Nonlocal analysis of the flexural–torsional stability for FG tapered thin-walled beam-columns

none5siThis paper addresses the flexural–torsional stability of functionally graded (FG) nonlocal thin-walled beam-columns with a tapered I-section. The material composition is assumed to vary continuously in the longitudinal direction based on a power-law distribution. Possible small-scale effects are included within the formulation according to the Eringen nonlocal elasticity assump-tions. The stability equations of the problem and the associated boundary conditions are derived based on the Vlasov thin-walled beam theory and energy method, accounting for the coupled interaction between axial and bending forces. The coupled equilibrium equations are solved numer-ically by means of the differential quadrature method (DQM) to determine the flexural–torsional buckling loads associated to the selected structural system. A parametric study is performed to check for the influence of some meaningful input parameters, such as the power-law index, the nonlocal parameter, the axial load eccentricity, the mode number and the tapering ratio, on the flexural–torsional buckling load of tapered thin-walled FG nanobeam-columns, whose results could be used as valid benchmarks for further computational validations of similar nanosystems.openSoltani M.; Atoufi F.; Mohri F.; Dimitri R.; Tornabene F.Soltani, M.; Atoufi, F.; Mohri, F.; Dimitri, R.; Tornabene, F

Reliability-based design optimization of shells with uncertain geometry using adaptive Kriging metamodels

Optimal design under uncertainty has gained much attention in the past ten years due to the ever increasing need for manufacturers to build robust systems at the lowest cost. Reliability-based design optimization (RBDO) allows the analyst to minimize some cost function while ensuring some minimal performances cast as admissible failure probabilities for a set of performance functions. In order to address real-world engineering problems in which the performance is assessed through computational models (e.g., finite element models in structural mechanics) metamodeling techniques have been developed in the past decade. This paper introduces adaptive Kriging surrogate models to solve the RBDO problem. The latter is cast in an augmented space that "sums up" the range of the design space and the aleatory uncertainty in the design parameters and the environmental conditions. The surrogate model is used (i) for evaluating robust estimates of the failure probabilities (and for enhancing the computational experimental design by adaptive sampling) in order to achieve the requested accuracy and (ii) for applying a gradient-based optimization algorithm to get optimal values of the design parameters. The approach is applied to the optimal design of ring-stiffened cylindrical shells used in submarine engineering under uncertain geometric imperfections. For this application the performance of the structure is related to buckling which is addressed here by means of a finite element solution based on the asymptotic numerical method

Measurement of constant radius swept features in cultural heritage

none3The dimensional characterization of archaeological fragment is a very complex operation and could prove to be useful for identifying the presence of standard attributes in the ceramics found from a specific archaeological site, or for making comparisons and analysis of similarities or for studying ancient technologies used for manufacture of objects. The dimensional analysis of the fragments is now carried out manually with traditional measuring devices. Typically, the results obtained are inaccurate and non-repeatable measurements. This paper focuses on the dimensional characterization of a specific geometric class of features: the constant radius swept features (called here CRS features). Several archaeological features, such as rims, bases, decorative motifs, processing marks and grooves are referable from a geometric point of view to the class of CRS features. These are detail features, which may be very interesting for the investigation of some aspects related to the historical-archaeological classification of the find. CRS features are often found on worn, damaged (e.g. chipped) or fragmented objects; they are frequently characterized, from a geometric point of view, by free form surfaces and by a limited cross sectional extension. In some cases, CRS features can be of axially symmetrical geometry: this occurs quite frequently in the case of archaeological pottery. For all these reasons, it is often difficult to apply traditional manual methods for the quantitative dimensional characterization of CRS features. This paper describes an original methodology for the measurement of CRS features acquired by scanning technologies. The algorithmic implementation of this methodology, consisting of a suitable processing of the feature nodes, allows to carry out automatically the dimensional characterization of the feature.Di Angelo L., Di Stefano P., Morabito A.E.Di Angelo, L.; Di Stefano, P.; Morabito, A. E

