Thin-walled Metallic Structures Research Articles

Hidden corrosion monitoring via phase shift evaluation of Lamb wave modes

Lamb wave inspection is a promising candidate for real-time monitoring of hidden corrosion in thin-walled metallic structures. The time-of-flight (ToF) which represents the variation of group velocity due to thickness reduction is commonly used, but its sensitivity is limited at the early stage of corrosion. To address this issue, the phase shift as a function of the phase velocity is defined and evaluated for corrosion detection in this paper. Specifically, the analytic cross-correlation method is applied, which estimates the group delay and the phase shift between two Lamb wave responses before and after the existence of corrosion simultaneously. The simulated examples show that the phase shift performs an obvious improvement on corrosion sensitivity compared to the ToF, and its value increases nearly linearly as the corrosion gets deeper. Ultimately, an experimental example is also introduced, where an active sensor network is deployed and a probabilistic imaging algorithm is introduced. The imaging results demonstrate that the proposed method could successfully identify and accurately localize the hidden corrosion.

Hidden corrosion monitoring via phase shift evaluation of lamb wave modes

Abstract Lamb wave inspection is a promising candidate for real-time monitoring of hidden corrosion in thin-walled metallic structures. The time-of-flight (ToF) which represents the variation of group velocity due to thickness reduction is commonly used, but its sensitivity is limited at the early stage of corrosion. To address this issue, the phase shift as a function of the phase velocity is defined and evaluated for corrosion detection in this paper. Specifically, the analytic cross-correlation method is applied, which estimates the group delay and the phase shift between two Lamb wave responses before and after the existence of corrosion simultaneously. The simulated examples show that the phase shift performs an obvious improvement on corrosion sensitivity compared to the ToF, and its value increases nearly monotonically as the corrosion gets deeper. Ultimately, an experimental example is also introduced, where an active sensor network is deployed and a probabilistic imaging algorithm is introduced. The imaging results demonstrate that the proposed method could successfully identify and accurately localize the hidden corrosion.

Crashworthiness in preliminary design: Mean crushing force prediction for closed-section thin-walled metallic structures

To design crash structures for disruptive aircraft designs, it is required to have fast and accurate methods that can predict crashworthiness of aircraft structures early in the design phase. Axial crushing is one of the key energy absorbing mechanisms during a crash event. In this study, various analytical models proposed for calculation of mean crushing force for thin-walled tubular structures are compared with a database of numerical and experimental values to ascertain their accuracy. Improvements to some of the models have also been proposed. Finally a generalized model based on the studied and improved analytical models for prediction of mean crushing force for closed section thin-walled tubular structures is introduced. The generalized model demonstrates high accuracy when compared against experimental/numerical dataset as evidenced by a high coefficient of determination (R2) value of 0.97 and can therefore be used to estimate the mean crushing force for closed-section thin-walled metallic tubular structures with various cross-sectional shapes and crushing modes early in the design phase.

ЗАСТОСУВАННЯ МЕТОДУ ГРАНИЧНИХ ЕЛЕМЕНТІВ ДЛЯ РОЗРАХУНКУ НАПРУЖЕНО-ДЕФОРМОВАНОГО СТАНУ ПРИ КРУЧЕННІ ТОНКОСТІННИХ РАМ АВТОМОБІЛІВ

