Engineering Analysis with Boundary Elements最新文献

Plates with rectangular cutouts is widely seen in the field of engineering structures. Therefore, it is crucial to examine analytical solutions for free vibration (FV) of these structures. Despite the existence of approximate/numerical methods, analytical solutions are lacking in the literature. In this study, we employ the symplectic superposition method to effectively analyze the FV problems encountered in plates with rectangular cutouts while integrating the domain decomposition technique. To address the issue of irregular geometry, the rectangular cutout plate is divided into multiple sub-plates. By dividing the problem into multiple sub-problems and solving them separately using variable separation and symplectic eigen expansion, we obtain analytical solutions. Finally, we combine the sub-problem solutions to resolve the initial issue. This solution method can be considered a logical, analytical, and systematic approach as it starts with the fundamental governing equation and is derived without assuming forms of solutions. The study presents a comprehensive set of numerical results that include mode shapes (MSs) and natural frequencies (NFs). The results are rigorously validated using the finite element method (FEM) and relevant literature. The symplectic superposition method demonstrates excellent convergence and precise accuracy, making it suitable for analytically modeling more complex mechanical problems of plates.

In this paper, a linear gradient smoothed meshless Galerkin method (LGSM) is presented to solve the static thermoelastic fracture problems. To accurately represent the discontinuity of temperature and displacement fields across the crack surface as well as the singularity of heat flux and stress fields near the crack tip, the diffraction method is combined with intrinsic enrichment basis to construct meshless approximation. Meanwhile, to effectively save computational cost, the smoothed temperature gradient and the smoothed strain fields are expressed as the linear forms with respect to the center point in each smoothing domain by using the recently proposed linear-gradient smoothed integral (LGSI) scheme, respectively. This leads to substantial reduction of the number of Gaussian integration points without lowing the accuracy of meshless method. The thermal stress intensity factor is evaluated using interaction integrals that considering thermal effects. The novelty of the current work is the extension of LGSI scheme to solve thermoelastic fracture problems, which further verifies that the LGSI scheme is accurate, efficiency, and stable for the integration computation in meshless Galerkin method based on polynomial basis as well as intrinsic enrichment basis. Several numerical examples have been performed to validate the accuracy, efficiency, and robustness of the presented LGSM.

The present paper is devoted for numerical analysis of interface phenomena of magnetic fluids in real space and time, when the Boundary Element Method (BEM) is employed. The BEM obtains not only the magnetic potential and the normal magnetic induction for static magnetic fields but also the fluid velocity potential and the normal fluid velocity for incompressible–irrotational fluids, on arbitrary-shaped interfaces. During the discretizing process, one of the problems is the multiplicity, that is, multi-valued physical quantities at the edges and corners of the domains, or sharp-pointed peaks on the interface. Another problem is the singularity in the diagonal discretization terms, which is inherent to the BEM. Discretization elements at the same position are grouped for the multiplicity. The sum rules for discretization coefficients are used to avoid the singularity, which is derived from the uniform vector field conditions as the extension from the conventional one. Based on the formulated equations, a computational code was produced, and applied for simplified and more general conditions. This code generates magnetic fields on the interface between the fluid and the vacuum as intended with the least numerical effects. It also generates the fluid velocity caused by ununiform distribution of the sum of interface stresses. The applicability for the stability analysis on the Rosensweig instability is also discussed.

In this study, machine learning (ML) methods are integrated with Rayleigh-Ritz method and first-order shear deformation theory (FSDT) to predict the vibration properties of Ti-SiC fiber-reinforced composite airfoil blade. The natural vibration characteristics of airfoil blade are largely determined by various geometric and material parameters, which leads to the high computational cost of numerical methods. Therefore, the low-cost ML models in conjunction with Ti-SiC fiber-reinforced composite material is developed to replace traditional numerical methods in order to predict the vibration characteristics of airfoil blade. Random Forest (RF), Gradient Boosting Decision Tree (GBDT) and Back Propagation (BP) neural network models are utilized to compare the predicted results with existing data. Among these models, the BP neural network demonstrates superior performance. Additionally, the SHapley Additive exPlanation (SHAP) method is utilized to elucidate BP neural network model, facilitating the prioritization of input features. This approach offers a feasible auxiliary solution for investigating the vibration characteristics of airfoil blade.

Due to the dual characteristics of material nonlinearity and geometric nonlinearity exhibited by silicone rubber-like hyperelastic incompressible materials, the dynamic problems involving such materials become complex and challenging. In previous research, the Absolute Nodal Coordinate Formulation (ANCF) has demonstrated its effectiveness in addressing geometric nonlinearities during large deformations. However, ANCF tends to suffer from mesh distortion and configuration distortion issues. On the other hand, the Moving Least Squares Method (MLS) from meshfree methods uses a substantial number of nodes when constructing shape functions, which effectively improves mesh distortion problems in finite element methods when dealing with large deformations. Therefore, this paper employs Hermite-type MLS approximation functions to construct three-dimensional interpolation shape functions that replace the finite element shape function used in the traditional ANCF, thus creating an MLS-ANCF(Absolute node coordinate method based on the moving least square method) approach. Additionally, three nonlinear material models are introduced to tackle the material nonlinearity of hyperelastic beams. Moreover, Lagrange multipliers and Hamilton's principle are used to derive the static and dynamic equations for the hyperelastic beams system. To further validate the correctness of the MLS-ANCF method, this study first compares its results with those obtained from commercial software ABAQUS and static equilibrium experiments, thereby demonstrating the accuracy and effectiveness of MLS-ANCF; Next, dynamic analysis of a cantilevered silicone rubber beam under gravity alone is conducted to show the advantages of MLS-ANCF over other methods and effectively solve the issue of geometric configuration distortion caused by meshing; Furthermore, this paper also investigates the influencing factor of dynamics analysis, such as the incompressibility constant k, weight function, damping coefficient, number of elements, and different nonlinear material models; Ultimately, a comparison with experimental data reveals that MLS-ANCF outperforms conventional ANCF beam elements in terms of agreement with experimental data. This demonstrates the significant role of MLS-ANCF in analyzing the dynamic characteristics of nonlinear hyperelastic beams.

