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Random vibration analysis is an important indicator for conducting fatigue analysis as well as reliability analysis of engineering structures. At present, the vibration analysis for plate and shell structures is mostly limited to simple plate and shell structures, while the analysis of random vibration of smart piezoelectric structures is really scarce. In this paper, an electro-mechanical coupling model is proposed to examine the stochastic vibration characteristics of smart piezoelectric structures based on the Spectral-Tchebychev method (S-T), whose type of random excitation is pseudo-excitation method (PEM). By comparing the FEM, the literature and experiments, it is observed that S-T electromechanical coupling model proposed in this paper consumes much less computational time in predicting the stochastic response than the existing methods. Secondly, we focus on the effect of the piezoelectric layer on the stochastic vibration characteristics of the host structure. Then, artificial spring technique is also adopted to simulate the general boundary of the coupled electromechanical model for the random vibration analysis. The research work on the random vibration of piezoelectric smart structures in this paper can provide practical engineering experience for the design and equipment of smart structures. [ABSTRACT FROM AUTHOR]

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]

This paper provides a semi-analytical solution for the scattering of seismic waves by the composite topography of the alpine valley based on the scaled boundary finite element method (SBFEM). Firstly, the near-field finite region is discretized using a quadtree mesh decomposition technique. The input of seismic waves is transformed into the traction force acting on the interface between the near and far fields, and thus the numerical modeling of the scattering of seismic waves by the composite terrain of the alpine valley is established. Then, the accuracy of this paper's method is verified by comparing the results with the existing results. Finally, the effects of related parameters such as mountain, valley and seismic waves on ground motion are discussed in detail. The results show that there are significant dynamic interactions between the alpine and valley, that the alpine has an inhibiting effect on the ground motion in the valley region under the vertical incidence of seismic waves, and the valley has an amplifying effect on the slope surface of the alpines close to the side of the valley. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive partitioning strategy and the proper orthogonal decomposition–Galerkin method are combined to formulate an adaptive partitioned reduced order model (APROM) for fast solution of peridynamic (PD) models involving fractures. A boundary layer separation approach is presented to tackle the inaccurate reproduction of nonlocal boundary conditions in the reduced order model (ROM). Cracks invariably make ROM results more sensitive to the snapshots, i.e. a set of high-fidelity solutions simulated by the full order model (FOM), and this challenge is overcome by an adaptive partitioning strategy. The internal computational domain is divided into two parts: the crack region is modeled by full PD model, and the remaining region is dimensionally reduced. The partitioned configuration is automatically updated with the damage evolution. Several numerical tests are executed to verify the performance of the APROM, which shows that the APROM is able to successfully simulate various fracture phenomena. A significant improvement in computational efficiency is found: the number of degrees of freedom in the full PD model is greatly reduced, leading to an approximately 10 times improvement in CPU time without loss of accuracy. This paper provides strong theoretical support for accelerating PD solutions, thereby promoting the practical application of PD theory in large-scale engineering projects. [ABSTRACT FROM AUTHOR]

Data interpolation is a fundamental problem in many applied mathematics and scientific computing fields. This paper introduces a modified implicit local radial basis function interpolation method for scattered data using polyharmonic splines (PS) with a low degree of polynomial basis. This is an improvement to the original method proposed in 2015 by Yao et al.. In the original approach, only radial basis functions (RBFs) with shape parameters, such as multiquadrics (MQ), inverse multiquadrics (IMQ), Gaussian, and Matern RBF are used. The authors claimed that the conditionally positive definite RBFs such as polyharmonic splines r 2 n ln r and r 2 n + 1 "failed to produce acceptable results". In this paper, we verified that when polyharmonic splines together with a polynomial basis is used on the interpolation scheme, high-order accuracy and excellent conditioning of the global sparse systems are gained without selecting a shape parameter. The scheme predicts functions' values at a set of discrete evaluation points, through a global sparse linear system. Compared to standard implementation, computational efficiency is achieved by using parallel computing. Applications of the proposed algorithms to 2D and 3D benchmark functions on uniformly distributed random points, the Halton quasi-points on regular or Stanford bunny shape domains, and an image interpolation problem confirmed the effectiveness of the method. We also compared the algorithms with other methods available in the literature to show the superiority of using PS augmented with a polynomial basis. High accuracy can be easily achieved by increasing the order of polyharmonic splines or the number of points in local domains, when small order of polynomials are used in the basis. MATLAB code for the 3D bunny example is shared on MATLAB Central File Exchange (Yao, 2023). [ABSTRACT FROM AUTHOR]