Currently, the main method of calculating the stress-strain state (SSS) is the finite element method (FEM), implemented in software packages such as ANSYS, Solid Works, MATLAB, and others. It is established that if the SSS structure is described by rod functions, then the finite element method gives accurate results. If the state of the object is described by other functions, then MSE can give only approximate results of SSS calculation. Therefore, in this work, the authors applied a more accurate method of calculating the SSS of thin-walled car frames – the numerical analytical method of boundary elements (NA BEM). The purpose of the study is to apply a more accurate method of calculating the SSS of thin-walled car frames with the help of BEM. The scientific and practical direction of the work is that the technology of a more accurate method of calculating the SSS of thin-walled car frames - NA BEM is applied. The research methodology is the construction of mathematical models for the calculation of thin-walled car frames – NA BEM. When designing thin-walled metal structures, SSS is described by hyperbolic functions, and FEM, in principle, cannot provide accurate results for calculating SSS of thin-walled structures. Therefore, in the work, it is proposed to apply the technology of the boundary element method, which is free from the shortcomings of FEM technologies, to calculate SSS torsion of thin-walled car frames. The paper presents the matrix functions of the solution of the differential equations of the finite torsion of thin-walled frames, which were used to calculate the SSS of the rod torsion of thin-walled car frames. A more accurate SSS calculation of thin-walled car frames has been performed. This, in turn, will make it possible to determine the exact dimensions of the cross-section of thin-walled car frames. The result of the conducted research is the construction of accurate models of the stress-strain state during torsion of thin-walled car frames. Systems of linear equations of the SSS calculation algebra of limited torsion of two inseparable beams, which are models of car frames, are given. The calculation of frames for compressed torsion is presented. Отримані точні результати розрахунку SSS обмеженого кручення рам автомобілів, що представлені у вигляді таблиць і епюр. Keywords: FEM, BEM, thin-walled car frames.

On the crashworthiness performance of thin-walled circular tubes: Effect of diameter and thickness

Thin-walled metal structures are known as an effective solution in absorbing impact energy and reducing the resulting reaction forces. The design of energy absorbers with higher energy absorption capability, lower weight and reaction forces, as well as lower manufacturing cost, has always been of interest. In this study, the effects of diameter and thickness of thin-walled Aluminum tubes on different crashworthiness criteria were investigated. To this end, different geometries were examined by simulating the uniaxial compressive test applying the finite element method. The results revealed that the optimal diameter for a simple circular tube (SCT), assuming constant length and thickness, is the smallest diameter in terms of resistance to global buckling. The SCT with an optimal diameter has the highest specific energy absorption (SEA), the lowest maximum crushing force (), and the highest crushing force efficiency (CFE). Moreover, in this study, the effect of thickness on the tubular absorber performance was numerically investigated according to four criteria: SEA, CFE, and energy absorption (EA), and the optimal dimensions were obtained. Based on the results, increasing the thickness increases CFE, and increasing the ratio of thickness to diameter (t/D) increases SEA and CFE. Eventually, by applying the regression analysis, two equations were presented to calculate and CFE, which can be used to predict the performance of thin-walled metal tubes.

Strengthening and converse strengthening effects of polyurea layer on polyurea–steel composite structure subjected to combined actions of blast and fragments

Coating polyurea can significantly enhance the blast and impact resistance of thin-walled metal structures. However, most current research focuses only on the condition of single damage factor, such as blast or penetration loading. In this paper, the protective performance of polyurea-coated steel plates under the combined actions of blast and high-speed fragments was studied by means of field tests. Test results showed that under the combined actions of blast and high-speed fragments, when the coating thickness was within a certain range, polyurea had a converse strengthening effect on the protective performance of steel plate no matter which configuration was adopted. Only when the coating thickness exceeded a certain value did polyurea play a strengthening role. In other words, an obvious inflection point effect occurred in the influence of polyurea thickness on the protective performance of steel plate. These phenomena seem to be related to the characteristics of combined actions, which was different from that of single load. On the basis of tests, the strengthening and converse strengthening effects of polyurea layer was explained through microscopic analysis, numerical calculation and stress wave propagation theory. The significance of this research was to reexamine the practical application method of polyurea in improving the protective performance of metal thin-walled structures under specific circumstances to provide technical guidance for engineering application.

