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This paper proposes a smooth finite element method (S-FEM) for efficient and accurate analysis of motor magnetic fields. The edge-based smooth finite element (ES-FEM) formulations are derived for two-dimensional triangular element meshes suitable for multi-material motor structures, and then a magnetic flux density calculation method appropriate for S-FEM to calculate nonlinear electromagnetic fields is introduced. In the calculation of motor magnetic field, ES-FEM has a proper softening effect on the stiffness matrix of the finite elements, which makes the calculation more accurate and more efficient than FEM. The magnetic flux intensity calculation method introduced in this paper is not only appropriate for ES-FEM to calculate the nonlinear electromagnetic field of motor, but also can improve the calculation accuracy of magnetic flux density. In the calculation of nonlinear magnetic field of motor, ES-FEM can also improve the calculation accuracy of magnetic field analysis compared with FEM. Several numerical examples demonstrate the improving effect of the ES-FEM discussed above on the motor's magnetic field calculation. [ABSTRACT FROM AUTHOR]

In this paper, an inverse design method for auxetic metamaterials is proposed. The conjugate gradient method is employed to minimize the errors of the required parameters of the designed shape. The interior point penalty method is used to convert constrained inverse problems into unconstrained ones. Using the Taylor expansion, the optimizing step size is derived as well. The boundary element method and the representative volume element are used to compute the effective stiffness matrix. Due to the advantages of the boundary element method, we only need the boundary elements and can easily re-mesh the optimized geometry during the inverse search. The validation test demonstrates that using the computed effective stiffness matrix yields nearly identical results to those obtained from direct finite element analysis. Then, using the proposed method, the authors successfully achieved all three design targets, which proved the effectiveness. Furthermore, the choice of penalty factor has been discussed in this paper as well. [ABSTRACT FROM AUTHOR]

Green's functions of stress and displacement due to wave propagation in a sandwich panel consisting of transversely isotropic face-sheets and aluminum foam core are developed in the present paper. Dynamic partial differential equations of equilibrium for the considered face-sheets and core are expressed in cylindrical coordinates (r, θ, z), and converted into two separate equations using two unknown potential functions. Then, by writing the potential functions as Fourier series in the circumferential direction and using Hankel transform in the radial direction, an analytical solution to the potential functions in Hankel transformed space is developed. Using the boundary conditions and continuity of the problem as well as the place of application of harmonic forces, Green's functions for displacements and stresses in the frequency domain are derived using Hankel's inverse integral transform. These functions are expressed as complex integrals and calculated numerically. To verify the methodology and results, a comparison study is performed for particular cases showing a high level of the accuracy. Green's functions obtained from this paper will give information about the loading models or materials causing the maximum normal stress, shear stress, vertical and radial displacements. In addition, based on the results, with an increase in the core thickness compared to that of face-sheets in a Sandwich panel, an increment in Green's functions of stress and displacement is observed in both real and imaginary parts. [ABSTRACT FROM AUTHOR]

Combining the advantages of the smoothed particle hydrodynamics method (SPH) in interface tracking and the finite volume method (FVM) in computational conservation, the SPH-FVM coupling method for interface flow simulation has been developed in recent years. The existing SPH-FVM coupling methods are based on the structured mesh which are difficult for the simulation of interfacial flows in irregular flow regions. In order to improve the applicability of SPH-FVM coupling method in the simulation of two-phase interfacial flow in irregular flow regions, a SPH-FVM coupling method based on triangular mesh is developed in this paper. The bidirectional transfer of information between the particles and the triangular grids is implemented in this study. A self-programming of SPH-FVM coupling method based on triangular mesh is realized. Some typical two-phase interfacial flows in regular and irregular flow regions are applied to verify the effectiveness and accuracy of the developed SPH-FVM coupling method. Results indicate that the SPH-FVM coupling method based on triangular mesh developed in this paper has good performance for the simulation of two-phase interfacial flow. Therefore, the SPH-FVM coupling method based on triangular mesh can be used as an optional method for the simulation of two-phase interfacial flow in irregular flow regions. [ABSTRACT FROM AUTHOR]

This paper represents Part 2 of the parallel paper Part 1, where the strong form hybrid RBF-FD method was developed for solving thermo-elasto-plastic problems. It addresses the industrial application of this novel meshless method to steel bars cooling on a cooling bed (CB) where the formation of residual stress is of primary interest. The study investigates the impact of the distance between the bars and the distance to the heat shield above the CB on radiative heat fluxes and, consequently, on thermo-mechanical response. The thermal model is solved on bars cross-section with a RBF-FD method where augmented polyharmonic splines are used for the local approximation. View factors, computed with a Monte-Carlo method, are included in radiative heat fluxes. The thermal solution is incrementally applied on a mechanical model that assumes a generalised plane strain state and captures bars bending. The study employs a hybrid RBF-FD method to resolve a nonlinear discontinuous mechanical problem successfully. The simulation of the process shows how different process parameters influence the thermo-mechanical response of the bars. [ABSTRACT FROM AUTHOR]

This study builds on a recent paper by Lai et al. (2018) in which a novel boundary integral formulation is presented for scalar wave scattering analysis in two-dimensional layered and half-spaces. The seminal paper proposes a hybrid integral representation that combines the Sommerfeld integral and layer potential to efficiently deal with the boundaries of infinite length. In this work, we modify the integral formulation to eliminate the fictitious eigenvalues by employing the integral equation of the Burton–Miller type. We also discuss reasonable parameter settings for the hybrid integral equation to ensure efficient and accurate numerical solutions. Furthermore, we extend the modified formulation for the scattering from a cavity in a half-space whose boundary is locally perturbed. To address the cavity scattering, we introduce a virtual boundary enclosing the cavity and couple the integral equation on it with the hybrid equation. The effectiveness of the proposed method is demonstrated through numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents the regularization of the parametric integral equation system (PIES) and the integral identity for 2D problems governed by the Laplace equation in polygonal and smooth domains. Due to the singularity of PIES and the existence of near-singularities in the integral identity, significant errors occur in the results near the boundary, even in the case of smooth boundaries. Additionally, polygonal domains have corner points where the boundary is not smooth, resulting in even greater errors when finding solutions within the domain near these points. These errors increase significantly as the distance to the corner points decreases. The purpose of the presented regularization is to eliminate singularities in PIES and nearly singularities in the integral identity that occur near the boundary, thus improving the accuracy of solutions. The main idea of the regularization is to introduce a regularizing function with two unknown regularization coefficients that need to be determined. As a result, the modified PIES and the integral identity become nonsingular. The paper includes several numerical examples with boundaries described by Bézier and NURBS curves that demonstrate the reliability of the regularization approach and highlight significant improvements in accuracy near the boundary and corner points. [ABSTRACT FROM AUTHOR]

