Traditional manual methods for measuring concrete crack depth are inefficient, time-consuming, and heavily reliant on operator experience, often resulting in inconsistent and subjective outcomes. Moreover, most existing studies on crack characterization primarily emphasize surface-level parameters such as crack length, width, and area. The crack depth, a key indicator of structural integrity and residual load-bearing capacity, remains insufficiently addressed. To bridge this gap, this study proposes an automated crack depth prediction framework that integrates infrared thermography (IRT) with an enhanced SE-ResNet-18 deep learning model. Concrete beam specimens with precisely calibrated crack depths were fabricated under controlled laboratory conditions, and corresponding thermal images were acquired to establish a robust training dataset. By embedding a squeeze-and-excitation (SE) attention mechanism into the conventional ResNet-18 architecture, the model’s capacity to capture and emphasize salient thermal features was significantly improved, resulting in more accurate and stable depth predictions. Experimental results demonstrate that the proposed SE-ResNet-18 achieves 93.77% accuracy within a ±1[Formula: see text]mm tolerance, outperforming the baseline ResNet-18 network by a substantial margin. This solution is fully automated in its predictive analysis and noncontact in its sensing modality. It shows strong potential for practical implementation in real-world structural health monitoring and provides a foundation for future research on field-scale applications and model generalization under varying environmental conditions.

In this study, a higher-order approach incorporating a new polynomial-exponential integral shear strain field is established to examine the vibration response of functionally graded (FG) nanobeams subjected to hygrothermal loading and material composition imperfections. The formulation employs a displacement field with undetermined integral terms and considers four hygrothermal environments: uniform, linear, nonlinear, and sinusoidal distributions. The nanobeam rests on a Winkler–Pasternak elastic foundation, and three porosity patterns based on cosine-type functions are examined. A power-law scheme describes the disparity of constituent materials across the thickness, including temperature-dependent mechanical properties. The analysis explores the influence of environmental conditions, material gradation, porosity profiles, nonlocal impacts, and foundation stiffness on natural frequencies. The outcomes deliver a comprehensive context for future research on the dynamic behavior of advanced graded nanostructures.

This study presents a novel algorithm that can solve a class of second-order nonlinear boundary value problems (BVPs) with arbitrary boundary conditions. The proposed approach combines the homotopy perturbation method (HPM) with multiscale functions. First, the HPM transforms the nonlinear governing equations into a series of linear subproblems. Multiscale functions are then employed to find approximate solutions to the linear equations. Rigorous convergence analysis and error estimates have been established for the algorithm. Numerical examples are examined to validate the efficiency and stability of the scheme. These examples include second-order nonlinear BVPs and systems of nonlinear equations incorporating various boundary conditions, such as Dirichlet, Neumann, integral and Robin types. The test results demonstrate that the proposed method yields highly accurate approximations that closely match the analytical solutions. Compared with several existing schemes documented in the literature, the proposed method offers improved accuracy.

This paper proposes a hybrid uncertainty propagation analysis method for problems involving both random and interval variables by synergistically integrating arbitrary Polynomial Chaos (aPC) with Chebyshev polynomials. In this method, the aPC method is adopted to handle random uncertainties, and an interval method based on Chebyshev is proposed to deal with interval uncertainties. The principal advantages of the proposed method are: (1) It characterizes random variables using aPC, requiring only statistical moments from sample data and eliminating the reliance on pre-assumed precise probability distributions. (2) It seamlessly integrates this with a Chebyshev-based treatment of interval variables, providing a robust and efficient analysis tool. The validity and advantages of the proposed method are demonstrated through numerical examples and representative engineering case studies.

Cohesive Element Method (CEM), the most popular method for composite delamination, suffers from rigorous element size requirements and great computational cost. In this work, the Extended Finite Element Method (XFEM) and Virtual Crack Closure Technology (VCCT) are combined to develop XFEM based on VCCT (XFEM-VCCT) for delamination analysis for the first time. In XFEM-VCCT, the geometry of delamination is represented by XFEM with VCCT as the delamination propagation criterion. A new method for the strain energy release rate in the frame of XFEM is created based on Irwin’s integration. The XFEM-VCCT is applied to three examples to validate. Through the three examples, some outstanding advantages of XFEM-VCCT show up compared with CEM. First, XFEM-VCCT can simulate delamination and its propagation without remeshing, thus simplifying the mesh work. Second, XFEM-VCCT does not require such a fine mesh as CEM, alleviating the element size requirement. Lastly, ignorant of material property degradation, iterations are not needed and the computational efficiency is greatly improved. Therefore, the newly developed XFEM-VCCT can provide more accurate results with simpler mesh work and less computational cost for composite delamination, compared with CEM.

