Closed-form solutions are derived for the regular and adjacent-singular integrals involving the two-dimensional Laplacian’s Green’s function and its normal derivative that arise in the Galerkin BEM. Motivation for their use is provided by comparing the accuracy and time required to compute the BEM system matrix relative to traditional numerical integration. Specifically, it is shown that the use of

In this paper, a numerical approach based on a three-dimensional (3D) standard coupled boundary element method-finite element method (BEM-FEM) formulation in the frequency domain is presented. The approach allows studying the dynamics response of a structure bonded to the surface of a layered transversely isotropic half-space subjected to time-harmonic loading. The FEM is used to model the structure

To address domain integration of meshfree Galerkin methods with quadratic base, we propose an efficient and accurate linear-gradient smoothing integration (LGSI) scheme in this study. In our scheme, the smoothed gradient is expressed as the linear polynomial form with respect to the center of the smoothing domain by means of Taylor's expansion. The unknown coefficients can be uniquely determined in

A new way is proposed to simulate the crack propagation paths of the multi-cracked structure. Firstly, the complete displacement and stress fields of the multi-cracked structure are calculated by the extended boundary element method (XBEM) coupled with characteristic analysis of the crack tip. Secondly, based on the maximum circumferential stress criterion by considering the contribution of the non-singular

In this paper, a new scheme is proposed to solve the Stokes interface problem. The scheme turns the Stokes interface problem into two coupled Stokes non-interface subproblems and adds a mixed boundary condition to overcome the numerical pressure oscillation. Since the interface becomes the boundary of the subproblems, the scheme has the advantage to deal with the interface problem with complex geometry

Randomly distributed liquid inclusions in elastic matrix exist in nature, biology, material science and other fields. In this paper, the isogeometic analysis boundary element method (IGABEM) is applied to study the mechanical properties of the elastic matrix with liquid inclusions, in which the liquid inclusion is assumed to be linearly compressible and the interface tension is neglected. Singularity

In this study, the flutter analysis of a rotating pre-twisted functionally graded graphene nanoplatelets reinforced composite (FG GPLRC) blade under supersonic airflow is investigated. The pre-twisted blade is multi-layered and reinforced with graphene nanoplatelets (GPLs) evenly distributed in each layer while the GPL weight fraction changes from layer to layer through the thickness direction. The

The rheological properties of emerging novel complex fluids are usually governed by multiple variables, which is challenging for traditional parameterized rheological models in the context of hydrodynamics modelling. In this paper, we propose a novel Data-Driven Smoothed Particle Hydrodynamics (DDSPH) method that, instead of applying the empirical rheological models, utilizes discrete experimental

We examine the utility of a new family of basis functions for use with the Complex Variable Boundary Element Method (CVBEM) and other mesh-free numerical methods for solving partial differential equations. The family of polygamma functions have found use in mathematics since as early as 1730 when James Stirling related the digamma function to the factorial function [1]. Now, we propose using the digamma

In this paper, wave scattering by an H-type porous barrier having nonlinear pressure drop boundary condition is analysed within the framework of small amplitude water wave theory. The H-type barrier is constructed using multiple thin (near zero thickness) rigid porous plates which are termed degenerate boundaries. The boundary value problem is solved using an iterative dual boundary element method

Our objective in this article is to develop weighted extended B-spline (WEB-spline) approximation of the first eigenpair of p(x)-Laplacian problem. One of the reason for choosing WEB-spline based mesh-free method for solving p(x)-Laplacian problem is that, it has additional advantages compared to usual finite element method. For example, it does not require any mesh generation procedure and hence eliminates

This paper proposes an accurate and robust meshless approach for the numerical solution of the nonlinear equal width equation. The numerical technique is applied for approximating the spatial variable derivatives of the model based on the localized radial basis function-finite difference (RBF-FD) method. Another implicit technique based on θ−weighted and finite difference methods is also employed for

Rotating cylindrical shells have been widely used in rotating machinery. The vibration characteristics of rotating composite cylindrical shells have a significant influence on the rotor dynamics. This paper provides a useful approach for the vibration analysis of a rotating functionally graded (FG) graphene nanoplatelets (GPLs) reinforced composite (GPLRC) cylindrical shell with matrix cracks. GPLs

A boundary element method (BEM) is implemented and applied to compute the band structures of phononic crystals taking account of three different kinds of imperfect interface layers. By using the Bloch theorem and the interface conditions the eigenvalue equations related to the wave vector are derived. The influences of the spring-interface model, mass-interface model and spring-mass-interface model

Underground engineering is becoming increasingly sophisticated in recent years, exemplified by shale gas recovery, nuclear waste disposal and enhanced geothermal systems. Displacement Discontinuity Method (DDM) and Fictitious Stress Method (FSM) are two branches of boundary element method which can efficiently and accurately simulate fractures and openings embedded in large spatial domains. Nevertheless