• A mechanical invariance based on the interaction consistency between the FEM and the PD is derived. • An arbitrary switching FEM - PD coupling at the particle level was developed. • The surface effect of PD boundary and FEM - PD coupling interface is eliminated. • The mechanical behavior of the composite materials at the interface can be captured accurately. The issue of coupling the finite element method (FEM) and peridynamics (PD) is a critical concern of widespread attention in PD. In this paper, some essential insights into particle interfaces are presented to address the challenges of coupling PD with FEM and to mitigate surface effects. The interaction consistency between FEM and PD is demonstrated, and then a mechanical invariance of interactions is derived. This mechanical invariance serves as the foundation for an arbitrary switching FEM - PD coupling (ASC), which allows for arbitrary switching between the two methods without introducing artificial deviations. Moreover, a strain - based surface effect correction (SB - SEC) is developed to rectify surface effects by leveraging the symmetry of the strain tensor. This correction allows for the direct application of FEM boundary conditions onto PD boundary, thereby enhancing the precision of simulation results. The reliability of ASC is validated through quantitative deformation and fracture examples, while the excellent mitigation effect of SB - SEC is illustrated. Furthermore, the examples related to composite materials highlight the promising potential of the proposed method for simulating composite materials. [ABSTRACT FROM AUTHOR]

This paper presents the application of the Galerkin Finite Block Method (GFBM) to address cracked solids associated with Functionally Graded Materials (FGMs), leveraging the foundational principles of the Galerkin method. The equilibrium equations pertinent to FGMs are articulated in their weak form. Employing Chebyshev polynomials as shape functions, the GFBM integrates mapping techniques to accommodate irregular finite or semi-infinite physical domains. Boundary and continuity conditions are enforced through the Lagrange Multiplier Method. The domain integrals are calculated through either analytical or numerical integration. The proposed method can easily solve the edge crack or diagonal crack problem by using the crack opening displacement method. The accuracy and convergence of the proposed method are illustrated through a selection of numerical examples. The obtained numerical solutions are verified with analytical solutions and the results from the Finite Element Method. [ABSTRACT FROM AUTHOR]

• The proposed method solves a series of 3D problems with sufficient complex interfaces such as banana-like and multi-interfaces. • The proposed method deals with different interfaces by only changing the level set function of the interface in the process. • An adequate comparison with the classical finite element-finite difference method [6,9] shows our meshless method is more accurate for the given examples in [6,9]. In this paper, a meshless method based on the generalized finite difference method is proposed for the 2D and 3D anisotropic elliptic interface problem. The method is convenient to deal with the mixed derivatives brought by the anisotropy, as well as the 2D and 3D complex geometries of the interfaces. Moreover, the treatment of different interfaces only needs to change their level set functions. Several 2D and 3D numerical experiments are provided and compared with the finite element-finite difference method to illustrate the features of the proposed method. [ABSTRACT FROM AUTHOR]

While topology optimization is promising for additive manufacturing structures, challenges arise in designing multi-material assemblies. The size often surpasses additive manufacturing build volumes, hindering successful manufacturing. Additionally, intricate topology-optimized structures complicate the assembly and decomposition of multiple material components. Addressing the aforementioned issues can be achieved by incorporating dimensional and assembly constraints into the optimization process. So far, these constraints have only been studied and implemented separately, leading to suboptimal solutions. Simply applying these two constraints together can also lead to excessive computational complexity. This paper introduces a multi-material topology optimization framework that considers both dimensional and assembly constraints. We propose an assembly direction-aligned method for dimensional constraints to reduce computational costs and an adaptive weighting factor for assembly constraints to enhance numerical stability. Validation through numerical examples and successful fabrication and assembly of a 3D-printed prototype underscore the framework's efficacy in ensuring the manufacturability and assemblability of structures designed via topology optimization. [ABSTRACT FROM AUTHOR]

Accurately predicting buffet frequency and aerodynamic noise level is crucial in transonic buffet noise reduction studies. In this study, the Random Forest (RF) algorithm is employed to predict the Power Spectral Density (PSD) and Overall Sound Pressure Level (OASPL) distribution over the supercritical airfoil RAE2822. The study indicates that the RF algorithm exhibits greater advantages over the Multi-Layer Perceptron (MLP). This algorithm does not suffer from the problems of high-frequency divergence or inflection distortion, maintaining a reduction in prediction errors for OASPL and PSD by approximately three to four orders of magnitude. Additionally, this paper proposes a priori criterion for evaluating the accuracy of PSD prediction. When there is a strong correlation between PSD at adjacent points, a data-driven modeling approach can achieve higher prediction accuracy. However, when the root mean square error of the cross-correlation functions, auto-correlation functions, and the PSD between adjacent points are both high, the generalization ability of pure data-driven modeling is insufficient, necessitating the additional monitoring points to ensure prediction accuracy. [ABSTRACT FROM AUTHOR]

A boundary-domain integral formulation inevitably arises when the boundary element method (BEM) is applied for solving the differential equation that governs linear elastostatic problems with body forces. Although the domain integrals introduced by the body forces can be evaluated using internal cells this destroys the boundary-only meshing feature of BEM and makes the integration processes inefficient. This paper shows that these problems can be solved more efficiently without using internal cells by the Radial Basis Integration Method (RBIM) which employs a meshless quadrature obtained by performing boundary-only offline computations. Using RBIM, weakly singular domain integrals can be computed via a simple selective quadrature procedure, whereas, strong singular domain integrals may be computed using two schemes: The first, is based on the same selective quadrature procedure, and the second is based on the singularity separation scheme. The present method, unlike classical radial integration method (RIM), does not have problems in calculating integrals in concave or multiple-connected domains. The results obtained in some 2D linear elastostatic problems with arbitrary body forces show that this method can be as accurate as RIM but less time-consuming than the latter. This method could be applied to other engineering problems involving source terms. [ABSTRACT FROM AUTHOR]

