This study proposes several key improvements based on detailed analysis of the Minkowski difference. In the Gilbert–Johnson–Keerthi (GJK) algorithm, a stable orthogonal search direction is constructed at the midpoint of a line-segment simplex to eliminate zero-vector degeneracy, while the origin position relative to a triangular simplex is rapidly determined using the triangle normal. In the Expanding Polytope algorithms (EPA), the simplex is expanded directly along the triangular normal to form a tetrahedron. A novel outward normal vector determination method is also introduced using the vector between two non-coplanar tetrahedral vertices, resolving failures when the origin lies on a face. The improved GJK-EPA algorithm was implemented in a discrete element framework for gravitational stacking simulations of ellipsoidal–polyhedral particles. Validation against physical experiments showed excellent agreement, with an average repose angle difference of only 4.18° and a relative error in pile height of 4%. Large-scale polyhedral stacking simulations demonstrated denser packing structures with smoother surface profiles. Compared with the conventional GJK-EPA, the proposed algorithm reduces computational time by 13%, decreases the maximum number of iterations by up to three, and improves maximum contact depth accuracy by 8%. Although its contact depth accuracy is slightly lower than that of the GJK-EPA-IPM method, its computational time is only 52% of the latter. These results confirm that the improvements provide a superior balance between accuracy and efficiency for polyhedral particle simulations.

In this paper, meshfree collocation with fast-moving least-squares reproducing kernel was implemented to write down and execute numerical solutions for some applications in elastostatics and elastodynamics. The spatial discretization using meshfree collocation method was carried out on the equilibrium differential equations of elastostatics and elastodynamics and the corresponding boundary conditions. The resulting discrete forms were solved for benchmark problems in the one- and two-dimensional cases. In each case, a convergence study was conducted to ascertain the utility and efficacy of the developed solutions. For elastodynamics, the time domain, however, was discretized using the Newmark beta time-integration scheme. The latter combination was implemented to solve suitable benchmark problems in the one-dimensional and two-dimensional cases. In each case, a stability study was conducted to demonstrate, again, the method’s efficacy in handling elastodynamic problems.

This paper presents a weak-form zonal free element method (ZFrEM) coupling with a Perzyna-type viscoplastic model within the von Mises framework to solve twodimensional viscoplastic problems. The proposed approach offers two main advantages. First, owing to the specific construction of the collocation elements, ZFrEM provides enhanced flexibility for model discretization. Second, the Perzyna model enables accurate simulations over a broad range of material parameters. Due to the inherent nonlinearity of the governing equations and the introduction of viscoplastic constitutive behavior, both the global equilibrium equations and the incremental update of the plastic multiplier are solved by using a Newton–Raphson iteration. In addition, because the elastic–plastic states vary among the nodes, the Perzyna model is also incorporated into the assembly of the global stiffness matrix. Numerical examples demonstrate that the proposed method attains accuracy comparable to that of widely used approaches for viscoplastic analysis.

This paper develops a Taylor Collocation Method (TCM) for solving systems of twodimensional Volterra integral equations with proportional delays. The proposed method constructs explicit formulas for the approximate solution directly, thereby avoiding transformation into large algebraic systems. A convergence analysis is presented to establish the reliability of the scheme. Several numerical examples are provided to illustrate the efficiency and accuracy of the algorithm. The results confirm that Taylor-based collocation techniques offer a powerful and practical tool for tackling multi-dimensional integral equations with delay effects.

Multi-scale flow fields can destabilize the training of data-driven models by weighting loss contributions unevenly. This study proposes a loss-independent pre-loss normalization module, used only during training, that independently scales predictions and targets prior to loss computation. Three normalization schemes are tested with four loss functions using a transformer model for laminar developing pipe flow. On the test dataset and two additional flow cases, Pre-Loss Normalization reduces the mean absolute error by 27–81% and improves the [Formula: see text]2 value of 0.186–0.630 over unnormalized training. Overall, this approach mitigates multi-scale effects and improves accuracy and robustness.

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.