Engineering Analysis with Boundary Elements最新文献

The rock-soil mass, subjected to complex and lengthy geological processes, exhibits heterogeneity which induces variations in mechanical properties, thereby affecting the overall stability of slopes. In this paper, a novel numerical model that incorporates the Weibull distribution function into the meshless numerical manifold method based on the strength reduction method (MNMM-SRM) to account for the slope soils heterogeneity and their influence on the factor of safety (F_s) and the critical sliding surface (CSS). Initially, the Weibull distribution is introduced into the MNMM-SRM model based on the complementary theory of subspace tracking, addressing the issue of multiple yield surface corners in the Mohr-Coulomb framework while simultaneously considering the heterogeneous nature of rock and soil formations. Subsequently, an intelligent method based on unsupervised learning is proposed to obtain reasonable CSS, utilizing the total displacement field at slope nodes and the equivalent plastic strain field as input variables. The results serve as criteria for terminating the strength reduction in the MNMM-SRM. The applicability of this method is verified through three typical examples, demonstrating its potential for widespread application in the assessment of heterogeneous slope stability.

In the era of Industry 4.0, the prominence of 3D printing as a pivotal manufacturing technology has greatly expanded, particularly within the domain of additive manufacturing (AM). Among the thriving research applications tailored for integration with AM, topology optimization (TO) has emerged as a resounding success. Given the prerequisite of TO for high-resolution meshing to ensure visual clarity in result depiction, researchers have been consistently driven to develop advanced techniques to refine optimal designs, thus elevating the challenge and popularity within this research realm. This paper presents a novel approach integrating an adaptive image-based octree mesh scaled boundary finite element (SBFE) framework with an evolutionary methodology that can effectively address the persistent challenges inherent to TO. A novel hierarchical SBFE mesh analysis not only facilitates efficient and precise TO but also substantially reduces computational resource demands. Furthermore, the pre-conditioned conjugated gradient (PCG) method is adopted to process practical-scale problems, minimizing computer memory resources. Additionally, the proposed work incorporates a post-processing technique utilizing the isosurface function based on a marching cube algorithm, thereby smoothing the boundaries of optimal results. Consequently, this research extends the horizons of design possibilities, particularly in the creation of intricate 3D structures, which can be seamlessly realized through additive manufacturing and 3D printing.

A three-dimensional hybrid Green function method is proposed to investigate the seakeeping and added resistance performance of ships advancing in waves. As for the method, the whole fluid domain is divided into two subdomains by introducing a regular virtual control surface. In the inner domain, the first order Taylor Expansion Boundary Element Method (TEBEM) based on simple Green function (Rankine source) is applied. Meanwhile, three-dimensional panel method based on the translating-pulsating panel source (3DTP-PS) Green function is adopted in the outer domain, to overcome the difficulty in proposing a proper boundary condition of the control surface for the Rankine source panel method. With respect to the coupled solutions in the two subdomains, the continuous conditions of velocity potential and its normal derivative are imposed on the virtual control surface. Different treatments of linearization of the free surface and the corresponding ship hull conditions in the inner domain are discussed. Furthermore, six ship models are selected to investigate: the Wigley III, Slender Wigley, Blunt Wigley, S-60, SCb-84 and RIOS ship models (which include different ship types, such as slender, blunt, with bulbous bow, and without bulbous bow). Firstly, through the calculations of radiation and diffraction forces on two modified Wigley hulls and S-60 with block coefficient equals to 0.7, the present method is proved to have good mesh convergence, and satisfactory results can be obtained. Then, the present numerical method is applied to evaluate the hydrodynamic responses of ships sailing in head and oblique waves. Finally, the ship motions and the wave‑induced mean second order wave forces are calculated, including multiple wave directions. Good agreement between the experimental measurements and the numerical results is obtained in all cases, indicating that the present hybrid Green function method is useful and applicable. For present hybrid Green function method, TEBEM is used instead of the traditional constant panel method, which has the advantages of accuracy, and provides a new way for ship hydrodynamic calculation.

The unsaturated zone profoundly affects groundwater (GW) flow induced by pumping and injection due to the capillary forces. However, current radial basis function (RBF) numerical models for GW pumping and injection mostly ignore the unsaturated zone. To bridge this gap, we developed a new three-dimensional weak strong form RBF model in this study, called CCHE3D-GW-RBF. Flow processes were modelled by the mixed-form Richards equation which was iteratively solved by the modified Picard iteration. Soil-water characteristic curves were represented by the widely applicable formulas, the van Genuchten (1980) model. Differential operators were approximated by the localized Gaussian RBF, and the weighted singular value decomposition method was used to construct stable bases. The injection/pumping wells and the flux boundaries were handled by the weak formulation using Meshless Local Petrov Galerkin method, and the strong-form equation using the collocation RBF method was enforced on the other points. Good agreement was found between the simulation results from our numerical model and the well-accepted solutions in all three verification cases, demonstrating the accuracy and applicability of this model. In addition, a smaller RBF shape parameter was found to produce a more accurate modelling resulting, indicating the necessity of implementing stable bases for RBF models.