• A new framework based on the PINNs is presented for bimaterial interface crack analysis. • An enriched PINNs is proposed to correctly capture the local crack-tip behavior. • The complex SIFs of interfacial cracks can be directly calculated with very high accuracy. This study explores the application of physics-informed neural networks (PINNs) to analyze interface crack problems within the context of elastic bimaterial fracture mechanics. Bimaterial interface cracks exhibit a distinct behavior compared to cracks in homogeneous materials, and this behavior often involves oscillatory phenomena that can pose challenges in numerical modeling. By employing neural networks for solution approximation, PINNs are meshless and are trained using batches of collocation points, which may be randomly or strategically sampled across the computational domain. To effectively capture the oscillatory singular behavior in the crack-tip regions, this paper introduces an enhanced PINNs formulation that enables the modeling of interface cracks without requiring any refinement near the crack-tip. The trainable parameters of the current PINNs are dynamically optimized throughout the training process to fulfill both the underlying differential equations and the associated initial/boundary conditions. One of the significant advantages of the present PINNs is that it uses enrichment functions to capture the behavior around the crack region, allowing for greater flexibility in handling irregular or complex crack paths. The method's accuracy and stability are validated across several benchmark examples. [ABSTRACT FROM AUTHOR]

The Generalized Finite Element Method (GFEM) is developed from the Partition of the Unity Method (PUM), which expands the standard finite element space by using non-polynomial function spaces called the enrichment spaces. GFEM has been successfully applied to various problems, but it still has some drawbacks. It lacks robustness in adjusting meshes when solving interface problems, and the condition number of the stiffness matrix will increase dramatically when the interface is close to the mesh boundary. This phenomenon can lead to ill-conditioned linear equations. A stable GFEM called SGFEM is proposed for the Stokes interface problem in this paper, which modifies the enrichment space. The SGFEM space of the velocity is divided into a basic part S F E M and an enrichment part S E N R ∗. The discretization of space (S F E M × Q h) uses Q 1 − Q 0 element or the Taylor-Hood element for the study. S E N R ∗ uses different interpolation functions. Numerical studies show that SGFEM has the optimal convergence order of the error and robustness. The growth rate of the scaled condition number of the stiffness matrix is the same as that of a standard FEM. • The stable GFEM is proposed for the Stokes interface problems. • Error convergence order same as FEM solving Stokes equation without interface. • Scaled condition number of stiffness matrix is the same growth order as standard FEM. [ABSTRACT FROM AUTHOR]

In the engineering design of modern wing panels and their optimal control system, the first step is to find and predict their dynamic characteristics. These characteristics are dependent on material properties, panel geometry, and boundary conditions. In addition, possible fracture existence, imperfections and environmental conditions may unpredictably change the frequency and modes shape of the panel and then the parameters of a control system. In the present paper, the effect of surface fracture depth and orientation on frequency and vibration mode switching of perovskite solar cells-based aircraft wing panels is investigated for the first time. The PSC (perovskite solar cell) panel is made of a polymer substrate reinforced with even-distributed graphene platelets (GPLs) and thin solar layers to enhance the overall electromechanical performance of the whole structure. Equations of motion of the panel are obtained by the Hamilton approach based on the properties of Reddy's third-order shear deformation theory and linear components of the Green-Lagrange strain tensor. The novel aspect is a line-spring model of surface crack by Cartmell et al. adapted to the model of the PSC panel under consideration. The discretization of the established equations of motion for the cracked panel is carried out by the element-free IMLS-Ritz method with mesh-free features. Validation of the obtained solutions is carried out by comparisons with results from previous studies for cracked laminated plates. First, material and geometric properties effect on vibration characteristics of the PSC structure was investigated. Next, partial surface crack depth and orientation angle are examined to show changes in frequency and vibration modes shape of the panel. It is shown, that there is a mode swapping between the second and third modes when transitioning from an intact panel to a cracked one. As the crack length increases, higher-order mode variations become more noticeable, potentially leading to their swapping or the excitation of new ones. Additionally, the findings demonstrate that the surface crack orientation angle significantly impacts the higher-order modes of the panel. When the orientation angle is 90°, the first six modes align with those of the intact plate. Mode shapes and frequency shifts are significant for crack orientation angles between 0° and 90°. [ABSTRACT FROM AUTHOR]

This paper presents the study of the plane strain problem of an infinite isotropic elastic medium subjected to far-field load and containing multiple Gurtin–Murdoch material surfaces located along straight segments. Each material segment represents a membrane of vanishing thickness characterized by its own elastic stiffness and residual surface tension. The governing equations, the jump conditions, and the surface tip conditions are reviewed. The displacements in the matrix are sought as the sum of complex variable single-layer elastic potentials whose densities are equal to the jumps in complex tractions across the segments. The densities are found by solving the system of coupled hypersingular boundary integral equations. The approximations by a series of Chebyshev's polynomials of the second kind are used with the square root weight functions chosen to satisfy the tip conditions automatically. Numerical examples are presented to illustrate the influence of dimensionless parameters and to study the effects of interactions. [ABSTRACT FROM AUTHOR]

This paper extends the recently proposed variant of meshless local Petrov Galerkin (MLPG) method, i.e., MLPG7, for solving time dependent PDEs. As test function, the method uses a novel modification of fundamental solution of Laplace operator that not only the test function itself but also its derivative vanish on boundary of local subdomains. Therefore, more stable local integral equations are obtained by replacing a boundary integral of derivatives of field variables with a domain integral of field variables itself. MLPG7 formulation converts the nonlinear governing equation into a system of first order ordinary differential equations (ODEs). For this system of ODEs, a theoretical stability analysis is carried out for the case of regularly spaced nodal points. Stability and convergence conditions for fully discretized equations by Euler (forward and backward) and Crank–Nicolson methods are investigated. The nonlinear term is treated iteratively. A numerical study investigates the convergence and stability of the method. A comparison is also done with some well-known methods and the results reveal the excellence of MLPG7. The convergence of the iterative approach is numerically verified by another illustrative test example. As nonlinear test problems, Allen–Cahn equations are studied. [ABSTRACT FROM AUTHOR]

In this paper, a linear smoothing scheme over eight-node Reissner-Mindlin plate element under the framework of the CS-FEM is employed to buckling analysis of laminated composite plates based on the first-order shear deformation theory. The modified stain matrix is computed by the divergence theorem between the nodal shape functions and their derivatives using Taylor's expansion. Isoparametric mapping and the computation of interior derivatives of shape function is not required in the proposed method, furthermore, all the computation are based on the global Cartesian coordinates. Some numerical examples are given at the end to demonstrate that the present method has good performance to alleviate the shear-locking phenomenon and improve the quality of the solutions with distorted meshes. [ABSTRACT FROM AUTHOR]

