Engineering Analysis with Boundary Elements最新文献

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.

We propose an overlapping algorithm utilizing the $K$-means clustering technique to group scattered data nodes for discretizing elliptic partial differential equations. Unlike conventional kernel-based approximation methods, which select the closest points from the entire region for each center, our algorithm selects only the nearest points within each overlapping cluster. We present computational results to demonstrate the efficiency of our algorithm for both two-dimensional and three-dimensional problems. For evaluation and validation, these results are compared with results obtained using the RBF-FD+polynomial method with different kernels.

Prediction of sound field generated by an infinitely long periodic structure is often required in engineering. One of the examples is the sound field created by vibration of the rail of a slab railway track, of which the radiating and scattering boundaries are periodic in the track direction due to the rail fasteners. To provide a proper computational tool for such problems, we develop the periodic acoustic boundary element method (PABEM) which only requires a three-dimensional (3D) boundary element mesh for a single cell. The development of the PABEM involves Floquet-transformation of the acoustic boundary integral equation of the infinite periodic structure, exploration of the Floquet-transformed Green's functions, and solution of the boundary integral equation using the boundary element method (BEM). Although the last step is largely the same as the conventional BEM, differences do exist and need to be carefully treated. Special attentions are given to the singularities of the Floquet-transformed Green's functions and to the numerical treatment of such singularities. The PABEM is shown to be directly applicable to sound radiation from a propagating vibration wave in an infinite periodic structure. This makes the PABEM useful for railway noise study since the response of the rail is often expressed as the sum of propagating waves at particular wavenumbers.

An iterative three dimensional Boundary Element Method (BEM) is formulated to investigate partial cavitating flows around cylindrical bodies at various angles of attack and validation is pursued through comparison with other numerical models. Also, in this article the effect of angle of attack on two types of head (conical and blunt-head) is investigated. The results show that the effect of angle of attack on variation of cavity shape at blunt-head cylinder is more considerable. The need for a very short time (less than 10 min) to reach the desirable convergence and also proper accuracy in calculating the properties of cavitating flows are considerable advantages of this method. Also, in this research, the effect of the length of a cylindrical body on the cavity length has been investigated. The results confirm that if the length of the body is greater than 1.7 times the cavity length, the effects of the negative pressure behind the cylindrical body on the cavity length can be neglected.