In this paper, we consider a time-fractional fourth-order nonlocal problem with Navier boundary conditions. First, we discuss the existence–uniqueness of the weak solution at the continuous level using Faedo–Galerkin method. Then this fourth-order problem is transformed into a system of two second-order equations. For this system, a fully discrete scheme is proposed which comprises the standard finite element method and the [Formula: see text] scheme on the graded mesh. For the proposed scheme, we derive [Formula: see text]-robust convergence estimates. Finally, numerical experiments are presented to validate the theoretical findings.

Sylvester tensor equation has widely applications in many fields, thus it is meaningful to construct effective methods to solve it. In this paper, we design two new gradient-based iterative-like algorithms for solving the Sylvester tensor equations to further improve computational efficiencies of some existing gradient-based iterative-like ones. By replacing the system matrices in mode products in the modified gradient-based iterative algorithm (Chen, Z. and Lu, L.-Z. [2013] “A gradient based iterative solutions for Sylvester tensor equations,” Math. Probl. Eng. 2013, 151–164) by their diagonal parts, we construct the accelerated modified gradient-based iterative algorithm for the Sylvester tensor equations, which requires less computational load and is more efficient than the modified gradient-based one. Besides, we apply a new updated strategy to the modified gradient-based one and develop an improved modified gradient-based iterative algorithm for the Sylvester tensor equations. Compared with the modified gradient-based one, the improved modified gradient-based iterative algorithm can make more full use of computed results and have better numerical performances. We establish the convergence conditions and convergence intervals of the proposed algorithms based on the spectral radius and matrix spectral norm. Finally, some numerical examples are performed to show that the proposed algorithms are efficient, and outperform several existing gradient-based iterative-like ones in terms of the number of iterations and computational time.

This paper conducts a comprehensive comparison of the vibrational responses of elastic wheels and standard wheels under various excitation conditions. The investigation focuses on a frequency range spanning from 500 to 3750[Formula: see text]Hz, within which we observe that the radial modes of the elastic wheel tend to be relatively concentrated. This concentration can have significant implications for the performance and stability of the wheel during operation. One of the key findings of this study is that the mobility of the elastic wheel is notably higher than that of the standard wheel. This increased mobility is a double-edged sword; while it may enhance the wheel’s ability to adapt to varying loads and road conditions, it also predisposes the elastic wheel to higher levels of rim vibration. Such vibrations can lead to potential issues in terms of ride comfort. The frequency spectrum beyond 3750[Formula: see text]Hz, a marked difference in vibration levels between the two types of wheels becomes apparent. In this higher frequency range, the vibration levels experienced by the elastic wheel are several orders of magnitude lower than those of the standard wheel. This significant reduction in vibration can primarily be attributed to the unique properties of the rubber layer in the elastic wheel design. The rubber material acts as a crucial dampening agent, efficiently dissipating vibration energy that would otherwise contribute to increased noise and structural fatigue.

This work is devoted to numerical analysis for transient heat transfer problems by the reduced integration and Richardson extrapolation (REQ method). This computationally efficient quadrature scheme is used to generate element matrices for functionally graded quadrilateral elements to analysis of unsteady state heat transfer. In the context of solving the finite element method (FEM) discrete formulations, the central difference method is considered for better accuracy, ensuring the reliability of the numerical solutions, since the central difference method posses stability and non-oscillatory nature, which are essential for achieving precise results. To assess the performance of the new numerical technique, the research focuses on validating the computational efficiency and accuracy that involves solving the benchmark reference problems and comparing the results with the outcomes obtained through conventional Gauss quadrature and other effective numerical methods from the existing literature. The validation process aims to demonstrate the superiority of the proposed REQ method in terms of computational speed and precision of the final results.

This study proposes an adaptive nodal density Solid Isotropic Material with Penalization (SIMP) method for topology optimization to improve computational efficiency by addressing the high computational cost of fixed meshes. By decoupling the density mesh from the analysis mesh, our method eliminates the need for generating complex unstructured analysis meshes and effectively mitigates discontinuities in the density field. Providing a practical framework for large-scale structural optimization, the proposed approach achieves a reduction of over 50% in computational complexity and more than a 36% reduction in computational scale of that required by a uniformly refined mesh. Optimization results for truss and cantilever beam structures demonstrate that this method enhances computational accuracy with fewer fine-scale features, yielding clearer structures with less computational effort. These results highlight the method's robustness and practical manufacturability.