Interactive buckling in thin-walled I-section struts

Compression members, made from slender metallic plate elements, are prone to a wide range of different elastic instability phenomena. A thin-walled I-section strut, made from a linear elastic material, can suffer from the nonlinear interaction between a global (Euler) buckling mode, and a local flange plate buckling mode. The interactive buckling behaviour is usually much more unstable than when the modes are triggered individually and hence significantly reduces the load-carrying capacity of real struts. The current work focuses on such a problem using an analytical approach, the methodology of which has been well established in previous works on sandwich struts and I-section beams. An analytical model that describes the interactive buckling of a thin-walled I-section strut under pure compression based on variational principles is presented. Analytical formulations combining the Rayleigh–Ritz method and continuous displacement functions are presented to derive a series of systems that comprise differential and integral equilibrium equations for the structural component. Solving the systems of equations with numerical continuation reveals progressive cellular buckling (or snaking) arising from the nonlinear interaction between the weakly stable global buckling mode and the strongly stable local buckling mode. The resulting behaviour is highly unstable and when the model is extended to include geometric imperfections it compares excellently with some recently published experiments. Imperfection sensitivity studies reveal high sensitivity to both global and local imperfection types. The worst forms of local imperfection are identified in terms of the initial wavelength, amplitude and degree of localization. The effect of the varying rigidity of the joint of the section web and flanges is also studied and a rapid erosion of the cellular buckling response is revealed with increasing rigidity of the flange–web joint. A shell-based nonlinear finite element model is presented, primarily for validation purposes. The results from the analytical and finite element models show a good comparison, particularly for higher rigidities of the flange–web joint. A parametric study is conducted for two limiting cases, where the flange–web joint is assumed to be fully pinned or fully rigid. For a chosen set of geometries, the most undesirable interactive region is identified for both global and local slendernesses, in terms of the strut length and the flange width respectively. Practical implications are discussed in terms of the idealized buckling design curve. An analytical framework for the structural analysis of the thin-walled I-section struts that exhibit the nonlinear interaction of a global and a local buckling mode, including cellular buckling, has therefore been established.Open Acces

An Overview Of Buckling And Imperfection Of Cone-Cylinder Transition Under Various Loading Condition

The current paper presents a brief survey of literature relevant to buckling of cone-cylinder intersection under different loads such as (i) internal pressure, (ii) external pressure, and (iii) axial compression. The paper explores the up-to-date knowledge on the buckling of cone-cylinder intersection and highlights the areas of gap in knowledge. This is aimed at contributing to better understanding of the relevant issues such as the influence of different types of imperfections in updating the current design guideline that is found to be vital in industrial practice. The review is thematically divided into: (i) the methods adopted in the past work (i.e., how the data were obtained, type of material used, type of design with/without reinforcement), (ii) the highlight and importance of past findings, (iii) the sensitivity to imperfection and its design implications and (iv) the current design recommendation and guidelines. Finally, the current paper provides a brief state-of-the-art and presents an update of related works for the future establishment of shells design guidelines