This paper aims to analyze a novel localized radial basis function method known as the 'direct RBF-based partition of unity method' for solving nonlinear fractional parabolic equations. In the proposed method, the weight functions are not operated on by the differential operators, resulting in a decrease in computational cost and algorithmic complexity. Another advantage of the direct RBF-based partition of unity method compared to the standard RBF-based partition of unity method is that in the direct method, it is possible to use discontinuous weights, which is not applicable in the standard method. Furthermore, we conduct a convergence analysis of the method and derive an error bound for the local approximation. This error bound is determined by considering conditions on the eigenvalues of the Laplacian operator matrix. To ensure the accuracy and reliability of our proposed approach, we conducted a numerical simulation and provided two numerical examples for comparison. We evaluated the consistency between the theoretical and numerical results. Our comparison between the standard RBF-based partition of unity and our proposed framework shows that the direct method is more efficient computationally, but both versions have relatively the same accuracy. [ABSTRACT FROM AUTHOR]

Simulating groundwater flows in heterogeneous aquifers is one of the most widely studied problems. The heterogeneity is modeled through random hydraulic conductivity fields log-normally distributed. In this paper, we aim to generate the realization of the log-normal hydraulic conductivity by summing up a finite number of random periodic modes with the Kraichnan algorithm. To address Neumann conditions, we propose a change of variables that results in Dirichlet boundary conditions along all boundaries of the computational domain. Then, we suggest using the radial basis function partition of unity method (RBFPUM) and RBFPUM with QR factorization (RBFPUM-QR) to analyze groundwater flow in the heterogeneous porous medium. We evaluate the performance of the proposed methods by increasing the number of random modes and the variance of the log-hydraulic conductivity fields using Gaussian and exponential correlation. In addition, we verify the effectiveness of the presented approaches in one and two dimensions using the method of manufactured solutions. Furthermore, we provide statistical inferences through Monte Carlo simulations. Numerical results demonstrate that RBFPUM-QR performs well in handling higher heterogeneity in both single realizations and Monte Carlo simulations. • A meshless numerical approach based on RBFs is proposed to solve Darcy's equation with a random hydraulic conductivity. • We use the Kraichnan algorithm to generate the log-normal hydraulic conductivity which is used to describe the heterogeneity. • The proposed approach avoids technical issues encountered in the case of an exponential correlation of the hydraulic conductivity. • The proposed numerical approach performs well to cope with higher heterogeneity. [ABSTRACT FROM AUTHOR]

• Two-phase flow regime identification using ML with enhanced interpretability. • Evaluation of various dimensionality reduction techniques to optimize feature representation. • Kernel Fisher discriminant analysis is the best performing dimensionality reduction technique. • AutoML can impartially select the most effective ML classifier. • Our workflow can develop a virtual flow regime map to automate flow regime recognition. Accurate identification of flow regimes is paramount in several industries, especially in chemical and hydrocarbon sectors. This paper describes a comprehensive data-driven workflow for flow regime identification. The workflow encompasses: i) the collection of dynamic pressure signals using an experimentally verified numerical two-phase flow model for three different flow regimes: stratified, slug and annular flow, ii) feature extraction from pressure signals using Discrete Wavelet Transformation (DWT), iii) Evaluation and testing of 12 different Dimensionality Reduction (DR) techniques, iv) the application of an AutoML framework for automated Machine Learning classifier selection among K-Nearest Neighbors, Artificial Neural Networks, Support Vector Machines, Gradient Boosting, Random Forest, and Logistic Regression, with hyper-parameter tuning. Kernel Fisher Discriminant Analysis (KFDA) is the best DR technique, exhibiting superior goodness of clustering, while KNN proved to be the top classifier with an accuracy of 92.5 % and excellent repeatability. The combination of DWT, KFDA and KNN was used to produce a virtual flow regime map. The proposed workflow represents a significant step forward in automating flow regime identification and enhancing the interpretability of ML classifiers, allowing its application to opaque pipes fitted with pressure sensors for achieving flow assurance and automatic monitoring of two-phase flow in various process industries. [ABSTRACT FROM AUTHOR]

Acoustic simulation in frequency-domain is related to solving Helmholtz equations, which is still highly challenging at high frequency with complex geometries. In this paper, a learning based numerical method (LbNM) is proposed for general boundary value problems of Helmholtz equation. By using Tikhonov regularization, the solution operator is stably learned from various data solutions especially fundamental solutions. The reconstructed solution operator is reusable and enables fast solution updating with new boundary inputs. The present method is featured by strong interpretability and generalizability. Numerical results demonstrate advantages in precision and efficiency. It can be applied to various engineering problems such as cabin acoustic simulations flexibly. [ABSTRACT FROM AUTHOR]

Recently, several numerical methods based on the radial basis functions have been applied to solving differential equations. Many researchers have employed the radial basis functions collocation technique and its improvements to get more accurate and efficient numerical solutions. The Schrödinger equations have several applications in the optic and laser. Accordingly, several numerical procedures have been proposed. In this paper, we present a new numerical algorithm based on the time-split approach, and rational radial basis functions collocation method. First, a second-order time-split approach is used to discretize the time variable. In this stage, the linear and nonlinear terms are separated. The linear term is solved by using a collocation technique based on the rational approach, the radial basis functions, and the partition of unity. The nonlinear term is does not have a differential operator thus we will only insert approximate solutions into it. Finally, several numerical examples have been reported to show the stability, convergence, and accuracy of the proposed numerical algorithm. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive coupling approach between meshless Smoothed Point Interpolation Methods (SPIMs) and the Finite Element Method (FEM) for the physically nonlinear analysis of quasi-brittle media. The nonlinear behaviour is represented by scalar damage and smeared-crack models. In the proposed adaptive coupling approach, the domain is initially discretised with a relatively coarse FEM mesh. During the solution process, FEM patches are replaced by meshless discretisations according to certain selection criteria. Refinement is also considered. • A new meshless-FEM adapting coupling is proposed. • The Kronecker delta property of smoothed point interpolation methods allows a straightforward coupling. • After each mesh modification the iterative process is repeated to guarantee the equilibrium of the model. • The irreversibility of damage is guaranteed throughout the adaptive process. [ABSTRACT FROM AUTHOR]

In this paper, a novel nodal integration technique for meshfree methods is introduced. This technique is based on the idea of the Cartesian transformation method, which prevents the presence of background cells during the numerical integration process. The Gauss–Lobatto quadrature is used instead of the conventional Gaussian quadrature to create the integration points so that the integration points coincide with the field nodes. This development gave rise to an innovative nodal integration method that eliminates the necessity for generating integration cells, thus advancing further toward a genuinely meshfree approach. The meshfree method chosen in this study is the radial point interpolation method due to the satisfaction of the Kronecker delta property. The curved shell is formulated by the first-order shear deformation theory (FSDT). The static and free vibration analyses of different geometry curved shells are conducted. Through several numerical examples, the accuracy and efficiency of the proposed technique are demonstrated and discussed. It is found that the current technique has better performance than the existing numerical integration techniques used in meshfree method. Furthermore, this new nodal integration technique also shows the ability to mitigate the shear-locking phenomenon when analyzing the problem of thin shells using the FSDT formulation. • A novel nodal integration based on the Cartesian transformation method is introduced. • The proposed nodal integration can mitigate the shear-locking phenomenon in thin shells. • A new discretization process is introduced. • High accuracy and computational efficiency are observed. [ABSTRACT FROM AUTHOR]

