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This study focuses on solving the geometric nonlinear dynamic equations of structures using the multi-point iterative methods within the optimal three-step composite time integration method (OTCTIM). The OTCTIM, initially devised for linear dynamic systems, is now proposed to encompass nonlinear dynamic systems in such a way that the semi-static nonlinear equations in time sub-steps can be solved using multi-point methods. The Weerakoon–Fernando method (WFM), Homeier method (HM), Jarrat method (JM), and Darvishi–Barati method (DBM) have been extended as multi-point solvers for nonlinear equations in OTCTIM, which exhibit a higher convergence order than the Newton–Raphson method (NRM), without requiring the calculation of second and higher derivatives. Several structural examples were solved to examine the performance of these methods in the OTCTIM approach. The results demonstrated that the multi-point iterative methods outperform NRM (in terms of the number of iterations) within the OTCTIM for geometric nonlinear structural dynamics and, among the multi-point methods, the JM and DBM converged with fewer number of iterations and lower error levels. Furthermore, it has been observed that when solving nonlinear dynamic equations for structures with a high number of degrees of freedom, the incorporation of the DBM into the OTCTIM mitigates the convergence iterations and the average elapsed time for iterative sub-steps. [ABSTRACT FROM AUTHOR]

In this article, a novel approach has been employed to identify structural damage in the wooden bridge structure by utilizing vibration data. This method encompasses the Fourier decomposition method that decompose the response of the bridge into a sequence of Fourier Intrinsic Band Functions (FIBF). These functions comprise the responses of the structure that contain inherent information of structure as well as noise from the vibrations. The time series modeling is utilized to extract damage-sensitive features. The residuals of the time series model of both undamaged and damaged structures are extracted for detecting any damage. To ascertain the presence of damage, supervised classification machine learning algorithms are employed. The algorithms are utilized consist of Artificial Neural Network (ANN), K-Nearest Neighbors (KNN), support vector machines (SVM), ensemble learning, and decision tree. The results indicate that the proposed method of feature extraction is highly effective and reliable in detecting damages. In addition, the capacity of decision tree and ANN algorithms to minimize type 2 error and enhance accuracy is demonstrated when evaluating different machine learning algorithms. The value of the type II error in the ANN model and the decision tree is equal to 13.85% and the accuracy of the model is 93.02%. [ABSTRACT FROM AUTHOR]

AbstractSemi-numerical methods hold significant value due to their efficiency in time-consuming calculations. Accordingly, this article proposes an effective strategy to derive the vibration parameters of cylindrical shells (CSs) with cutout utilizing a semi-analytical approach entitled differential transform method (DTM). To achieve this, the governing equations of motion are first introduced based on Sander’s theory of shells. These equations give rise to a coupled system of linear ordinary differential equations, which pose a challenge in solving the eigenvalue problem. It should be emphasized that the classical version of the differential transform method could not be directly applied to solve the eigenvalue problem related to the above-mentioned coupled differential equation. An innovative technique is employed and discussed in the paper to remedy these difficulties, which could be widely used in similar problems. As a result, the natural frequencies and mode shapes of some CSs with cutouts, various internal angles, and diverse material characteristics are attained. The outcomes undergo validation through the hybrid finite element method, and the proposed method’s accuracy is rigorously proved. In conclusion, the proposed DTM provides an efficient solution to the eigenvalue problem of coupled differential equations and offers a valuable tool for obtaining accurate vibration parameters of CSs. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the reliability analysis and safety evaluation of dynamic stresses are presented for Al–Al2O3 functionally graded (FG) thick hollow cylinder subjected to sudden unloading as a mechanical shock loading. The FG cylinder is considered to have infinite length and axisymmetry conditions. The constitutive mechanical properties of Al and Al2O3 are assumed as random variables with Gaussian distribution and also the mechanical properties are considered to vary across thickness of FG cylinder as a non-linear power function of radius. The radial and hoop stresses are obtained by solving Navier equation in displacement form and stress–displacement equations. The FG cylinder is divided to many linear functionally graded elements across thickness of cylinder and hybrid numerical method (Galerkin finite element and Newmark finite difference methods) along with the Monte Carlo simulation are employed to solve the statistical problem. The reliability of radial and hoop stresses are calculated in various points across thickness for different grading patterns in functionally graded material (FGM) and several yield stresses. The variability of the dynamic stress reliability of the FG cylinder to the values of coefficients of variation (COVs) is examined and discussed in details. [Copyright &y& Elsevier]