This article presents a numerical formulation based on the Boundary Element Method for the transient dynamic analysis of cracked thick symmetrical composite shells. The integral formulation uses the static fundamental solutions for thick orthotropic symmetric plates and the anisotropic plain elasticity fundamental solution. Domain integrals associated to distributed loads, curvature and inertial terms are evaluated employing the Radial Integration Method. The crack was modeled using the sub-region method. The developed formulation is implemented computationally and validated through the analysis of several proposed examples. The obtained results demonstrate the validity and robustness of the developed formulation.

Working with a special coordinate system, this study demonstrates how to obtain numerical solutions with geometric convergence for the eigenstates of a Laplacian operator in irregular prismatic domains (both annular and single) that are simply connected. An appropriate coordinate system, which defines a tightly bounded domain, allows for a fair mesh for series approximation nodes. Three independent criteria were used to verify the consistency of the solutions: the Rayleigh quotient, the divergence theorem, and a partial derivative equation (PDE) transformed from an eigenvalue problem to a boundary value problem with Robin conditions. Supporting the proposed method, examples show a few hundred eigenstates obtained in a single computation, with at least 10 significant figures and a low computational cost.

Granite is often encountered in underground engineering, and its mechanical properties and failure behavior directly determine its stability and seepage characteristics. Unlike other rocks, granite is usually considered heterogeneous. Based on the Weibull distribution, this paper proposes a novel modeling method for heterogeneous granite via the combined finite-discrete element method (FDEM), and the mechanical properties and failure behavior of granite under uniaxial and triaxial compression, Brazilian splitting, and direct tension, as well as the influence of the loading rate, were investigated. The research results indicate that (1) the new modeling method can be used to construct a heterogeneous granite numerical model that includes three types of randomness (mineral spatial distribution randomness, mineral size randomness, and mineral shape randomness) and can quantitatively change the mineral composition; (2) uniaxial and triaxial compression simulation tests reveal that as the content of weak minerals (biotite) increases, the uniaxial compressive strength and equivalent cohesion decrease as a power function, and Young's modulus decreases as a linear function, while the equivalent internal friction angle decreases as an exponential function; (3) heterogeneous granite exhibits different mechanical properties and failure behaviors under Brazilian splitting and direct tension due to their different failure modes; typically, the tensile strength obtained from direct tension testing is lower than the value obtained from Brazilian splitting testing; and (4) as the loading rate increases, the strength, stiffness, and number of cracks of the specimen first stabilize and then increase as a power function, with a critical rate of v=1 m/s.

Physics-Informed Neural Networks (PINNs) have been extensively used as solvers for partial differential equations (PDEs) and have been widely referenced in the field of physical field simulations. However, compared to traditional numerical methods, PINNs do not demonstrate significant advantages in terms of training accuracy. In addition, electromagnetic field computation involves various governing equations, which necessitate the construction of specific PINN loss functions for training, which limits their applicability in computational electromagnetics. To address these issues, this paper proposes a general algorithm for multi-scenario electromagnetic field calculation called DAL-PINN. By reformulating Maxwell's equations into a general PDE with variable parameters, different electromagnetic field problems can be solved by simply adjusting the source and material parameters. Based on D'Alembert's principle and fixed-point sampling, the algorithm is effectively improved by replacing interpolation functions with random variables (virtual displacements). The performance of the proposed algorithm is validated through the electromagnetic field calculation in static, diffusion, and wave scenarios.

The interface problem is highly challenging due to its non-smoothness, discontinuity, and interface complexity. In this paper, a new and simple Deep Interface Alternation Method (DIAM) is developed to solve elliptic interface problems to avoid dealing with interfaces. It combines the ideas of domain decomposition methods and deep learning methods. Specifically, we first transform the interface problem with discontinuous derivatives into multiple continuous subproblems based on the Dirichlet–Dirichlet algorithm of domain decomposition. Then, we establish different fully connected neural networks for each subproblem to approximate parallelly the continuous solutions in the subdomain. The interface information is especially exchanged among the different loss functions of each subdomain neural network while minimizing the loss functions of each subdomain separately to obtain solutions to the entire interface problem. Numerical experiments were conducted on two-dimensional and three-dimensional elliptical interface problems with different coefficient contrasts and interface complexity. The results indicate that the Deep Interface Alternation Method has effectiveness and accuracy.

The null-field method (NFM) and the method of auxiliary sources (MAS) have been both used extensively for the numerical solution of boundary-value problems arising in diverse applications involving propagation and scattering of waves. It has been shown that, under certain conditions, the applicability of MAS may be restricted by issues concerning the divergence of the auxiliary currents, manifested by the appearance of exponentially large oscillations. In this work, we combine the NFM with the surface equivalence principle (SEP) and investigate analytically the convergence properties of the combined NFM-SEP with reference to the problem of (internal or external) line-source excitation of a dielectric cylinder. Our main purpose is to prove that (contrary to the MAS) the discrete NFM-SEP currents, when properly normalized, always converge to the corresponding continuous current densities, and thus no divergence and oscillations phenomena appear. The theoretical analysis of the NFM-SEP is accompanied by detailed comparisons with the MAS as well as with representative numerical results illustrating the conclusions.