Experimental analysis of shear-lag effect in reinforced concrete T-beams

The non-uniform distribution of normal stresses within wide flanges of beam sections is typically referred to as shear-lag effect. Shear lag is a result of the interaction of normal and tangential stresses or correspondingly by the influence of shear strains on longitudinal strains. In structural engineering, the shear-lag effect has been a concern in the flanges of thin-walled metallic structures or the slab of composite steel–concrete elements, among others. Though existing codes of practice provide a simplified way to address shear lag by means of the effective width concept, such provisions can be insufficient for concrete structures, for which a deeper knowledge on the real influence of shear lag is necessary due to the current trend to design wide concrete bridge girders, with geometric configurations of the cross-sections which can be sensitive to shear lag (i.e. box- or T-sections). Moreover, the influence of the behaviour of structural concrete (cracking, rheology, yielding of reinforcement) has not been dealt with in detail so far. In the present paper, an experimental campaign on two reinforced concrete T-beams is presented. The beams have been subjected to two types of tests: firstly, to time-dependent effects governed by concrete shrinkage and creep; secondly, to the application of increasing direct loads to cover the whole concrete behaviour (uncracked, cracked and ultimate stage). The strain distribution at the top slab of the T-sections has been studied with extensive strain measurements at different cross-sections. The experiments have shown a distinct intensity of shear-lag effect depending on the load type. Moreover, the shear-lag impact varies longitudinally for each cross-section. In case of direct load tests, it has been also found that the strain distribution on the top slab changes as a function of the load level, which indicates that the different behavioural stages of concrete affect the shear lag, especially cracking. The experimental results have been analyzed with the help of analytical and numerical models, which have allowed understanding the progressive modification of the strain distribution within the top slab and the shear-lag intensity.

Large deflection and post-buckling of thin-walled structures by finite elements with node-dependent kinematics

In the framework of finite elements (FEs) applications, this paper proposes the use of the node-dependent kinematics (NDK) concept to the large deflection and post-buckling analysis of thin-walled metallic one-dimensional (1D) structures. Thin-walled structures could easily exhibit local phenomena which would require refinement of the kinematics in parts of them. This fact is particularly true whenever these thin structures undergo large deflection and post-buckling. FEs with kinematics uniform in each node could prove inappropriate or computationally expensive to solve these locally dependent deformations. The concept of NDK allows kinematics to be independent in each element node; therefore, the theory of structures changes continuously over the structural domain. NDK has been successfully applied to solve linear problems by the authors in previous works. It is herein extended to analyze in a computationally efficient manner nonlinear problems of beam-like structures. The unified 1D FE model in the framework of the Carrera Unified Formulation (CUF) is referred to. CUF allows introducing, at the node level, any theory/kinematics for the evaluation of the cross-sectional deformations of the thin-walled beam. A total Lagrangian formulation along with full Green–Lagrange strains and 2nd Piola Kirchhoff stresses are used. The resulting geometrical nonlinear equations are solved with the Newton–Raphson linearization and the arc-length type constraint. Thin-walled metallic structures are analyzed, with symmetric and asymmetric C-sections, subjected to transverse and compression loadings. Results show how FE models with NDK behave as well as their convenience with respect to the classical FE analysis with the same kinematics for the whole nodes. In particular, zones which undergo remarkable deformations demand high-order theories of structures, whereas a lower-order theory can be employed if no local phenomena occur: this is easily accomplished by NDK analysis. Remarkable advantages are shown in the analysis of thin-walled structures with transverse stiffeners.

Accurate through-the-thickness stress distributions in thin-walled metallic structures subjected to large displacements and large rotations

The present paper presents the evaluation of three-dimensional (3D) stress distributions of shell structures in the large displacement and rotation fields. The proposed geometrical nonlinear model is based on a combination of the Carrera Unified Formulation (CUF) and the Finite Element Method (FEM). Besides, a Newton-Raphson linearization scheme is adopted to compute the geometrical nonlinear equations, which are constrained using the arc-length path-following method. Static analyses are performed using refined models and the full Green-Lagrange strain-displacement relations. The Second Piola-Kirchhoff (PK2) stress distributions are evaluated, and lower- to higher-order expansions are employed. Popular benchmarks problems are analyzed, including cylindrical isotropic shell structure with various boundary and loading conditions. Various numerical assessments for different equilibrium conditions in the moderate and large displacement fields are proposed. Results show the distribution of axial and shear stresses, varying the refinement of the proposed two-dimensional (2D) shell model. It is shown that for axial components, a lower-order expansion is sufficient, whereas a higher-order one is needed to accurately predict shear stresses.