The Burton–Miller method is a widely used approach in acoustics to enhance the stability of the boundary element method for exterior Helmholtz problems at so-called critical frequencies. This method depends on a coupling parameter $\eta$ and it can be shown that as long as $\eta$ has an imaginary part different from 0, the boundary integral formulation for the Helmholtz equation has a unique solution at all frequencies. A popular choice for this parameter is $\eta =\frac{i}{k}$, where $k$ is the wavenumber. It can be shown that this choice is quasi optimal, at least in the high frequency limit. However, especially in the low frequency region, where the critical frequencies are still sparsely distributed, different choices for this factor result in a smaller condition number and a smaller error of the solution. In this work, alternative choices for this factor are compared based on numerical experiments. Additionally, a way to enhance the Burton–Miller solution with $\eta =\frac{i}{k}$ for a sound hard scatterer in the low frequency region by an additional step of a modified Richardson iteration is introduced.

When simulating plate and shell structures characterized by large aspect ratios, reduced-dimensional models are frequently employed due to their notable reduction in computational overhead in contrast to traditional isotropic full-dimensional models. However, in scenarios involving variations in the thickness direction, where adequate resolution in this dimension is required, reduced-dimensional models exhibit limitations. To capture variations in the thickness direction while simultaneously mitigating computational costs, an anisotropic full-dimensional model, integrated with an adaptive smoothed particle hydrodynamics method (ASPH), is developed for simulating behaviors of plate and shell structures in this study. The correction matrix, which is applied to ensure the first-order consistency, is modified accordingly by incorporating the nonisotropic kernel into it within the total Lagrangian framework of ASPH. A series of numerical examples, along with a specific application concerning the deformation of a porous film due to nonuniform internal fluid pressure in the thickness direction, are conducted to assess the computational accuracy and efficiency of the proposed ASPH method. Comparative analyses of our results against reference data and traditional isotropic SPH solutions demonstrate close agreements, affirming the suitability of the present ASPH method across various scenarios.

In this paper, the elastic-like surface Green's functions for an anisotropic viscoelastic half-plane are derived using the time-stepping method. Using the elastic-like surface Green's functions as the core analytical solutions, we develop semi-analytical models (SAMs) and apply them to solve two different contact problems with anisotropic viscoelastic materials. As new modeling approaches, the SAMs developed here can provide fast and efficient approaches to solving contact problems. These methods enable us to consider contact problems with generally anisotropic viscoelastic solids, in which the contact surface is frictional and either smooth or rough, and the applied loads and boundaries can be time-variant. The correctness of the derived surface Green's functions is demonstrated by comparing the numerical results obtained by SAMs and those achieved from the analytical solutions or boundary element methods. Using the obtained numerical results, the impacts of time step size, anisotropy, frictional coefficient, roughness, and applied loads on the contact responses are further analyzed and discussed.

Spring-damper systems have a wide application in engineering, especially playing a key role in vibration suppression and sound modulation. In this paper, a unified method is proposed for investigating the effect of spring-damper systems on the vibro-acoustic characteristics of mass-loaded plates. The system of the vibro-acoustic coupling model is obtained by combining Hamilton's principle and the Rayleigh-Ritz method, and the strong coupling between the structure and the fluid is considered through the work done by the sound pressure. Arbitrary boundary conditions are modeled by adjusting the value of the constraint spring stiffness. The spectral-geometry method (SGM) is used to expand the midplane displacements of the structure and additional functions are added to overcome potential discontinuities. The sound radiation of the plate is calculated by Rayleigh integration. The accuracy of the method is verified by comparing the finite element method (FEM) with the theoretical method. The effects of strong and weak coupling, boundary conditions, parameters of the spring-damper system and plate geometry on the vibro-acoustic characteristics of plate structures are discussed. This paper provides a useful reference for spring-damper systems in vibration control and sound modulation of plate structures.

This article investigates the interaction between oblique waves and rectangular porous structures (bottom standing and surface piercing) in the presence of ocean current. The study employs the Sollit and Cross model to analyze wave behavior past porous structures, utilizing both analytical (eigenfunction expansion method) and numerical (boundary element method) approaches to solve the boundary value problem. In the boundary-element method (BEM), the boundary value problems undergo a transformation into integral equations along the physical boundaries. These boundaries are then subdivided into discrete elements, leading to the formulation of a set of linear algebraic equations. Then, the impact of the geometry of structure and properties of porous material is analyzed. Also, the impact of following and opposing currents is discussed. The research explores wave reflection and wave forces on the porous structure, revealing higher magnitudes in the presence of surface piercing structure compared to bottom standing structures.