Piezoelectric materials find widespread applications in high-precision actuators and sensors. However, the traditional finite element method falls short in meeting the simulation needs of piezoelectric structures due to complexities in mesh generation and precision requirements for accurate simulations. This paper focuses on adapting and generalizing the meshless modeling technique based on the radial point interpolation method to address three-dimensional simulations of piezoelectric structures and accurately model positive and inverse piezoelectric behaviors. The piezoelectric body is discretized into point cloud data, and displacement and potential are approximated by interpolating values through the radial point interpolation method. Subsequently, a 3D meshless model for general piezoelectric structures is formulated based on the principle of minimum potential energy. The influences of key factors on interpolation accuracy and computational cost were discussed. Numerical examples, featuring a 3D piezoelectric bimorph beam as actuators and sensors, validate the efficacy of this extended approach. Results affirm that the three-dimensional meshless method, rooted in the radial point interpolation technique, achieves superior accuracy in predicting piezoelectric behavior compared to the traditional finite element method. This adaptation not only enhances the applicability of meshless modeling but also represents a significant advancement in accurately simulating complex three-dimensional piezoelectric structures. • Multi-field coupling meshless modeling for 3D piezoelectric structures based on RPIM. • Valuable insights are provided for selecting meshless model parameters. • Uniformly distributed nodes helps improve the numerical calculation accuracy. [ABSTRACT FROM AUTHOR]

• A new singular boundary element is constructed to model the singular stress fields. • The proposed method can obtain good results without much computational cost. • The first four amplitude coefficients can be determined without post processing. The stress singularity occurs near a V-notch. The conventional boundary element method can only approach to the exact results with gradually refined mesh. In this paper, by introducing the Williams asymptotic expansion, a novel semi-analytical element is proposed. The new element models the geometry and the known physical fields with linear interpolation, while the unknown physical fields will be simulated by the asymptotic expansion. The new element introduces six unknowns: two displacement components at the notch tip and four amplitude coefficients in the asymptotic expansion. By collocating two semi-analytical elements on both sides of the notch, the unknown displacement fields can be depicted with the asymptotic expansion, while the remaining part can be modeled by means of the conventional boundary element. The direct integral method and singular integral separation technique are adopted for the different kinds of singular integrals in the boundary integral equations. After the system of equations are solved, not only the unknown boundary physical quantities, but also the first four amplitude coefficients in the asymptotic expansion can be determined at the same time. The stress intensity factors can be determined from the amplitude coefficients in the asymptotic expansions without any post processing. [ABSTRACT FROM AUTHOR]

In this paper, an updated Lagrangian method based on peridynamic differential operator (PDDO) is proposed to study the natural convection and heat transfer of magnetic nanofluids under the fluid and magnetic coupled filed. The governing Navier-Stokes equations considering the effects of Lorentz force in Magnetohydrodynamics (MHD) and the magnetization intensity in Ferrohydrodynamics (FHD) are reformulated in their integral form using a second-order PDDO. Non-local integration of the discretized material points avoids the discontinuous of the field variables, thus, lead to a more flexible way to simulate natural convection of pure fluid and nanofluid under multi-physical fields for stable and convergent solutions. The efficiency, accuracy and capability of the present method has been demonstrated by several numerical examples. Subsequently, the effects of the Rayleigh number, Hartmann number, and Magnetic number on the convective behavior of magnetic nanofluids are investigated and discussed. [ABSTRACT FROM AUTHOR]

Fractional differential equations (FDEs) offer numerous capabilities for modeling unusual phenomena. So, the study of these models is essential. This paper proposes an efficient meshless technique for obtaining the numerical solution of a space fractional diffusion model with Caputo derivative type. Typically, in a meshless processes based on moving Kriging (MK) interpolation, the MK technique is used to calculate the shape functions and their derivatives with positive integer order against space variables to discretize the governing equation in space variables. However, in this study, we employ the Taylor series of MK interpolation's correlation function to enhance the shape function derivatives for arbitrary order 0. 5 < α < 2. Moreover, the finite difference technique is employed to discretize the model in the time dimension and its characterized by unconditional stability and a rate of convergence of O (τ). This approach converts the primary problem into a system of linear algebraic equations. Finally, we present several examples in one and two dimensions and compare the results with other well-known schemes to show the capability and accuracy of this approach. [ABSTRACT FROM AUTHOR]

This paper presents a polynomial layer-wise model in the framework of Carrera's Unified Formulation for the bending analysis of a magneto-electric shells with variable radii of curvature. A parametric surface is used to model the middle surface of the shell. Lame Parameters and Radius of Curvature are calculated by using Differential Geometry. The mechanical displacement, along with the electric and magnetic scalar potential functions, are expressed and modeled using Chebyshev polynomials of the Second Kind. The shells are exposed to different mechanical, electrical and magnetic loads. The Principle of Virtual Displacement is employed for obtaining the governing equations which are discretized by Chebyshev-Gauss-Lobatto grid distribution and solved in semi-analytical manner by the so-called Differential Quadrature Method (DQM). The basis function selected is the Lagrange polynomial. The DQM is employed for its straightforwardness in tackling complex yet regular shell structures under various multiphysical loads. A simple stress recovery technique based on 3D equilibrium equations is introduced to obtain the out-of-plane shear and normal stresses, transverse electric, and magnetic induction. Close-to-3D solutions have been achieved for classical shell structures. Furthermore, benchmark solutions for complex smart shells featuring variable radii of curvature, such as parabolic and cycloidal shells, are introduced. [ABSTRACT FROM AUTHOR]

