In this study, a coupled framework combining the method of fundamental solutions and particle swarm optimization (MFS–PSO) is proposed for the numerical solution of two-dimensional elliptic boundary value problems. The method aims to systematically address the well-known sensitivity of the conventional MFS to the placement of source points. By representing the source locations in polar coordinates, the angular positions of the sources are uniformly prescribed, while the radial distances are treated as optimization variables. Particle swarm optimization is employed to determine the optimal radial distances of the source points by minimizing the averaged residual norm of the MFS collocation system. The proposed approach decouples the numbers of boundary collocation points and source points, allowing flexible configurations to be examined. Five numerical examples are presented. Results for the first four benchmark problems involving the Laplace, Helmholtz, modified Helmholtz, and biharmonic equations are evaluated against analytical solutions, while the MFS–PSO solution to a fifth problem without a prescribed analytical solution is cross-validated against GFDM results. The results show accurate and stable solutions for the analytical benchmarks and closely overlapping MFS–PSO and GFDM contours for the problem without an analytical solution. The proposed framework provides a systematic and efficient strategy for source location determination and enhances the applicability of the method of fundamental solutions to a broad class of elliptic boundary value problems.
Compared with conventional uniform cross-section truss lattice structures (UCTLSs), variable cross-section truss lattice structures (VCTLSs) enable better mechanical performance due to their enlarged design freedoms. This paper proposes an inverse design framework for the VCTLSs by adopting a surrogate-assisted evolutionary optimization algorithm to minimize structural compliance. Specifically, a level set-based topology description function is employed to explicitly describe the geometrical shape of complex cross-sectional struts with simple parameters, which forms the periodic unit cell (PUC) of VCTLSs by interconnecting each other at nodes. As the key factors of controlling their geometry, these explicit parameters of cross-sectional struts are defined as design variables, and thus the dimension of design variables is reduced to only several or tens of dimensions, drastically enhancing the computational efficiency for subsequent optimization procedures. A mathematical optimization model is established for VCTLSs with the objective of structural compliance minimization and the constraint of given volume fraction. An efficient surrogate-assisted particle swarm optimization (ESPSO) algorithm is utilized to solve this optimization model by meticulously searching the optimal parameters of each strut. During the optimization process, the effective properties of the PUC at the microscale are evaluated by a numerical homogenization method, and further used for displacement field analysis at macroscale to calculate overall compliance objective. Both 2D and 3D numerical examples are provided to illustrate the effectiveness of the proposed inverse design method. Quantitatively, the optimized VCTLSs for cantilever beam achieve structural compliance reductions of 14.55%-19.75% in 2D cases and 25.76%-38.93% in 3D cases under various volume fractions, respectively. Numerical results and simulation analyses indicate the mechanical advantage of optimized VCTLSs over the conventional UCTLSs, especially in more complex boundary conditions.
Hydrodynamic lubrication analysis often requires repeated solutions of the Reynolds equation over ranges of operating and geometric parameters. This study developed a parameterized multidimensional physics-informed neural network surrogate and a grouped residual-based adaptive refinement strategy, in which candidate residual points were partitioned by parameter groups before resampling. One- and two-dimensional Reynolds equations were examined using soft and hard boundary constraints. For the one-dimensional problem, the working-condition grouping strategy combined with hard boundary enforcement achieved mean L1 and L2 errors of 0.030 % and 0.045 % within the training domain. For 0–20 % extrapolation of the film-thickness parameter and boundary pressure, the errors did not exceed 0.117 % and were lower than those obtained using conventional residual-based adaptive refinement. However, errors increased with extrapolation distance; for 0–100 % extrapolation in the two-dimensional problem, the mean L1 and L2 errors reached 3.241 % and 5.701 %, respectively. In the mechanical seal application, mean errors in film thickness and opening force were 0.458 % and 0.0003 %. Post-training inference was 14.1–37.5 times faster than the finite element method, excluding approximately 120 min of offline training. The developed framework is primarily applicable to repeated in-domain analyses and constrained extrapolation tasks.
