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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]

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]

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]

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]

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]

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 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]

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]

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]

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]

• 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]

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]

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]

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]

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]

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 B-spline material point method (BSMPM) has been shown to be a promising approach to effectively mitigate the cell-crossing instability by using high-order B-spline basis functions. However, the BSMPM still suffers from the quadrature error, another well-known source of inaccuracy in the material point methods. On the other hand, the convected particle domain interpolation (CPDI) method effectively reduces the quadrature error by using alternative basis functions. The B-spline basis functions can be naturally used within the CPDI formulation, here called the BSCPDI method. The BSCPDI may be prone to the cell-crossing instability since the alternative basis functions in the BSCPDI are always C0-continuous despite the high-continuity of the B-spline basis functions used as the original grid basis functions. In this paper, the reproducibility of the BSCPDI effective basis function gradients and the susceptibility of the method to the cell-crossing instability are investigated analytically and numerically. The effectiveness of the BSCPDI in mitigating the quadrature error is also investigated through numerical simulations. [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]

• 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]

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]

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]

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 this paper, the dynamic analysis of shear deformable shells was conducted using the hybrid displacement boundary element method (HD-BEM). The approach involved utilizing the fundamental solution as a trial function to derive the 8-node element stiffness matrix, while approximating the boundary variables with quadratic shape functions. To ensure efficient computations and avoid singular integrals, the source points were strategically positioned outside the domain. For accurate calculations of the proposed 8-node element mass matrix, only four Gauss points were relied upon. It is important to note that both the element mass and stiffness matrices demonstrate symmetry. Throughout the study, free, forced, and harmonic analyses were considered. Encouragingly, the results obtained from the study exhibited exceptional accuracy levels, even when employing a coarse discretization approach. [ABSTRACT FROM AUTHOR]

In this paper, a novel extended meshfree method is presented based on the integrated radial basis functions (iRBF) for crack analysis in bending plate problems. The new method is named XiRBF. The First-order Shear Deformation Theory (FSDT) is adopted to describe the deformation and stresses in cracked plate structures. The advantage of the iRBF approach is that it starts the approximation process with the highest-order derivative of the primary function first and then the lower-order derivatives are obtained by integration. This approximation style can give more accurate results for derivative values that appear a lot in governing equations of boundary value problems. In addition, the iRBF shape function also satisfies the Kronecker delta property, so essential boundary conditions can be applied as simply as the finite element method. In fracture analysis, to model the discontinuous behavior of crack surfaces, the Heaviside function is used, and to capture the singularity at the crack tip, the enriched functions are selected suitably based on the asymptotic analysis from the analytical solution. Various numerical tests are performed in which the stress resultant intensity factors (SRIFs) are calculated and the crack paths are visualized for crack propagation in the plate problems. The accuracy and efficiency of the proposed method are confirmed by comparing the present results with those obtained by other existing methods. • An extended iRBF meshfree method is presented for crack analysis in plate structure. • Static SRIFs calculations and quasi-static crack growth analysis in cracked plate problems are performed. • High accuracy of SRIFs evaluation and crack path can be obtained by the proposed approach. • Desirable features of the development are highlighted through the presentation of numerical examples. [ABSTRACT FROM AUTHOR]

The vibro-acoustic responses of combined composite laminated shell structures with variable thickness immersed in acoustic medium is investigated by using a meshfree method in this paper. The theoretical model of structural field is established by employing the energy principle in conjunction with the first-order shear deformation theory (FSDT) and the theoretical model of acoustic field are established by using Kirchhoff-Helmholtz integral equation. The displacement components of shell segments and the sound pressure variables of acoustic medium are described by using the meshfree Tchebychev point interpolation (TPIM) shape function and Double Fourier series in meridional and circumferential directions. The non-uniqueness problem of Kirchhoff-Helmholtz integral equation is overcome by adopting CHIEF method. The validation of the presented theoretical model is proved by comparing the results calculated by the proposed model with those results of existing literature and FEM/BEM. Based on the established theoretical model, vibro-acoustic responses of combined composite laminated shell structures with variable thickness immersed in acoustic medium are performed by analyzing the influences of thickness parameter, external load and boundary condition on the sound pressure level (SPL) and sound power level (SWL) of combined composite laminated shell structures. The above investigations can provide the theoretical thesis and technique guidance of preliminary design of combined composite laminated shell immersed in various acoustic medium. [ABSTRACT FROM AUTHOR]

An improved element-free Galerkin method (IEFGM) is proposed in this paper to solve the two-dimensional elasticity problems. In the IEFGM, the dimension-splitting moving least squares (DS-MLS) method is used to construct the trial functions, and the Galerkin variational weak form coupled with the integral coordinate transformation is applied to derive the final discrete equations of the elastic problems. The DS-MLS method is developed from the dimensional splitting method and the moving least squares (MLS) approximation. Since the shape function of the DS-MLS method is derived independently from the direction of dimensional splitting and the splitting subdivision surface, the dimension and complexity of matrix operations are greatly reduced in solving the shape function of the MLS approximation, thereby improving the calculation efficiency. Some typical examples are discussed to show the effectiveness of the improved meshless method in this paper. From the numerical results, because the DS-MLS method reduces the dimensionality when solving the shape functions, the improved meshless method in this paper can consume less CPU time and acquire a higher accuracy solution than the EFG method. [ABSTRACT FROM AUTHOR]