Efficient CUF-based method for the vibrations of thin-walled open cross-section beams under compression

This study proposes an efficient method for the evaluation of vibrations and buckling in thin-walled beams with complex geometries subjected to progressive compressive loads. A comprehensive study is conducted in order to investigate the effects of compressive loads on the natural frequencies of the thin-walled beams. Namely, a numerical simulation of the Vibration Correlation Technique is provided in this study. Finite Elements (FEs) are built in the framework of the Carrera Unified Formulation (CUF), and the displacements of complex geometric shapes of the thin-walled beams are evaluated using low- to higher-order Taylor and Lagrange polynomials. The results are compared with the experimental results of the available literature and the numerical results by the shell models. The cross-sectional deformations of the beam due to the vibration modes are also compared, and the importance of structural theories capable of accurate detection of complex cross-sectional deformations is highlighted. The obtained results are demonstrated to be promising and accurate and match reasonably well with the experiments and shell models, which are more expensive in terms of computational costs compared to the efficient CUF ones proposed here

Numerical vibration correlation technique for thin-walled composite beams under compression based on accurate refined finite element

This paper investigates the virtual vibration correlation technique for the evaluation of the variations of the natural frequencies for highly flexible thin-walled composite beams. In this regard, refined finite element based on the Carrera Unified Formulation (CUF) is developed. Thin-walled composite beams with various cross-sections of box, I-shaped and channel-shaped types, are investigated. Additionally, a comparison of the CUF results with the implemented shell models and the available literature is presented in order to evaluate the accuracy and efficiency of the proposed method. It is indicated that classical beam theories such as Euler–Bernoulli and Timoshenko beam theories failed to have an accurate prediction of the natural frequencies and dynamic response of thin-walled beam structures. Therefore, the necessity of employing higher-order and refined beam theories capable of capturing cross-sectional deformations is highlighted. Furthermore, to fully demonstrate the capabilities of the CUF-1D method with efficient Lagrange expansion, a more complex structural problem of a channel-shaped composite beam with the different numbers of transverse stiffeners is studied, and conclusions about the buckling behavior and variations of natural frequencies are drawn. It is shown that the numerical assessments by the proposed efficient CUF method in this paper correlate well with the shell results which are more computationally expensive

Static analysis of thin-walled beams accounting for nonlinearities

This paper presents numerical results concerning the nonlinear analysis of thin-walled isotropic structures via 1D structural theories built with the Carrera Unified Formulation (CUF). Both geometrical and material nonlinearities are accounted for, and square, C- and T-shaped beams are considered. The results focus on equilibrium curves, displacement, and stress distributions. Comparisons with literature and 3D finite elements (FE) are provided to assess the formulation’s accuracy and computational efficiency. It is shown how 1D models based on Lagrange expansions of the displacement field are comparable to 3D FE regarding the accuracy but require considerably fewer degrees of freedom

Benchmarks for higher-order modes evaluation in the free vibration response of open thin-walled beams due to the cross-sectional deformations

Highly flexible thin-walled beams with complex open cross-sections are sensitive to torsional and warping effects. The analysis of higher-order vibration modes in these structures needs more accurate and precise methods in order to achieve reliable results and detect the cross-sectional deformations in the structures’ free vibration response. This paper analyzes higher vibration modes in a series of thin-walled beams, which were proposed by Chen as benchmark problems. These are all open-section thin-walled beams with complex geometries. Global vibration modes, such as bending and torsion, related to the rigid cross-sectional deformations can be detected via classical and shear refined theories. However, cross-sectional deformations appear at higher frequencies, and these modes are mixed with the global ones. To highlight this fact, this paper compares classical beam theories with refined ones based on the Carrera Unified Formulation (CUF) and the shell results using the commercial finite element (FE) software and the data available from the literature. The CUF FEs based on the power of cross-sectional deformation coordinates (x, z) and those based on the Lagrangian polynomials are implemented and compared using Modal Assurance Criterion. A number of interesting conclusions are drawn about the effectiveness of classical and CUF-based results. The need for models capable of detecting cross-sectional deformations is outlined. In fact, many modes are lost by classical beam theories; on the other hand, they show rigid cross-section modes that do not really exist. This fact is also confirmed by the shell models, which are more expensive in terms of computational costs regarding the efficient CUF ones proposed here