In the present paper, a previously introduced numerical method, GDDR (Generalized Differential Dynamic Relaxation), is developed to analyze ratcheting behavior of moderately thick rectangular plates. The validity of the method is verified by comparison with literature data and finite element method results. Classical Plate Theory (CPT) and First-order Shear Deformation Theory (FSDT) are utilized to define the displacement field of plates. Incremental strain equations are derived according to von Karman relations. Prandtl-Reuss flow rule and von Mises yield criterion and are used to express the behavior of the plates in the plastic region. The Armstrong-Frederick nonlinear kinematic hardening model is incorporated for elastic-plastic analyses. Finally the results of ratcheting analysis obtained by GDDR method based on two mentioned theories are compared. Results showed that higher amounts of strains are predicted when FSDT theory is employed. Moreover, the area of hysteresis loops obtained by FSDT analysis are larger than those of CPT analysis, meaning that FSDT approach predicts more energy dissipation during each cycle of loading compared with CPT approach. Finally, comparing the results for different ratios of thickness to width shows that GDDR method can predict more accurate results, especially for higher ratios, when it utilizes FSDT theory. [ABSTRACT FROM AUTHOR]

• The polyhedral formula of the Cosserat theory has been derived. • The precision of the proposed method can approach that of quadratic elements. • The meshing performance is enhanced benefiting efficient octree techniques. The Cosserat continuum offers high accuracy in micro-structure analysis and stress concentration simulation due to its consideration of mechanical factors such as coupled stress and internal length scale. However, existing methods are mainly developed based on the isoparametric conventional continuum framework, with relatively simple element shapes and weak adaptability to complex geometries. Therefore, this paper proposes an improved Cosserat continuum theory based on the three-dimensional (3D) polyhedral scale boundary finite element method (PSBFEM). The main work is as follows: (1) The Cosserat continuum theory formula is deduced within the SBFEM framework by integrating a polygon mean-value shape function; (2) The analytical accuracy of the proposed method is examined through classical micro-structure test examples; (3) An efficient octree algorithm is introduced to evaluate the comprehensive performance of the proposed method for the analysis of complex structures, and the selection and impact of the internal length scale are discussed. The results indicate that the proposed method incorporates the good performance of SBFEM and the Cosserat continuum, and its accuracy can approach the traditional quadratic Cosserat continuum elements; The stress concentration problem can be effectively addressed, leading to a more accurate representation of structural stress characteristics. Additionally, complex polyhedral elements can be directly calculated, and the element library of traditional Cosserat theory has been greatly expanded. [ABSTRACT FROM AUTHOR]

In the present work, analytical numerical solutions of the static behavior of fully clamped functionally graded (FG) doubly-curved panels are presented. The mechanical model is based on the Carrera Unified Formulation (CUF) under the Equivalent-Single-Layer (ESL) approach. The governing equations, in their strong form, are derived from the Principle of Virtual Displacements (PVD). The main novelty of this work is the integration of CUF and the Boundary-Discontinuous solution methodology. This merging yields a remarkably accurate and robust procedure that can handle different shell theories with arbitrary order of expansion. Besides, a new branch of future interesting applications of this purely analytical procedure is discussed. Several ceramic-metal graded shells with two different distribution-law variations subjected to uniform distributed load (UDL) are studied. Various thickness ratios, radius-to-thickness ratios, and order of expansion of the displacement field are considered. The accuracy of the proposed solution in predicting static displacements and stresses of thick and thin FG panels is evaluated and discussed by comparing it with those of the literature for various case problems. As the proposed approach solution presented in this paper is unique, the numerical results might be useful as benchmarks for validating new FG shell theories. [ABSTRACT FROM AUTHOR]

This paper analyzes nonlinear free vibration of plates that move axially and in partial contact with liquid. The von Kármán nonlinear plate theory is employed in the theoretical model. The fluid is characterized as an ideal fluid and represented using the velocity potential and Bernoulli's equation. The fluid pressure exerted on the plate is equivalent to a virtual additional mass, which is considered as part of the total mass of the structure. Employing the Hamilton's principle to derive the immersed moving plates' governing equations. Afterward, the nonlinear frequencies of plates moving axially and contacting with liquid are evaluated by the Chebyshev collocation method combined with the direct iterative technique. The results indicate that the Chebyshev collocation method exhibits excellent convergence and exceptional accuracy. It has been observed that the immersed moving plates' nonlinear frequencies gradually increase with the decrease of the axial velocity. The increase of immersion level or fluid density reduces nonlinear frequencies, but has little influence on nonlinear to linear frequency ratios. [ABSTRACT FROM AUTHOR]

This paper extends the meshless local exponential basis functions to the analysis of doubly curved laminated and sandwich shallow shells. The method discretizes the shell domain by some nodes at which the degrees of freedom are defined. A specific number of nearby nodes, only based on their distance, are selected as a cloud. Within every cloud, the total solution is set in homogeneous and particular parts. The former is adjusted by exponential basis functions to exactly satisfy the homogeneous governing equation, as in Trefftz approaches. Overlapping of adjacent clouds integrates the solution function over the entire domain. While Trefftz methods usually implement trial and error approaches for eigenvalue problems, we introduce a novel technique for the free vibration solution in one step by treating the frequency including part as a loading term. Three deformation theories, namely CST, FSDT and TSDT will be adopted for the formulation. Various boundary conditions such as simple, clamped and free are applied to the edges. It will be shown that the method benefits from high accuracy and fast convergence rate, not adversely affected by irregularity of the nodal grid. Additional results are also provided for interested researchers. [ABSTRACT FROM AUTHOR]

In this paper, a time-domain local radial basis function collocation method (LRBFCM) combined with the Houbolt method is developed for the anti-plane elastic wave propagation analysis in 2D phononic crystals. The periodic boundary conditions are applied to a unit-cell to simplify the analysis. In the first step, the time-dependent displacement field is computed by using the proposed time-domain LRBFCM. Then, the Fast Fourier Transform (FFT) is applied to transform the displacement field from the time-domain to the frequency-domain, from which the frequency band structures can be further obtained. To enhance the stability of the proposed LRBFCM, the direct method is used to calculate the spatial derivatives arising in both periodicity and interface continuity conditions. The proposed time-domain LRBFCM provides an alternative numerical tool to many frequency-domain methods for the band structure analysis of phononic crystals. [ABSTRACT FROM AUTHOR]

Domain decomposition method (DDM) is an efficient tool for solving multi-domain problems. Many kinds of DDM have been proposed in literature, such as the d -N alternating method and optimized Schwarz method, etc. The main difference between these methods lies in the transmission conditions on the interfaces between subdomains. Most DDMs have at least one relaxation parameter which must be properly chosen to ensure convergence. To avoid prior determination of a constant relaxation parameter, dynamic relaxation parameters are devised based on error analysis. Another, difficulty of DDM is that special preprocessor has to be used to handle cases where interior cross-points exist among the domains. In dual interpolation boundary face method (DiBFM), boundary integral equation (BIE) is collocated on nodes inside elements, therefore naturally avoids the interior cross-points problem. In this paper, we have implemented some main kinds of DDM in the frame of DiBFM and conducted comparative studies accounting for different interface conditions and relaxation parameters, using examples that involve different topological connections between subdomains. [ABSTRACT FROM AUTHOR]