Recently, we derived the Green's function for an infinite thick laminated composite plate subjected to concentrated forces and moments. By serving this Green's function as the fundamental solutions, in this paper for the first time we develop the associated boundary element method (BEM), which is applicable to general problems of thick laminated plates with various types of deformations. For example, the in-plane stretching and out-of-plane bending deformations may be coupled together, which occurs for the unsymmetric laminated composite plates. Besides, the transverse shear deformations are also incorporated based upon the first order plate theory. To complete the entire development of the proposed BEM, all the involved issues, such as the boundary integral equations, the fundamental solutions and their derivatives, the mathematical formulation for the selected isoparametric quadratic boundary element, and the treatments of singular integrals are elaborated in this paper. The calculations of complete solutions at boundary or internal points are provided as well. The accuracy and efficiency of the proposed BEM are demonstrated through numerical examples, which show that it outperforms the conventional finite element method and is applicable for general thick laminated plates with unrestricted coupling effects. [ABSTRACT FROM AUTHOR]

This paper proposes a novel isogeometric topology optimization method to obtain the hierarchical structures, where a special porous microstructures of identical topologies but with different length-width ratios are considered. First, the floating projection technique without penalization is adopted to find the topological configurations of hierachical structures, which make the optimized hierachical structures not easy to fall into the local optimums. Second, the isogeometric analysis based on the non-uniform rational B-spline basis functions, is utilized to calculate the structural compliances and sensitivity information. Third, this paper presents a limited number of microstructures with the changing aspect ratios, to satisfy arbitrary boundary conditions of macrostructures. The macroscopic equivalent properties are evaluated by the isogeometric analysis-based homogenization method. Finally, four numerical examples are provided to illustrate the effectiveness of the proposed method in designing hierarchical structures, and the influence of micro-structural properties on the macro-structural performances. [ABSTRACT FROM AUTHOR]

We propose an isogeometric boundary element (IGABEM) parallel fast direct solver based on OpenMP to solve three-dimensional multiple crack problems. In this paper, the orderly and randomly distributed cracks are studied to observe the influence of the multiple crack interaction on the effective elastic properties. This paper designs the parallel implementation of the matrix low rank approximation and the matrix assembly for the hierarchical off-diagonal low rank (HODLR) matrix. In the matrix low rank approximation, we propose the m - n tree to improve the accelerated hybrid algorithm to balance the CPU performance and memory usage. The numerical results show that the effective elastic properties can respond to the strong interaction to a certain extent, but the maximum stress intensity factors (SIFs) of multiple cracks still need to be calculated to diagnose the possible crack initiation points. On the other hand, the numerical results also show that the IGABEM parallel fast direct solver can greatly improve the computational efficiency on the premise of ensuring the computational accuracy. [ABSTRACT FROM AUTHOR]

In this paper, the meshless smooth particle hydrodynamics (SPH) method is used to simulate the transport process of pollutants in the environment by solving the convection-diffusion equation of pollutants under the Lagrangian framework. This method avoids various numerical problems caused by mesh distortion or mesh movement and the calculation of the derivative of the kernel function when approximating the second derivative kernel. In order to reduce the original virtual particle method of SPH to solve the boundary problem due to the large amount of particle searches will increase the amount of redundant calculation and other factors, selected with the finite difference method to solve the boundary. To verify the proposed Lagrangian particle model, numerical experiments were carried out. The one-dimensional calculation results are compared in detail with the results of different schemes in the finite difference method, and the L 2 , L ∞ and relative errors are analyzed. The simulation results show that the SPH-based model requires fewer particles. In addition, the model is numerically analyzed under the condition of ensuring accuracy. The numerical solution is in good agreement with the analytical solution. The research results of this paper can provide a new solution and idea for environmental pollution early warning. [ABSTRACT FROM AUTHOR]