КОНЦЕНТРАЦИЯ ТЕМПЕРАТУРНЫХ НАПРЯЖЕНИЙ В МЕТАЛЛИЧЕСКИХ МАТЕРИАЛАХ И КОНСТРУКЦИЯХ ПРИ ЛОКАЛЬНОМ НАГРЕВЕ

significant thermal stresses arising in thin-walled metal materials and structures loaded with tensile stresses can lead either to their complete destruction or to the appearance of discontinuity zones in them. The equations for calculation of temperature stresses in flat thin-walled structures at their localized thermal heating caused by the action of concentrated energy flows are analyzed. As an example, a thin-walled stretched plate subjected to strong local heating in a circular spot is considered. The developed model takes into account the change of elastic characteristics under strong local heating and the change in the thickness of the material in the heating spot. As an example, the diagram of the distribution of tangential stresses for a stretched plate in the area of a circular heating spot is given. Thus, the results of the study show that there is a rupture and concentration of stresses along the contour of the heating spot from the cold zone.

Additive manufacturing of miniature marine structures for crashworthiness verification: Scaling technique and experimental tests

Undoubtedly, the main advantage of the additive manufacture technology is to allow building miniature structural parts with a large degree of complexity such as to replicate structural details of real-scale marine structures. This work presents a new technique for reproducing the structural response of large-scale thin-walled metallic structures when subjected to crushing loadings by using scaled-down additive manufactured models. This technique couples scaling laws for strain rate sensitive materials and a thickness distortion technique based on the structural collapse mode. In order to validate this coupled technique, the structural response of a large-scale crushing test of a web girder structure was experimentally replicated by using a 1/40 scale reduction model. The results and conclusions summarize the prospects and limitations of additive manufacturing of miniature complex marine structures for structural purposes and crashworthiness verification.

Concentration of Thermal Stresses in Metal Materials and Constructions under Local Heating

Considerable thermal stresses arising in thin-walled metallic materials and structures loaded with tensile stresses can lead either to their complete destruction or to the appearance of discontinuity zones in them.

Thin-walled metal deposition with GTAW welding-based additive manufacturing process

The arc welding-based additive manufacturing technology is in its developing state. This technology can be utilized to produce free-form metallic structures for the aerospace and biomedical industry. The current article presents the design of semi-automatic gas tungsten arc welding-based additive manufacturing system for fabricating thin-walled metallic structures. This study aims to analyze the effect of process variables on the output parameters, such as deposition width and deposition height. The set of experiments were performed based on the design developed by Taguchi method. The experimental data have been analyzed to study the effect of the significant process parameters like current, torch speed, wire feeding speed and torch angle. The optimization of the significant process parameters has been done to ensure thin-walled deposition with minimum wall thickness and better geometric characteristics. Experimental results showed that as the angle of inclination increases the deposition width increases and the deposition height decreases. The surface appearance of the bead sample deposited at a different angle of inclination was investigated. The thickness of the wall obtained in this study was found to be the lowest wall thickness achieved by the arc welding-based additive manufacturing process deploying filler material of 1.2 mm diameter.

Nonlinear analysis of compact and thin-walled metallic structures including localized plasticity under contact conditions

This work presents the numerical analysis of elastoplastic contact problems of compact and thin-walled metallic structures. The emphasis is on the use of higher-order 1D elements with pure displacement variables and based on the Carrera Unified Formulation (CUF) to capture localized effects and cross-sectional distortions. Contact interactions are normal and frictionless via a node-to-node contact algorithm with the penalty approach for contact enforcement. The analysis considers the material nonlinearity via the von Mises constitutive law. Numerical assessments compare the CUF solutions with 3D finite element analysis concerning the solution quality, computational size, and analysis time. The results show the ability of 1D CUF models of accurately evaluating localized deformations and plasticity. The CUF results are in good agreement with reference 3D finite element solutions, and require an order of magnitude fewer degrees of freedom and analysis time, making them computationally efficient.