Many practical structural problems can be considered as infinite-domain problems. Infinite-domain problems with traction boundary conditions on their internal boundaries can be solved using boundary-type methods by discretizing only these boundaries, without changes to the formulation. In such problems, the rigid-body motion of the domain is arbitrary and requires no additional consideration in the solution procedure. However, for infinite-domain problems with displacement or mixed boundary conditions on internal boundaries, a unique rigid-body motion at infinity arises. The parameters of this rigid-body motion are not known a priori and cannot be ignored; therefore, they must be considered as additional unknowns. In this study, apparently for the first time, this important class of infinite-domain problems, which has significant applications in engineering, is investigated and analyzed by discretizing only internal boundaries. The method of fundamental solutions (MFS) and the boundary element method (BEM), two well-known boundary-type methods, are employed to solve the aforementioned infinite-domain elasticity problems. With the presented techniques, the governing equations and boundary conditions are exactly satisfied at infinity, while only the internal boundaries of the infinite domain need to be discretized. The advantages, limitations, accuracy, and efficiency of the two methods are studied through several numerical examples.
Deep learning models have demonstrated promising performance in deep excavation deformation prediction. However, their application in geotechnical engineering remains limited by insufficient physical interpretability under spatially variable soil conditions and complex construction scenarios. This study proposes a physics-consistent interpretable convolutional neural network framework for multi-point deformation prediction of deep excavations. Spatial variability of soil properties is represented using random fields and incorporated into network inputs, while excavation conditions are integrated through a unified spatial encoding strategy to improve model generalization. To overcome the black-box limitation of CNN-based surrogate models, Grad-CAM is employed to identify critical spatial regions affecting deformation predictions and interpret the model decision process. Furthermore, a physics-consistency verification strategy is established by comparing Grad-CAM attention patterns with mechanically weak regions identified based on the Mohr–Coulomb criterion. The results demonstrate strong spatial correspondence between model attention regions and physically weak zones controlling excavation-induced deformation. The proposed framework achieves accurate multi-point deformation prediction while providing physically meaningful insights into deformation mechanisms. By integrating deep learning with geotechnical principles, this study improves the transparency and interpretability of CNN-based surrogate models and provides a potential approach for deformation prediction and risk assessment in deep excavation engineering.
Discrete topology optimization within the binary density space {0,1} constitutes a typical NP-hard combinatorial optimization problem. Conventional heuristic algorithms, including genetic algorithms and simulated annealing, frequently suffer from slow convergence, susceptibility to local optima entrapment, and prohibitive computational costs in large-scale design domains. To address these challenges, a quantum–classical hybrid discrete topology optimization method is proposed based on an Ising Hamiltonian mapping model and a quantum annealing mechanism. A discrete topology optimization model targeting structural compliance minimization subject to volume constraints is presented. A quantitative mapping relationship between the transformation of the topology optimization objective variables is then established, enabling the transformation of the topology optimization objective function into a quadratic unconstrained binary optimization (QUBO) Hamiltonian. Coupling coefficients incorporating volume penalty terms and neighborhood connectivity constraints are designed to ensure material distribution feasibility and structural domain continuity. A quantum–classical hybrid iterative strategy is subsequently constructed, wherein the annealing-based Ising solver explores the discrete combinatorial design space through a stochastic search process, while the classical finite element module performs structural response evaluation, sensitivity updating, and feasibility correction. Numerical experiments on benchmark topology optimization problems demonstrate that the proposed method achieves over 60% improvement in convergence rate and 45% enhancement in objective function value compared with the genetic algorithm, validating its effectiveness and superiority for discrete topology optimization.