Buckling and post-buckling of anisotropic flat panels subjected to axial and shear in-plane loadings accounting for classical and refined structural and nonlinear theories

Abstract This article investigates the large deflection and post-buckling of composite plates by employing the Carrera Unified Formulation (CUF). As a consequence, the geometrically nonlinear governing equations and the relevant incremental equations are derived in terms of fundamental nuclei, which are invariant of the theory approximation order. By using the Lagrange expansion functions across the laminate thickness and the classical finite element (FE) approximation, layerwise (LW) refined plate models are implemented. The Newton–Raphson linearization scheme with the path-following method based on the arc-length constraint is employed to solve geometrically nonlinear composite plate problems. In this study, different composite plates subjected to large deflections/rotations and post-buckling are analysed, and the corresponding equilibrium curves are compared with the results in the available literature or the traditional FEM-based solutions. The effects of various parameters, such as stacking sequence, number of layers, loading conditions, and edge conditions are demonstrated. The accuracy and reliability of the proposed method for solving the composite plates' geometrically nonlinear problems are verified

A low cost and highly accurate technique for big data spatial-temporal interpolation

The high velocity, variety and volume of data generation by today's systems have necessitated Big Data (BD) analytic techniques. This has penetrated a wide range of industries; BD as a notion has various types and characteristics, and therefore a variety of analytic techniques would be required. The traditional analysis methods are typically unable to analyse spatial-temporal BD. Interpolation is required to approximate the values between the already existing data points, yet since there exist both location and time dimensions, only a multivariate interpolation would be appropriate. Nevertheless, existing software are unable to perform such complex interpolations. To overcome this challenge, this paper presents a layer by layer interpolation approach for spatial-temporal BD. Developing this layered structure provides the opportunity for working with much smaller linear system of equations. Consequently, this structure increases the accuracy and stability of numerical structure of the considered BD interpolation. To construct this layer by layer interpolation, we have used the good properties of Radial Basis Functions (RBFs). The proposed new approach is applied to numerical examples in spatial-temporal big data and the obtained results confirm the high accuracy and low computational cost. Finally, our approach is applied to explore one of the air pollution indices, i.e. daily PM2.5 concentration, based on different stations in the contiguous United States, and it is evaluated by leave-one-out cross validation

Copula-based probabilistic assessment of intensity and duration of cold episodes: A case study of Malayer vineyard region

Frost, particularly during the spring, is one of the most damaging weather phenomena for vineyards, causing significant economic losses to vineyards around the world each year. The risk of tardive frost damage in vine-yards due to changing climate is considered as an important threat to the sustainable production of grapes. Therefore, the cold monitoring strategies is one of the criteria with significant impacts on the yields and prosperity of horticulture and raisin factories. Frost events can be characterized by duration and severity. This paper investigates the risk and impacts of frost phenomenon in the vineyards by modeling the joint distribution of duration and severity factors and analyzing the influential parameter’s dependency structure using capabilities of copula functions. A novel mathematical framework is developed within this study to understand the risk and uncertainties associate with frost events and the impacts on yields of vineyards by analyzing the non-linear dependency structure using copula functions as an efficient tool. The developed model was successfully vali-dated for the case study of vineyard in Malayer city of Iran. The copula model developed in this study was shown to be a robust tool for predicting the return period of the frost events

Static analysis of thin-walled beams accounting for nonlinearities

This paper presents numerical results concerning the nonlinear analysis of thin-walled isotropic structures via 1 D structural theories built with the Carrera Unified Formulation (CUF). Both geometrical and material nonlinearities are accounted for, and square, C- and T-shaped beams are considered. The results focus on equilibrium curves, displacement, and stress distributions. Comparisons with literature and 3 D finite elements (FE) are provided to assess the formulation’s accuracy and computational efficiency. It is shown how 1 D models based on Lagrange expansions of the displacement field are comparable to 3 D FE regarding the accuracy but require considerably fewer degrees of freedom. </jats:p