A beam formulation with 3D capabilities for the free vibration analysis of thin-walled metallic and composite structures

Abstract The present article proposes an advanced Ritz formulation with 3D capabilities for the analysis of thin-walled metallic and composite beam structures. Various set of admissible functions such as: Legendre, Chebyshev and algebraic polynomials, as well as hybrid functions are employed. The investigation is carried out by using the method of power series expansion of displacement components based on 2D-Taylor polynomials. The governing equations (GEs) are derived in their weak form via Hamilton's Principle and are solved by using the Ritz method. Convergence and stability of both cross-section and admissible functions have been thoroughly analysed. The high level of accuracy of the proposed formulation has been comprehensively examined in three selected case studies: (i) slender beams with arbitrary boundary conditions, and both solid and thin-walled cross-sections; (ii) a fully-clamped three-layer non-homogenous circular cylindrical shell; (iii) a fully-clamped functionally graded material (FGM) box resting on two-parameter elastic foundation.

On lateral compression of circular aluminum, CFRP and GFRP tubes

Thin-walled structures made of lightweight materials, e.g. aluminum, fiber reinforced composites, have been increasingly used as energy absorption structures in vehicles. This work aimed to characterize the lateral crushing behaviors of circular aluminum, glass fiber reinforced plastics (GFRP) and carbon fiber reinforced plastics (CFRP) tubes with different geometric configuration such as diameter-to-thickness (D/T) ratio or thickness. In the experimental investigation, four different D/T ratios varied from 10.78 to 48.02 were considered here for the aluminum, GFRP and CFRP tubes. Crushing behaviors such as force-displacement curves, deformation histories, and crushing force were quantified. The experimental results revealed that the load carrying capacities, energy absorption (EA) and specific energy absorption (SEA) of the circular tubes decline with increasing D/T ratio. It was found that better crashworthy characteristics of thicker composites, with a smaller D/T ratio, were due to the more favorable failure modes occurring throughout lateral compression. The lateral crashworthy performance of the GFRP tubes was marginally better than that of the CFRP counterparts. Due to ductile behavior of aluminum tubes and brittle behavior of composites, aluminum tubes showed much better lateral crashworthiness than that of the composite counterparts. Moreover, with the increase in the D/T ratio, aluminum tubes exhibited greater advantage on crashworthiness than the composite tubes. On the basis of the experimental data, explicit finite element analysis was further carried out for modeling the lateral crushing behavior of aluminum, GFRP and CFRP tubes. The numerical results were in good agreement with the experimental data, demonstrating the validity of these finite element (FE) models in predicting lateral crushing responses of aluminum, GFRP and CFRP tubes. The proposed FE models can be exploited to further study similar thin-walled metal and composite structures for design optimization.

BEHAVIOUR OF VERTICAL CYLINDRICAL TANK WITH LOCAL WALL IMPERFECTIONS

Design of modern thin-walled metal structures is widely used around the world. In recent decades, more comprehensive research is carried out to investigate the behaviour of various thin-walled structures. Generally, the structure with regular geometry is investigated. In various countries such as USA, Russia, and the European Union issued the standards on regulation of the construction, design and maintenance of thin-walled structures. The actually used period of tanks usually is longer than recommendatory period. Recommendatory maintenance period of metal tanks is 15–20 years. Therefore, for such structures one of the most considerable questions is the residual load bearing capacity beyond the end of the maintenance period. This phase of using of structures is associated with complex investigation and numerical analysis of thin-walled structures. In this paper the load bearing capacity of the steel wall of the existing over-ground vertical cylindrical tank in volume of 5,000 m3 with a single defect and with a few contiguous local defects of the shape is analyzed. Calculations carried out are taking into account all the imperfections of the wall geometry. A major goal of the research – developing a realistic numerical model of the object analyzed, taking into account all the imperfections, determining the wall stress and strain state, exploring the places of extreme points, calculating the residual load bearing capacity of the tank and scrutinizing possible strengthening schemes for defective areas.