Computation of piled-raft interaction effects based on boundary element method (BEM) achieves high accuracy. However, it's not preferred, due to the impractical requirement for huge computational time. In this paper, a simplified coding technique which is generally applicable to any BEM application is demonstrated for pile-soil-pile interaction problems. The proposed simplified technique is based on parallel computing to optimize computational performance. Three parallel computing approaches have been developed in order to take full advantage of the computer's power. The approaches are based on CPU Multithreading, GPU Multithreading, and a hybrid system that combines both. The approaches have been tested on five machines with different hardware (CPU, GPU, and Memory) configurations to analyze four practical examples with different load cases, geometric details, interaction methods, and cases of interactions. The parallelization approaches performance illustrated high efficiency with large-scale computations and the consumed time has been reduced by 95 % for both the GPU and hybrid system approaches and 90 % reduction for the multithreading on the CPU. The analysis results confirmed the validity of the proposed methods without affecting the accuracy of the numerical results. The strength of the proposed technique is in its simplicity and scalability to be used for any BEM code. [ABSTRACT FROM AUTHOR]

This paper presents a two-dimensional fast multipole boundary element method designed for the efficient analysis of large-scale anisotropic elastic problems subjected to centrifugal loads. The expansions and fast multipole operations employed in this study bear resemblances to those utilized in existing formulations of the fast multipole boundary element method, previously proposed for addressing potential and isotropic elastostatic problems. The anisotropic fundamental solutions adopted here are rooted in the Leknitskii formalism and have been suitably expanded to facilitate the implementation of fast multipole operations. The treatment of problems involving centrifugal loads are taken into account by the utilization of the modified boundary condition method. This approach entails augmenting the boundary condition with a specific solution tailored to the problem. Following the solution of the linear system, the particular solution is subsequently subtracted from both displacements and tractions. Importantly, this procedural step obviates the need for generating additional vectors or matrices within the integral equation. To evaluate the accuracy and efficiency of the proposed method, numerical solutions are juxtaposed against analytical solutions and benchmarked against the conventional boundary element method. The formulated approach exhibits quasi-linear computational complexity, rendering it particularly well-suited for tackling large-scale problems. The key inference drawn from this work is that the proposed formulation outperforms the conventional BEM in terms of effectiveness. It offers reduced computational time and memory utilization, thereby enabling the analysis of larger problems within shorter time. • The fast multipole boundary element method is presented for anisotropic elastic plane problems. • The code and the expansions were obtained based on the FMBEM for potential problems. • The formulation has a quasi-linear complexity, ideal for large scale problems. [ABSTRACT FROM AUTHOR]

The fast multipole method (FMM) based on the plane wave expansion is known to suffer from numerical instability in the low-frequency regime. This paper presents a low-frequency fast multipole boundary element method (LF-FMBEM) for acoustic problems in a subsonic uniform flow. First, a hybrid convected boundary integral formula based on the Burton-Miller method is derived to overcome the non-uniqueness difficulty at fictitious eigenfrequencies. The explicit evaluation of hypersingular integrals in the convected boundary integral formulae is also introduced. Then, the formulae of FMM based on the series expansion for convected BEM are derived to improve the calculation efficiency. The recursive calculation method is derived in the expansion of the derivative of the integrands. Besides, the rotation-coaxial translation-rotation back (RCR) technique is employed to accelerate the multipole translation. The numerical implementation process of the developed algorithm is presented in detail. Several numerical experiments are performed to validate the computational efficiency and accuracy of the developed LF-FMBEM. Results show that the proposed algorithm can achieve large-scale computation of one million degrees of freedom (DOF) on a personal computer, and the computational accuracy is still high when the Mach number reaches 0.95. The non-uniqueness problem for convected acoustics problems is also effectively overcome. [ABSTRACT FROM AUTHOR]

To investigate accurately unique and advanced wave properties in elastic metamaterials advanced and efficient numerical methods are needed. The paper presents an extended boundary integral equation method for simulating elastic wave scattering by doubly periodic arrays of rectangular crack-like voids. The convergence of the arising double series is proved and the convergence rate is carefully analyzed. Employing the results of the investigation of the convergence rate, an algorithm for fast numerical calculation of double series is proposed to reduce computational costs through preliminary analytical evaluation and the proposed summation strategy. The efficiency of the extended boundary integral equation method is demonstrated and examples of the calculated transmission coefficients exhibiting the influence of the introduction of the doubly periodic array are given. [ABSTRACT FROM AUTHOR]

• The stratification and anisotropy of the soil are taken into consideration. • The impact of the bedrock underlying the soil is taken into account. • The stiffness of the footing is considered. • Explicit expressions for stress and displacement are provided. This paper presents explicit expressions of stress and displacement in the physical domain of layered transversely isotropic soil under strip footing for the first time. The method proposed in this study is not only applicable to analysing problems related to flexible footings, but can also be utilized for analysing problems related to rigid footings. The stress function of each layer can be represented by two single-valued analytic functions. Each layer of soil is mapped to a unit circle using affine and conformal transformations. Within the unit circle, the single-valued analytic function can be expanded into a Taylor series with unknown coefficients. By establishing equations based on the boundary conditions and stress-displacement continuity conditions, the unknown coefficients can be determined. To validate the proposed method, the calculation results were compared with ANSYS finite element results. [ABSTRACT FROM AUTHOR]

Time-domain boundary element method (TDBEM) can be applied in studying transient acoustic wave problems, especially in solving exterior problems. However, in order to avoid calculations of coefficients at different time steps, TDBEM usually requires storing or recomputing the coefficients at each time step. This can lead to significant amount of memory usage or long computing time. In this paper, an acoustic TDBEM based on a kernel-function library (KFL-BEM) is proposed, in order to reduce the memory consumption of the time-domain conventional BEM (CBEM) and speedup the computation. In this approach, the storage requirement is reduced from O (N 2 N t min) to O (N 2), where N represents the number of degrees of freedom of the model, and N t min is the minimum number of time steps for which coefficients need to be computed and stored. To demonstrate the effectiveness of the KFL-BEM, two verification examples are presented using the problems of a pulsating sphere and sound propagating in a channel. Compared with the CBEM, the KFL-BEM can save significantly the memory storage as it does not require storing coefficients for any previous time steps. This method can also be applied to solve vibro-acoustic problems in the time domain. As an example, the acoustic radiation responses of a tuning fork under different striking loads are studied using the finite element method and the proposed KFL-BEM, which clearly shows the potentials of the KFL-BEM in solving time-domain acoustic problems. [ABSTRACT FROM AUTHOR]