Nanotalade võnkumise numbriline analüüs

Väitekirja elektrooniline versioon ei sisalda publikatsiooneKäesolevas väitekirjas uuritakse nanomaterjalist valmistatud talade omavõnkumisi mitmesuguste kinnitusviiside korral. Väitekirjas on välja töötatud meetodid nanotalade omavõnkesageduse määramiseks astmelise nanotala jaoks erinevate kinnitustingimuste korral; kusjuures astmete nurkades asuvad stabiilsed praod või prao-tüüpi defektid. Prao mõju võnkesagedusele modelleeritakse nn kaalutu väändevedru meetodil. Selle meetodi kohaselt tuleb reaalne astmega tala asendada kahest elemendist koosneva süsteemiga, kus elemendid on omavahel ühendatud väändevedruga, mille jäikus on pöördvõrdeline pinge intensiivsuse koefitsiendiga prao tipu juures. Kuna pinge intensiivsuse koefitsiendi väärtused on leitavad kataloogidest, siis see meetod võimaldab omavahel siduda nanotala omavõnkesageduse ning prao pikkuse ja laiuse. Väitekiri koosneb sissejuhatusest, viiest peatükist ning kirjanduse loetelust, mis sisaldab 82 nimetust. Sissejuhatus kujutab endast esimest peatükki. Teises peatükis on toodud põhivõrrandid ning põhieeldused. Esimesed kaks peatükki on referatiivsed, ülejäänutes esitatakse originaalseid tulemusi. Kolmandas peatükis esitatakse nanotalade võnkumise võrrandid, mis arvestavad tala elementide pöördeinertsi. Need on Euler-Bernoulli võrrandite üldistuseks juhule, kui pöördeinertsi arvestamine on kohustuslik. See süsteem on lahendatav ka muutujate eraldamise teel. Neljandas peatükis lahendatakse põhivõrrandite süsteem numbriliselt. Näidatakse muuhulgas, et süsteemi saab hõlpsasti lahendada Maclaurini rea abil. Viies peatükk on pühendatud nanotalade võnkumise uurimisele juhul, kui nanotala on kinnitatud elastsete tugede abil st. toed ei ole jäigad. Kuuendas peatükis uuritakse pragudega nanotalade võnkumisi arvestades termilisi mõjutusi st. temperatuuripingeid. Väitekirjas saadud tulemusi on võrreldud erijuhtudel kirjandusest leitavate tulemustega ning veendutud, et väitekirjas esitatud tulemused on heas kooskõlas teiste uurijate poolt saadud tulemustega. Väitekirjas saadud tulemuste põhjal on avaldatud koos juhendajaga 10 teadusartiklit.In this dissertation, an analysis of the dynamic behavior of nanobeams with different physical and geometrical properties using several numerical techniques is presented. Euler-Bernoulli beam theory and nonlocal theory of elasticity are used to simulate the nanobeam. Nanobeams are considered with some special requirements such as tapered, axially graded, and double beams. First of all, in a tapered beam, the width of the beam is varying exponentially along the x-axis from one end to another end. The properties of the tapered beam are to reduce material consumption and provide the cross-sectional area according to the moment distribution. Secondly, in an axially graded beam, material properties such as elasticity and density are varying exponentially from one end to another end. The axially graded beam can be considered as a non-homogeneous as well as a composite beam. In this beam, the material properties can be distributed according to the requirement. The axially graded beam overcomes the limitation of conventional composite. Finally, in a double beam, two identical nanobeams are connected by a Winkler-type spring layer. Double beams are used for absorbing the vibration. It reduces deflection and vibration. The double beam is modeled by the coupled differential governing equations. Some adverse effects such as cracks and the influence of the temperature are considered. Cracks are common defects in nanostructures. Single and multiple cracks are considered in this analysis. According to the model, the crack is replaced by a rotational spring where the crack divides the beam into two segments that are connected to each other by the spring at the crack position. Cracks reduce the overall stiffness of the beam. The effect of temperature is significant for the vibration of nanobeams. The thermal load is compatible with the mechanical load where the thermal load is modeled as an axial load. It reduces the natural frequency. The main objective of this research is to find suitable techniques for a reliable, cost-effective design that is able to fulfill the desired requirements. That is why the important feature of this research is to apply numerical techniques for solving these problems. Three different approximation techniques such as homotopy perturbation technique, power series method, and Maclaurin series method are used for solving these problems. These techniques are useful for solving linear and non-linear differential equations. However, these techniques are rare to analyze the nano-material. These techniques are applied effectively to scrutinize the model of nanobeams. Obtained results are verified with the results of other researchers in the existing literature. This analysis can be used to design nano-electromechanical devices effectively.https://www.ester.ee/record=b550871