The paper focuses on the derivation of a local variant of the boundary knot method (BKM) for the cases of Stokes flow and the biharmonic equation. Compared to the global variant, the local one leads to a sparse result matrix of the system of equations and thus makes the solution of especially large-scale problems more efficient. It is also important to keep the conditionality of the interpolation matrix within reasonable bounds. For the localization, a combination of BKM and finite collocation method was used. The results of the local variant were compared on several examples and the dependence of the solution on the density of the point network and the dimensions of the stencil used was also tested in the paper. [ABSTRACT FROM AUTHOR]

• This paper proposes a centroid-enriched edge-based / face-based smoothed RPIM (CE-ES-RPIM and CE-FS-RPIM) to address the volumetric locking problem in nearly incompressible problems. • A centroid-enriched scheme is creatively used and implemented into the traditional ES-RPIM and FS-RPIM framework. • The strain-smoothing technique is performed on the triangle (2D) or tetrahedron (3D) mesh to maintain the linear exactness of the radial point interpolation method. • The collocation of centroid-enriched scheme and strain smoothing technique makes the ratio of the number of displacement equations to the number of incompressible constraints reach the optimal value of 2. While edge-based (2D) and face-based (3D) smoothed radial point interpolation methods (ES-RPIM and FS-RPIM) have demonstrated excellent performance in solid mechanics, the volumetric locking problem limits their applications in nearly incompressible problems. This paper develops a centroid-enriched edge-based/face-based smoothed RPIM (CE-ES-RPIM and CE-FS-RPIM) to address the volumetric locking problem in nearly incompressible problems. The proposed method comprises the following elements: (1) a centroid-enriched scheme is creatively used and implemented into the traditional ES-RPIM and FS-RPIM framework, in which the centroids of triangular mesh are added as spatial discretization nodes; (2) the strain-smoothing technique is performed on triangle (2D) or tetrahedron (3D) mesh to maintain the linear exactness of the radial point interpolation method; and (3) the combination of the centroid-enriched scheme and strain smoothing technique makes the ratio of the number of displacement equations to the number of incompressible constraints reach the optimal value of 2, effectively eliminating volumetric locking. The accuracy, effectiveness and efficiency of the proposed method are validated on several 2D and 3D nearly incompressible benchmark examples. All results demonstrate that the proposed method can provide accurate numerical results under an incompressible limitation and provide better performance than conventional quadratic element methods. [ABSTRACT FROM AUTHOR]

The non-ordinary state-based peridynamic (NOSB-PD) method has significant advantages in solving crack propagation problems due to its non-local characteristics, but it also faces problems such as numerical oscillations and boundary effects. In order to solve the above defects, the paper first discusses the NOSB-PD method within the Galerkin framework. After that, the peridynamic differential operator (PDDO) approximation was introduced by extending the calculation of the deformation gradient tensor F in NOSB-PD. Since the zero-order approximations in the PDDO approximation and the reproducing kernel (RK) approximation are identical, the distinctions between the two approximations have been thoroughly analysed. Although the two approximations show the same consistency, only the RK approximation satisfies the integrable condition. Therefore, a RK-PD coupling method is proposed in the paper, and an implicit iterative algorithm suited to the RK-PD method is presented as well. At last, several numerical examples demonstrate that the proposed method does not suffer from numerical oscillations and can be used to solve the three-dimensional crack propagation problems. [ABSTRACT FROM AUTHOR]

In the contemporary data-driven era, the fields of machine learning, deep learning, big data, statistics, and data science are essential for forecasting outcomes and getting insights from data. This paper looks at how machine learning approaches can be used to anticipate solar power generation, assess heat exchanger heat transfer efficiency, and predict the thermo-physical properties of nanofluids. The review specifically focuses on the potential use of machine learning in solar thermal applications, perovskites, and photovoltaic power forecasting. Predictions of nanofluid characteristics and device performance may be more accurately made with the development of machine learning algorithms. The use of machine learning in the creation of new perovskites and the assessment of their effectiveness and stability is also included in the review. Additionally, the paper explores developments in artificial intelligence, particularly deep learning, in this area and offers insights into techniques for forecasting solar power, including PV production, cloud motion, and weather classification. [ABSTRACT FROM AUTHOR]

