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.

Flaws can develop on the weld surface of a rail during welding or in corrosive environments. If a flaw exceeds the critical initial flaw size (CIFS), it can propagate under repeated wheel loads, leading to rail fracture. This study employed 3D thermo-elastic-plastic finite element analysis (FEA) to simulate the residual stress in a flash-butt welded rails made of R260 rail steel. Under 4-point bending, the stress intensity factor range ([Formula: see text]) for a semi-circular crack at the rail foot was calculated using 3D linear-elastic FEA. The crack size was increased until [Formula: see text] reached the threshold value ([Formula: see text]), determining the CIFS. For small cracks, compressive residual stress at the rail foot’s outer edge counteracted tensile stress, preventing crack propagation. In contrast, larger cracks extended into the tensile residual stress region near the middle of the rail foot, promoting crack opening and reducing fatigue resistance. The study showed that welded rails have a larger CIFS than unwelded ones due to the influence of compressive residual stress at the rail foot’s outer edge. These findings provide valuable guidelines for determining CIFS, maintaining flash-butt welded rails made of R260 rail steel, and improving the welding process to enhance rail durability.

B-spline wavelet on the interval (BSWI) has the advantages of interval interpolation and nested approximation, which is suitable for numerical solution of partial differential equations (PDE) and integral equations. This method combines B-spline wavelet on the interval with the traditional boundary element method. By taking advantage of the nested approximation characteristics of B-spline wavelet on the interval, it provides a new numerical calculation method for the field of computational mechanics. In the present, interval B-spline wavelet boundary element method (BSWI-BEM) using the nested approximation has been presented to solve elasticity problems. First, the lifting scheme of BSWI basis functions is developed for nested approximation. Second, the boundary variables represented by the coefficients of wavelets expansion in wavelet space are transformed into the physical space via the corresponding multi-scale transformation matrices. Last, the BSWI-BEM computational schemes for 2D and 3D elasticity problems are derived using the fundamental solution of the elasticity problems in association with weighted residual techniques. Numerical simulations using typical examples of 2D and 3D elasticity problems are given and the corresponding accuracies are verified by comparison with closed-form solutions.

In numerical simulations and experimental observations, flow field data are often limited by insufficient spatial resolution and incomplete time series, which in turn affect the accurate capture and modeling of flow structures and their evolution processes. To address this challenge, this paper proposes an end-to-end high-resolution flow field prediction framework that can rely solely on low-resolution input data to reconstruct the fine spatial structure at the current moment and predict the high-resolution evolution state at future moments. The framework consists of three types of deep neural network modules working together: the U-Net-based super-resolution reconstruction module (U-Net-SR) implements high-resolution spatial reconstruction at the current moment, the long short-term memory module (LSTM) models the temporal evolution trend of low-resolution sequences, and the U-Net-based multi-source fusion prediction module (U-Net-Pred) integrates the information from both to achieve accurate prediction of the high-resolution flow field at future moments. This method is validated in three typical flow field tasks: laminar flow around a cylinder, laminar flow over a controlled pitch airfoil, and experimental turbulent flow field under cross-wind gusts passing through a flat plate airfoil. In multiple typical flow field tasks, the framework demonstrates excellent spatiotemporal modeling capabilities. Overall, the average peak signal-to-noise ratio (PSNR) of the prediction results generally remains in the range of 40–48[Formula: see text]dB, and the structural similarity index measure (SSIM) index is mostly stable above 0.95, accurately capturing key structural features and maintaining good temporal evolution consistency. Compared with traditional single-path models that only handle spatial reconstruction or temporal prediction, the innovation of this framework lies in its dual U-Net collaborative mechanism: U-Net-SR provides the high-resolution state at the current moment as a spatial benchmark, LSTM captures the overall evolution trend of the flow field, and U-Net-Pred completes cross-scale fusion and information collaboration in the feature space, thereby achieving better super-resolution prediction.