In this study, a novel meshless stable numerical solver is proposed to solve the non-conservative form of shallow water equations. Since they form a hyperbolic system of equations, discontinuous solutions are allowed to transmit during the simulation. The generalized finite difference-split coefficient matrix method, recently proposed, is applied and improved using the flux limiter to eliminate the

In this paper, a new refined quasi-3-dimensional logarithmic shear deformation theory (RQ-3DLSDT) and an advanced moving Kriging interpolation (AMKI) based-meshless method is combined for the first time to study the static bending, free vibration, and compressive buckling analysis of isotropic and sandwich functionally graded plates laid on elastic foundations. The RQ-3DLSDT considering the effect

In terms of solving fracture mechanics problems of quasicrystals, the boundary element method known as Trefftz Method is used for the first time. In this paper, the collocation Trefftz method as an indirect Trefftz method has been demonstrated to be an excellent numerical method for the anti-plane fracture problems in quasicrystals plate, which can exactly satisfy the governing equations and approximately

The analysis of liquid sloshing remains a challenging computational mechanics topic due to its complex underlying physics. The rapid simulation of sloshing problems requires accurate modelling of two-phase fluid dynamics and sloshing impacts on solid tank boundaries by suitable Flexible Fluid Structure Interaction (FFSI) models. This paper presents a hydroelastic model for the prediction of sway induced

The aim of this paper is to investigate the unstable nature of pressure computation focusing on incompressible flow modeling through the projection-based particle methods. A new approach from the original viewpoint of the momentum conservation regarding particle-level collisions, hereinafter refered to as time-scale correction of particle-level impulses (TCPI), is proposed to derive new source terms

The research is focused on the development of the Meshless Finite Difference Method with higher order approximation schemes and its application in elliptic problems. On the contrary to the Finite Element Method and other meshless methods, the approximation order may be raised without introducing any new nodes or degrees of freedom. The main concept is based upon the consideration of additional correction

The purpose of the present paper is to solve the lid-driven cavity problem for a non-Newtonian power-law shear thinning and shear thickening fluid by a meshless method. Results are presented for Re=100 and Re=1000, where different levels of shear thinning and thickening are considered. Furthermore, the lid-driven cavity case is made geometrically more complex by adding several circular-shaped obstacles

Highly oscillatory integrals are frequently involved in applied problems, particularly for large-scale data and high frequencies. Levin method with global radial basis functions was implemented for numerical evaluation of these integrals in the literature. However, when the frequency is large or nodal points are increased, the Levin method with global radial basis functions faces several issues such

Modeling nonlinearities, including damage, in the boundary element method (BEM) is usually carried out in implicit way, or in other words via applying initial stresses or strains over a discretized domain part. Such initial values have no physical meaning. They are only used to compensate the stress level due to the occurred nonlinearity. In this paper explicit implementation of nonlocal damage is

In this paper, we study a penny-shaped crack model with electrically and thermally semi-permeable boundary conditions in a three-dimensional transversely isotropic piezoelectric semiconductor. An extended displacement discontinuity boundary element method together with an iterative process is proposed to analyze the penny-shaped crack model. The extended displacement discontinuities across crack face

The isogeometric boundary element method (IGABEM) is developed to simulate the crack propagation and the inclusion-crack interaction in 3D infinite isotropic medium. The influence of complex shape inclusions on the stress intensity factors (SIFs) along the crack front is studied from the aspects of shape, stiffness, size and position. The non-uniform rational B-spline (NURBS) basis functions can be

In the current article, an analysis of heat transfer in the spine of different profiles is carried out. A nonlinear differential equation that includes the effect of temperature-dependent thermal conductivity, variable heat transfer coefficient, and surface radiation is solved using a predictor-corrector scheme and the meshless local Petrov-Galerkin (MLPG) method. The moving least square (MLS) method

The NMM (numerical manifold method) was widely adopted to deal with many types of engineering problems involving moving boundaries, such as multiple crack propagation in rock masses. With regular triangular mathematical meshes, the NMM is further developed for two typical steady seepage problems, such as the confined seepage analysis and the unconfined seepage analysis. For unconfined seepage analysis

This work presents the combination of the direct interpolation boundary element method (DIBEM) and the domain superposition technique (DST) to address piecewise inhomogeneous two dimensional Helmholtz problems, in which the internal constitutive property in each sector varies smoothly according to a known function. The domain integrals generated by the medium's heterogeneity are transformed into boundary