This paper presents a new high-order embedded-/immersed-boundary method, based on point collocation, smooth extension of the solution and integrated radial basis functions (IRBFs), for solving the elliptic partial differential equation (PDE) defined in a domain with holes. The PDE is solved in the domain without holes, where the construction of the IRBF approximations is based on a fixed Cartesian grid and local five-point stencils, and the inner/immersed boundary conditions are included in the discretized equations. More importantly, nodal values of the second-, third- and fourth-order derivatives of the field variable are incorporated into the IRBF approximations, and the forcing term defined in the holes is constructed in a form that gives a globally smooth solution. These features enable the proposed scheme to achieve high level of sparseness of the system matrix, and high level of accuracy of the solution together. Numerical verification is carried out for problems with smooth and non-smooth inner boundaries. Highly accurate results are obtained using relatively coarse grids. • This paper presents a new high-order embedded-boundary method for solving elliptic problems. • It is based on point collocation, smooth extension of the solution and high-order 5-point integrated RBF stencils. • High level of accuracy of the solution and high level of sparseness of the system matrix are achieved together. [ABSTRACT FROM AUTHOR]

In this paper we present analytical expressions for the computation of singular integrals obtained in the discretisation of boundary integral equations for the Laplace and creeping flow (Stokes) problems with triangular or quadrilateral boundary elements with linear interpolation of the potential and constant interpolation of the flux. We compare the singular integrals computed with the presented analytical expressions with the same integrals computed with numerical quadrature and find that a considerably larger computational effort has to be made for numerical quadrature to achieve high accuracy than with the analytical expression. Furthermore, we show that the accuracy in solving a Laplace test case and a creeping flow test case using analytical expressions for singular integrals is better than the accuracy achieved with numerical quadrature. The analytical expressions are listed in the appendix of the paper and their implementation in computer code is available online. [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]

The acquisition of drinking water is discussed in this paper by three-dimensional modeling of a solar desalination plant focusing on renewable energies. The reservoir of the desalination plant contains aluminum nanoparticles with a constant weight percent. A layer of n-Eicosane phase change material (PCM) with various thicknesses is used at the bottom of the desalination plant reservoir. The objective of the present paper is to examine the entropy generation, including frictional, thermal, and total entropy generation in the flow of steam and air inside the desalination plant and the use of the PCM layer. The angle of the glass changes from 10 to 45°, and the thickness of the PCM layer varies during the day. The nanofluid flow is assumed to be two-phase, and the finite element method (FEM) is employed to solve the equations using COMSOL software. The results show that increasing the glass angle enhances the frictional entropy generation, and decreases the thermal entropy generation. Using PCM with a thickness of 50 mm reduces the thermal entropy generation in the steam, especially in the afternoon. The amount of PMC thickness changes the total entropy generation in the PMC. [ABSTRACT FROM AUTHOR]

In this paper, we construct two deep neural network (DNN) approaches based on the hybridized discontinuous Galerkin (HDG) method for solving some elliptic problems. The main idea is to use an HDG scheme for spatial discretization and then estimate solutions using the deep learning idea. In fact, by employing DNN, we can achieve robust methods compared to classical methods for solving noisy and high-dimensional problems. A brief analysis shows that the loss functions corresponding to the proposed methods, which are called DNN-HDG-I and DNN-HDG-II, converge to zero as the mesh step size reduces. By testing several examples in one, two, and three dimensions, we demonstrate the performance of the proposed methods that show their apparent advantages especially compared to classical HDG methods. As we expected, the DNN-HDG methods can efficiently and accurately extract the pattern of the solutions in all three dimensions. To show the superiority of the proposed schemes, the DNN-HDG methods are compared with the classical HDG method for solving a problem involving some noisy data. Specifically, we employ the proposed methods for solving a problem which its exact solution is not accessible and compare it with the HDG solution. In this paper, the uniformly random data and Jacobi polynomial roots are considered, respectively, as the training data on the boundary and quadrature points for approximating integrals. Also, we find that the proposed methods are not required a high number of neurons (at most 30) and hidden layers (at most 10) for satisfactory results with acceptable accuracy. [ABSTRACT FROM AUTHOR]