Optimization strategies for robotic additive and subtractive manufacturing of large and high thin-walled aluminum structures

Wire and arc additive manufacturing (WAAM) based on gas metal arc welding (GMAW) is a potential technology for fabricating large-scale metallic structures due to its high deposition rate, high energy efficiency, and low cost. It can produce near net-shape components by depositing metallic material layer by layer using a welding process. This paper presents a robotic additive and subtractive manufacturing system. In manufacturing large and high thin-walled structures, a critical issue is the unevenness of the layers. The accumulation of layers with poor flatness leads to significant differences in the heights of different positions in a layer, making it unable to continue the multi-layer material depositing process. The objective of this research is to investigate optimization strategies for manufacturing large and high thin-walled metallic structures with the robotic additive and subtractive manufacturing system. Three optimization strategies are proposed to obtain flat layers, including deposition with weaving, arc igniting and arc extinguishing control, and local measuring and milling strategy. Experiments were designed to explore the effect of these strategies. The experimental results show that the combination of these strategies can improve the surface flatness of layers, reducing the differences in the heights of a layer. Using these strategies, a large and high thin-walled component is manufactured, demonstrating the potential for fabricating large metallic parts in a very short time by the robotic additive and subtractive manufacturing system. Besides, regression models were generated for establishing the relationship between process parameters and bead geometry in deposition with weaving.

Analytical solutions for crack opening displacements of eccentric cracks in thin-walled metallic plates

In the context of the prevalence of thin-walled metallic aerospace structures, the added resistance to crack propagation offered by a built-up structure is desirable from a damage tolerance standpoint. The analysis of failure in such structures, however, is limited by the lack of crack opening solutions. This paper develops analytical models that calculate crack opening displacements (CODs) for a more general cracking scenario, i.e. non-symmetric cracks. The proposed models are based on the Westergaard stress functions. It is then found that the COD solution of one model is particularly accurate. The potential significance of the obtained solutions lies in analysing failure in built-up structures containing non-symmetric cracks. The crack opening solution is particularly useful in estimating the load transfer between cracked body and intact bridging structures in built-up structures using the principle of displacement compatibility.

Crashworthiness optimisation of a composite energy-absorbing structure for railway vehicles

By coupling thin-walled metal and aluminium honeycomb structures, a composite energy-absorbing structure with a high strength to weight ratio was designed. The validity of equivalent models of the thin-walled metal structure and the aluminium honeycomb was separately verified by carrying out trolley impact and quasi-static compression tests. The polynomial response surface models (PRSMs) of specific energy absorption (SEA) and initial peak force (F ip) during a collision were respectively established based on an orthogonal experimental design (OED) and the polynomial response surface method. The precisions of the three PRSMs were, in descending order, quartic, cubic, and quadratic PRSM (PRSM-4 > PRSM-3 > PRSM-2) as found by error analysis. The three PRSMs were separately optimised by using single-objective particle swarm optimisation (SOPSO) and the optimal values of SEA and F ip within the design range obtained from the PRSM-4 were respectively 33.5224 kJ/kg and 231.6860 kN among these PRSMs. The relative errors between the above optimal results of the PRSM-4, and the results obtained by numerical simulation, were 0 and −0.67%, respectively. Moreover, a Pareto front of double optimisation objective SEA and F ip was obtained after being optimised by multi-objective particle swarm optimisation (MOPSO), and SEA max was 33.0936 kJ/kg (the maximum SEA) and $$ {F}_{{\mathrm{ip}}_{\mathrm{min}}} $$ was 232.3510 kN (the minimum F ip) as separately obtained by using the PRSM-4. The errors between the above results and those (SEA = 33.5224 kJ/kg and F ip = 233.2406 kN) obtained through numerical simulation were separately 1.28% and −0.38%, which also indicates that the optimisation result is reliable.