 defined as the ratio of dynamic to static load was proposed.

Shape optimisation of stainless steel corrugated cylindrical shells for additive manufacturing

Axially compressed circular cylindrical shells with large diameter-to-thickness ratios are highly susceptible to local buckling, and their load-carrying capacities are known to be very sensitive to initial geometric imperfections. Hence, severe knock-down factors on their theoretical buckling loads are typically prescribed in design specifications, which greatly impair their structural efficiency. With the aim of enhancing load-bearing resistance and reducing sensitivity to imperfections, the shape optimisation and assessment of compressed free-form wavy cylindrical shells, the realisation of which is now viable through additive manufacturing, are the subject of the present study. The adopted optimisation framework employs the Particle Swarm Optimisation (PSO) algorithm, integrating computer-aided geometric design, nonlinear numerical simulations and imperfection sensitivity analyses. The structural performance of the optimised free-form wavy shells is analysed and compared to that of reference circular shells, as well as other types of non-circular shell profiles, including sinusoidally corrugated shells, Aster shells and stringer-stiffened shells. The optimised free-form wavy shell profiles are shown to exhibit increases in ultimate stress of up to 136% compared with the reference circular shell profiles; in general, greater benefits are achieved for more slender cross-sections. In future work, the proposed optimised shells will be manufactured in stainless steel by means of powder bed fusion (PBF), and their structural performance will be further verified through physical experiments.

Post-Buckling Behaviour of Steel Structures with Different Types of Imperfections

In this paper, the stability of steel members with a complex initial geometrical imperfection pattern are analysed. This issue is extremely important in the case of slender structures, characterised by multiple close critical loads and modal interactions, which can lead to unstable post-critical paths and imperfection sensitivity. Despite the fact that the loss of stability, as a result of complex geometrical imperfections, is a very common mechanism for the destruction of slender steel structures, there is still no unambiguous and adequate research in the literature and in scientific research taking into account multimodal buckling. Therefore, in this study, special attention was focused on the analysis of the equilibrium path of the structure in the pre- and post-buckling range. This was studied by introducing a model of a structure composed of four rigid bars connected by elastic nodes. For this model, as well as for the structure with and without initial geometrical imperfections, a set of nonlinear algebraic equations of equilibrium was developed. A complex pattern of imperfections was taken into account using a linear superposition of buckling modes obtained from a linear eigenvalue problem. In order to investigate the nature of bifurcation points, the concept of minimum of potential energy was adopted. By means of numerous examples, the influence of imperfections on the structural behaviour was discussed. It was found that, for special imperfection patterns, an increase in the amplitude of initial geometrical imperfection can result in an increase in the value of the critical load defining the bifurcation point. In these cases, initial geometrical imperfections can play a positive role, resulting in stable post-buckling behaviour. This phenomenon corresponds with the so-called “modal nudging” which aims to improve the buckling response of slender elastic structures by introducing a small disturbance in the primary geometry of the structure, which results in equilibrium paths of greater load-carrying capacity. Among other observations, a snap-through phenomenon caused by transition from the local to the global minimum of potential energy was also noted. The observed snap-through was caused by the specific configuration of initial geometrical imperfections, which in this case played quite a dangerous role. It should be emphasised that the proposed model structure allows for a full description of the post-critical behaviour and a trace of the influence of complex imperfection configurations in a simple and clear manner.

A pressure vessel with a special barrelled shape

The paper is devoted to a pressure vessel with a special barrelled shape. The analytical model of this vessel composed of shells of revolution is developed. Based on the membrane theory the state of stress in the vessel is determined analytically. Moreover, a numerical FEM model (ANSYS – system) of the vessel is formulated. The distribution of the stresses in the exemplary vessels with the use of two methods are calculated and compared. The proposed shape, for selected geometrical properties, assures that the stress distribution is relatively smooth as for the multi-shell tank. The stability analysis of selected shells showed that the post-buckling behaviour of the presented structure is unstable and the imperfection sensitivity is high.