The collocation boundary element method is consistently outlined in a companion (Part I) paper for the general three-dimensional, static case of elasticity on the basis of a weighted-residuals statement that leads to the Somigliana's identity. Arbitrary rigid-body displacements, as for elasticity, are naturally taken into account, and traction force parameters are always in balance independently of problem scale and mesh discretization. For generally curved boundaries, the correct definition of traction force interpolation functions enables the enunciation of a general convergence theorem, the introduction of patch and cut-out tests and, not least, a considerable simplification of the numerical implementations. Simple code schemes are proposed in a second companion (Part II) paper for 2D problems of potential and elasticity, which rely exclusively on Gauss–Legendre quadrature and lead to arbitrarily high – actually only machine-precision dependent – computational accuracy of all results of interest independently of a problem's geometry and topology. We present here numerical results and convergence assessments – including numerical illustration of convergence Theorem 1 of the companion paper I – for 2D potential and elasticity problems with very challenging topology issues and even for subnanometer source–field distances — maybe with approximations due to a coarse mesh discretization but never introducing unduly singularities. We dare say the present results cannot be replicated by any code implementation other than the ones of our own, which resort to no ad hoc means beyond the problem's correct mathematics. In fact, we present the objective and controllable tools of separately assessing a mesh discretization for a given practical problem in terms of precision, accuracy and liability to round-off-errors. We also evaluate the distance threshold for a source point to be considered sufficiently close to demand the proposed exact mathematical treatment, as, for large distances, only Gauss–Legendre quadrature is required, be it in terms of quadrature adaptivity of even a fast multipole scheme. [ABSTRACT FROM AUTHOR]

Overcoming the challenging circumstances encountered in aerospace components has led to the widespread use of small-scale reinforcements to improve structure-related performance. Accordingly, the vibrational properties of coupled conical-cylindrical shells (CCCSs) made of a matrix material reinforced by functionally graded graphene oxide powder (FGGOP) are numerically investigated under various boundary conditions (BCs) in this paper. To enhance the vibrational feature of the CCCS reinforced by graphene oxide powder (GOP), three models are measured regarding distribution related to this small-scaled material within the polymer along with the thickness related to the CCCS. The Halpin-Tsai homogenization form is also employed to develop the mechanical values associated with the GOP-nanocomposite materials. The main equations related to the CCCSs are obtained by joining Donnell's theory and the first shear deformation theory (FSDT). Additionally, using variation calculation (Hamilton's principle), the motion equations (MEs) of the CCCS reinforced by FGGOP are determined. Then, the generalized differential quadrature method (GDQM) is utilized to produce the system related to the MEs. Next, standard eigenvalue determination obtains the frequencies of the CCCS made of the FGGOP-nanocomposite. Finally, the frequencies of various benchmarks are compared with those determined here to validate the proposed scheme. Also, more than a few new and interesting samples are designed and solved numerically to indicate the impacts of the GOP, geometrical values, and various BCs on the vibration responses of the CCCS made of GOP-nanocomposite. Remarkably, this paper is the first evaluation related to the free vibration of the coupled conical-cylindrical shells reinforced by FGGOP under different BCs. [ABSTRACT FROM AUTHOR]

• The ISNS-RPIM is presented to explore composite structures. • The paper analyzed the behavior of FGMEE in hygrothermal environment. • The factors influencing structural static and dynamic responses were examined. In this paper, an inhomogeneous stabilized node-based smoothed radial point interpolation method (ISNS-RPIM) is developed for analyzing functionally graded magneto-electro-elastic (FGMEE) structures in hygrothermal environment. The change of material gradient follows the exponential function distribution. Combining with the gradient smoothing technique (GST) and the coupling constitutive relationship, and considering the hygrothermo-magneto-electro-elastic (HMEE) coupling effects of FGMEE material, the equations for ISNS-RPIM are deduced. The generalized displacement of the FGMEE structures is obtained, and the error in total energy norm, CPU time and efficiency of ISNS-RPIM, NS-RPIM and FEM are researched. Numerical examples are provided to explore the influence of the following parameters in FGMEE structures including exponential factor, hygrothermal loading and empirical constants, and demonstrate the correctness, high effectivity and insensitivity to mesh distortion of ISNS-RPIM. The present method has shown great potential in solving practical complex problems. [ABSTRACT FROM AUTHOR]