Engineering Analysis with Boundary Elements最新文献

A singular integral equation method is proposed to analyze the complex plane cracks in one-dimensional (1D) orthorhombic quasicrystals. Using the Somigliana formula, the singular integral equations of the curved crack are derived. Based on the general situation of the curved crack, the singular integral equations of the inclined crack and the arc crack are given. Then the analytical solutions for the singular phonon and phason stresses near the tips of the inclined and the arc crack are obtained. Gauss-Chebyshev quadrature method is introduced to calculate the singular integral equations, and a numerical algorithm for solving the stress intensity factor (SIF) is proposed. Numerical solutions for the phonon and phason SIFs of some examples are solved and discussed.

In this paper, a novel method is developed to solve the free-field motion of the non-horizontally layered half-space subjected to seismic excitation in the time domain. The total wave motions are decomposed into a known and an unknown wave motion. Making use of the fact that the nodal forces at nodes in half-space resulted from the two motions will be zeros, the scattering problem resulted from the seismic excitation is transformed into a radiation problem. The radiation damping of the unbounded layered foundation in the time domain is expressed by the acceleration unit-impulse response matrix obtained using the scaling surface based Scaled Boundary Finite Element Method (SBFEM). In the numerical examples, firstly, the accuracy of the scaling surfaced based SBFEM in simulating the radiation damping is demonstrated by surface excitations in the layered half-space. Then, a time-domain analysis of the free-field motion of a horizontally layered half-space is studied to verify the accuracy and validity of the proposed method. Finally, a study of the free-field motion of non-horizontally layered half-space is investigated, and the results show that increasing the dimensions of the computational domain can significantly improve the accuracy.

Smoothed particle hydrodynamics (SPH) has attracted significant attention in recent decades, and exhibits special advantages in modeling complex flows with multiphysics processes and complex phenomena. Its accuracy depends heavily on the distribution of particles, and will generally be lower if the particles are distributed non-uniformly. A high-order SPH scheme is proposed in the present work for simulating both compressible and incompressible flows. It uses a Gaussian quadrature rule to perform the particle approximation of SPH by introducing Gaussian nodes. Unfortunately, the Gaussian nodes hardly overlap with SPH particles due to the Lagrangian feature, and thus we use a high-order interpolation method to obtain the corresponding physical quantities at the Gaussian nodes. The accuracy and robustness of the proposed Gaussian SPH are demonstrated by several numerical tests, including the Sod problem, Poiseuille flow, Couette flow, cavity flow, Taylor–Green vortex and dam break flow, and a convergence analysis is also conducted to evaluate the effects of particle resolution and distribution for reconstructing a given function. The simulation results for each test case are in good agreements with the available analytical, experimental or numerical results, showing that the proposed Gaussian SPH method is accurate and reliable but expensive for simulating compressible and incompressible flow problems.

Several strategies for solving a nonlinear eigenvalue problem are evaluated. This problem stems from the boundary integral equation solution of propagation in photonic crystal fibers. The origin and specificities of the eigenvalue problem are recalled before considering the solution of this eigenvalue problem. The first strategy, which is the starting point to illustrate the difficulties, is to solve the problem using Muller’s method. We then look at more recent techniques based on contour integrals or a rational interpolant that can be used to compute several eigenmodes simultaneously and considerably reduce the volume of computations.

Deep learning techniques, particularly neural networks, have revolutionized computational physics, offering powerful tools for solving complex partial differential equations (PDEs). However, ensuring stability and efficiency remains a challenge, especially in scenarios involving nonlinear and time-dependent equations. This paper introduces novel residual-based architectures, namely the Simple Highway Network and the Squared Residual Network, designed to enhance stability and accuracy in physics-informed neural networks (PINNs). These architectures augment traditional neural networks by incorporating residual connections, which facilitate smoother weight updates and improve backpropagation efficiency. Through extensive numerical experiments across various examples—including linear and nonlinear, time-dependent and independent PDEs—we demonstrate the efficacy of the proposed architectures. The Squared Residual Network, in particular, exhibits robust performance, achieving enhanced stability and accuracy compared to conventional neural networks. These findings underscore the potential of residual-based architectures in advancing deep learning for PDEs and computational physics applications.

Pump-jet propulsor excitation transfers to submarine hull along rotor-shaft and duct-stator paths simultaneously. The investigations on the effects of excitation transfer paths on structural vibration and acoustic radiation of submarine are limited. The present work aims to investigate vibro-acoustic characteristics of coupled shaft-submarine hull system utilizing a theoretical wavenumber analysis method and conduct acoustic design. The energy functional of the coupled structure-fluid system of the research object is first developed, and the displacement components of the jointed shell and the acoustic pressure are expanded by the Fourier series along circumferential direction. This allows for obtaining vibro-acoustic responses in the circumferential wavenumber-frequency domain, by which the predominant wavenumbers contributing to acoustic radiation are identified. The discussions reveal that the modes n = 0 and n = 1 respectively dominate the acoustic radiation under axial and vertical rotor loads. The acoustic radiations under duct-stator load are mainly contributed by mode n = 0, and the higher order modes n = 1 and n = 2 determine several acoustic peaks. Furthermore, two acoustic design schemes are proposed to suppress the wavenumbers with high radiation efficiency. It is proven that the design of the symmetric inner foundation and the application of new material are two efficient ways to improve acoustic performance of the submarine.

A novel hybrid boundary element is developed for polygonal holes in finite anisotropic elastic plates based on two different special fundamental solutions for holes. Since these special fundamental solutions satisfy traction-free condition along the hole's boundary, there is no mesh required on the boundary of polygonal holes. Various types of polygonal holes with rounded corners, such as triangles, rhombuses, ovals, pentagons, are considered by adding proper perturbation to an elliptical hole. The developed hybrid element is a mixture of two special boundary elements: one is based on the special fundamental solution derived through nonconformal mapping and the other is based on the solution derived through perturbation technique with conformal mapping. The special boundary element methods are combined through submodeling technique. First, the global model is solved using the perturbation solution. Then, using the displacements obtained from global model, an auxiliary submodel is set up and the results are evaluated with the nonconformal solution. The present method is compared and validated with conventional boundary element method and finite element method. The effect of hole curvature, material anisotropy, and loading condition on the stress distribution around the hole is presented.

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.