Accidental internal explosions in earth-covered magazines (ECMs) can cause severe structural break-up and ejection of high-velocity fragments, posing significant secondary hazards to surrounding facilities and personnel. This study investigates structural failure and fragment ejection in earth-covered magazines (ECMs) under internal blast loading using a coupled PBM-FEM-SPH method in LS-DYNA, which integrates Particle Blast Method, Finite Element Method, and Smoothed Particle Hydrodynamics to capture complex nonlinear fracture and fragmentation. The numerical method is validated against RC slab close-in blast tests and KASUN-III internal explosion experiments. Parametric simulations examine the influence of loading density (Q/V) on ECM damage evolution. Results reveal three distinct failure regimes: gas‑pressure‑dominated bending damage, impulse‑dominated bending‑shear failure, and shock‑dominated global disintegration. The front wall is identified as the most vulnerable component. Soil cover effectively mitigates roof fragment velocities at low and intermediate loading densities, but its restraining effect saturates under high‑density conditions. These findings provide theoretical guidance for safety assessment and protective design of ECMs.
Active thermography analyses often represent a subsurface defect as a local layer with an adjusted thermal conductivity. Although this approach can reproduce a measured surface temperature history, the fitted conductivity may combine phase contrast, imperfect contact, lateral heat flow bypass, and partial interruption of transfer paths. This study develops a one-dimensional peridynamic differential operator (PDDO) interaction attenuation model that retains the thermal properties of intact concrete and attenuates only interactions crossing an equivalent defect interval. The macroscopic transmissibility μ controls the strength of the connectivity loss, while the horizon determines the spatial range over which the attenuation is distributed. The intact PDDO solution closely reproduces the Fourier reference. For a representative thermographic experiment, calibration gives μ with a normalized root mean square error of 0.417 percentage points, whereas a local layer constrained by an artificial subsurface defect conductivity of 0.35Wm−1K−1 overpredicts the thermal delay. Within the investigated configuration and parameter ranges, sensitivity analyses show that μ has the largest influence on the rear surface heating delay and temperature rise, while the horizon and kernel order have smaller effects on the measured response. A stochastic micro interaction model provides a physical interpretation of μ in terms of intact-like and high-resistance transfer states. The proposed formulation offers a compact reduced-order description of defect-induced loss of heat transfer connectivity without replacing the entire defect interval by a single homogeneous apparent conductivity.
Active learning Kriging methods are widely used in structural reliability analysis, but existing methods still face limitations in coordinating global exploration and local exploitation, improving sample efficiency, and ensuring reliable stopping decisions. To address these issues, this study proposes AK-TSEFU, a two-stage active learning method that integrates global and local search. In the global stage, the error function (EF) is used to identify highly informative regions near the limit state surface. A transition anchor is then identified, and a local region is constructed, thereby adaptively narrowing the search space from the global candidate pool to a local candidate pool. In the local stage, the U learning function is employed to refine critical boundary regions. The HESC dual layer stopping criterion further ensures sufficient local boundary learning and accurate global failure probability estimation. Across the four examples, AK-TSEFU reduces the mean number of added samples by 8.07%–43.92% and the relative error in failure probability estimation by 49.62%–87.63% compared with other active learning methods. The proposed method achieves a favorable balance between computational efficiency and estimation accuracy and provides an effective approach for reliability analysis involving costly finite element and boundary element models.
Overlapping grids are widely used for complex multi-body flows and large relative motions, yet practical deployment is often limited by the grid-assembly stage, which typically depends on empirically tuned thresholds and becomes a scalability bottleneck in unsteady simulations. This paper presents a scalable, parameter-free automatic overlapping-grid assembly algorithm for cell-centered unstructured meshes. The method reformulates overlap processing through inter-grid cell mapping (cell-center inclusion) and introduces a cell-weight metric derived from mapping statistics to drive parameter-independent cell classification, naturally positioning cutting interfaces near comparable mesh scales. To enforce topological consistency and eliminate cavity/isolated artifacts, an infection-based hole-cutting strategy propagates cell states from boundary seed sets on the cell-adjacency graph. After hole cutting, consistent interpolation layers and donor–receiver relations are constructed to close the assembly loop. Accuracy and robustness are demonstrated on five progressively challenging cases, including a supersonic dual-cylinder shock interaction, a spinning projectile (Magnus effect), wing–store separation with 6-DOF motion, rocket stage separation, and a 31-million-cell helicopter hover simulation. Results show close agreement with single-grid and commercial overlapping solutions and validate stability under strong shocks and large motions while enabling efficient heterogeneous CPU/GPU workflows.