• A modified RI-IGABEM for viscoelastic problems is proposed. • The method eliminates the need for recalculating strain and stress at each time step. • The error accumulation typically associated with the TRM is avoided. • No strongly singular integrals appear in the BIE. • An analytical solution for calculating the radial integral in the RIM is provided. In this paper, an improved isogeometric boundary element method based on radial integration method (RI-IGABEM) is proposed to solve the viscoelastic problems. Prony series are utilized to discretize the stress with the two most recent time-step strains. The boundary integral equation (BIE) for the viscoelastic problems is derived. The domain integral related to stress is decomposed into the linear combination of two sub-integrals by volumetric–deviatoric split. The radial integration method (RIM) is applied to transform all the domain integrals into equivalent boundary integrals. The present method has several advantages. Firstly, the present method eliminates the need for stress calculation at each time step, thus avoiding the error accumulation associated with the traction recovery method (TRM). Secondly, the BIE for the viscoelastic problems contains only weakly singular integrals. In addition, we provide an analytical solution for the radial component of the equivalent boundary integrals, which is transformed using RIM. To sum up, the present method improves the accuracy and efficiency of RI-IGABEM by reducing the required computational steps, eliminating error accumulation, and providing analytical solutions for certain integrals. Numerical examples demonstrate that the proposed RI-IGABEM is an efficient and accurate method suitable for viscoelastic problems. [ABSTRACT FROM AUTHOR]

This paper presents a nonlocal energy-informed neural network to address the inherent zero-energy mode instability in peridynamic correspondence material models. Starting from the principle of virtual work, the task of solving peridynamic equilibrium equation is reformulated as a variational minimum problem of total potential energy, serving as the natural loss function for neural network. By minimizing the potential energy of the peridynamic body, the proposed neural network effectively eliminates the zero-energy modes. Importantly, this approach preserves the original peridynamic formulation without introducing a supplementary force vector state or modifying the nonlocal deformation gradient tensor. Additionally, there is no need for an artificial damping coefficient in adaptive dynamic relaxation, and the high memory consumption in implicit schemes is avoided. To improve the prediction accuracy near boundaries and to impose boundary conditions consistently with the local continuum theory, variable horizon method is introduced. Comparative studies of the proposed neural network with analytical solutions, finite element analyses or other control methods are conducted to verify the feasibility and accuracy of the proposed neural network in suppressing zero-energy mode oscillations. Furthermore, the convergence of the proposed approach and the influence of different activation functions on the prediction accuracy and convergence rate are investigated. [ABSTRACT FROM AUTHOR]

The computational accuracy of near singular integrals is the key to determine the overall accuracy and stability of BEM in solving elastic variables, and even the success or failure of BEM analysis. In this paper, an alterative sinh transformation method is developed for solving the near singular boundary integrals in the structural analysis of thin structure. Firstly, the original sinh method is modified into the form include minimum distance and approximate expansion of local coordinates, and Newton-Raphson and cubic equation solving methods are used to obtain the position of the near singular projection point. To facilitate the implementation of the near singular integral, the integral element in the local coordinate space is mapped to the integral parameter space, and then the element integration is performed directly by sinh transformation in this space. The results of several numerical examples show that the proposed method can be used to regularize the nearly singular boundary integral effectively, and to accurately solve the elastic physical variables in the analysis of thin structures. [ABSTRACT FROM AUTHOR]

In response to nonrenewable energy consumption and environmental pollution, the development of electric vehicles has accelerated. The safety of electric vehicles has garnered considerable attention. There are numerous incalculable foreign objects on the road that may collide with or scratch the battery-pack's frontal, resulting in battery-pack system damage or even explosion. This poses a significant risk to the safety of passengers and drivers. In this paper, a diversity of mechanical safety prediction models for battery-pack systems are proposed. These models support data-driven structural optimization of the battery-pack system by utilizing the numerical results of the bottom shell deformation. These simulation-based prediction models combine response surface method and machine learning algorithms. First, a nonlinear finite element model of the battery-pack system is established. The efficacy of the model is verified using constrained modal analysis in a variety of commercial software packages. Second, the collision simulations are executed and the data in various collision conditions are collected. Different sample sizes are used to develop various response surface models and machine learning models. The machine learning algorithms adopt support vector machine, Gaussian process regression, and neural network models. Third, the prediction accuracy of multiple prediction models is investigated according to error functions. The results show that the neural network model can predict the most accurate deformation under the condition of low speed frontal impact. The prediction average absolute percentage error of the neural network model is only 0.34% within the design domain, and only 2.54% outside the design domain. The proposed prediction model can be used for reliable design of the battery-pack system in electric vehicles. It also can be employed to design the early warning system of the battery-packs. [ABSTRACT FROM AUTHOR]

Functionally graded materials (FGMs) are widely utilized due to their excellent mechanical properties, prompting a need to explore the dynamic response of FGMs. To accurately and efficiently analyze elastodynamics problems, the radial integration boundary element method (RIBEM) is coupled with the proper orthogonal decomposition (POD) method in this paper. The POD method can transform a high-dimensional model into a low-dimensional system with high precision. Using the basic solution (Kelvin solution), the governing partial differential equation for the linear elastic dynamics problem of FGMs is transformed into a boundary-domain integral equation. The radial integration method is employed to convert the domain integral arising from material inhomogeneity and inertia terms into an equivalent boundary integral. This establishes a solution for the elastic dynamics problem of FGMs without the need for internal grid RIBEM. The Newmark time integration scheme is applied to solve the second-order ordinary differential equations. The displacement field obtained by RIBEM is utilized to construct the snapshots matrix, from which the POD reduced-order model is established. Numerical examples validate that the POD method significantly reduces the model's order, enhancing computational efficiency while also demonstrating the high accuracy of the POD method. [ABSTRACT FROM AUTHOR]

Accurate estimation of domain integrals is of crucial importance for the pseudo-initial condition method applied in transient heat conduction analysis. When small time step is used, the integrand of the domain integral changes dramatically and is close to singular. A straightforward evaluation of the domain integrals using Gaussian quadrature may produce large errors. To improve the computational accuracy of two-dimensional domain integrals in boundary integral equation, a new distance transformation method is presented in this paper. The proposed method takes the time step as the transformation parameter, implementing the new transformation in the radial direction directly. With the new distance transformation method, the integrand of the domain integral can be smoother, thus more accurate results can be obtained. Numerical examples have demonstrated the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]