A new fast multipole boundary element method (FM-BEM) is proposed to analyze 2-D elastostatic problems by using linear and three-node quadratic elements. The use of higher-order elements in BEM analysis results in more complex forms of the integrands, in which the direct Gaussian quadrature is difficult to calculate the singular and nearly singular integrals. Herein, the complex notation is first introduced

This paper presents an axisymmetric BEM analysis of layered elastic halfspace with volcano-shaped mantle and cavity under internal gas pressure. The problem is of interest to understand the behavior of volcanoes, tectonic earthquakes and other oil and gas reservoirs. The volcano-shaped mantle ground topography and the internal spherical or ellipsoidal cavity are added to the conventional model of layered

In this paper, a hybrid immersed smoothed point interpolation method (hybrid IS-PIM) is proposed, which employs a hybrid force approach to impose fluid-structure interaction (FSI) force condition. Compared with the original IS-PIM using a complete body force, the hybrid IS-PIM still utilizes the form of body force for pressure term to enhance the stability of numerical algorithm, and the shear force

The application of control systems in composite structures is of great significance in reducing their vibration and protecting components. The current study proposes a sophisticated meshfree finite volume approach to actively control the vibration of temperature-dependent piezoelectric laminated composite plates. The moving least square shape functions are practiced in the approximation of the field

Consider the Dirichlet problem for Laplace’s/Poisson’s equation in a bounded simply-connected domain S. The source function qln|PQ*¯| is a fundamental solution (FS), and it can be found in many physical problems. The singularity occurs when the boundary value data affected by qln|PQ*¯| as the source node Q* is located near the boundary Γ(=∂S). So far, there is no comprehensive study on this kind of

This paper introduces a boundary condition scheme for weakly compressible (WC) renormalised first-order accurate meshless Lagrangian methods (MLM) by considering both solid and free surface conditions. A hybrid meshless Lagrangian method-finite difference (MLM-FD) scheme on prescribed boundary nodes is proposed to enforce Neumann boundary conditions. This is used to enforce symmetry boundary conditions

Floating breakwaters have better performance than fixed breakwaters in deep water conditions owing to their higher durability and lower cost. To evaluate the hydrodynamics of a floating breakwater system, a coupling model between smoothed particle hydrodynamics and a multisegmented quasi-Static method is developed. The free-floating and the moored cases are firstly employed as benchmarks to validate

In this paper, an improved node moving technique was developed for adaptive solution of some flow problems. Collocated Discrete Least Squares Meshless (CDLSM) method was applied for simulation. This method is a truly meshless method and also enjoys the symmetric and positive-definite property. Then, an improved node moving technique was developed based on the spring analogy. In this mechanism, each

This manuscript brings the derivation of influence functions for a three-dimensional full-space under bilinearly-distributed time-harmonic loads. The differential equations describing the medium are decomposed in terms of uncoupled vector fields. A double Fourier transform allows the system of equations to be solved algebraically in the transformed space, where the bilinear-loading boundary conditions

This paper adopts an efficient localized meshless technique for computing the solution of the nonlinear sinh-Gordon equation (NShGE). The NShGE is one useful description for many natural processes such as solid state physics, surface theory, fluid dynamics, nonlinear optics and dislocation in materials. In the proposed method, at the first step, a second-order accurate formulation is implemented to

Deformable landslide body is modeled as a rheological material when SPH methods are used for numerical simulations. To increase accuracy, Carreau-Yasuda rheological model is chosen in this study. The model overcomes the weakness of the power-law model in predicting viscosity at zero and infinite shear strain rates. Also, a fully explicit three-step algorithm is proposed to solve governing equations

Two types of splitting algorithms are proposed for approximation of Cauchy type singular integrals having high frequency Fourier kernel. To evaluate non-singular integrals, modified Levin collocation methods with multiquadric radial basis function and Chebyshev polynomials are proposed. In the scenario of interval splitting, a multi-resolution quadrature is used to tackle the singularity ridden kernel

This paper presents a new version of the method of fundamental solutions (MFS) for two-dimensional linear elasticity problems based on the stress function (Airy stress function), which is different from the MFS utilizing the fundamental solutions of displacement. The displacement compatibilities are derived by the single-valuedness of displacements in multiply-connected region. Based on the strain

The unified gradient elasticity theory with applications to nano-mechanics of torsion is examined. The Reissner stationary variational principle is invoked to detect the differential and boundary conditions of equilibrium along with the consistent form of the constitutive laws. An efficient meshless numerical approach is established by making recourse to the Reissner variational functional wherein

In this paper, a stable node-based smoothed finite element method with PML (SNS-FEM-PML) is proposed to solve the scattering problem of a time-harmonic elastic plane wave by a rigid obstacle in two dimensions. In the algorithm, the stability term is constructed by the Taylor expansion of the gradient to cure the instability of the original NS-FEM. The linear variations of the gradient with respect

In this paper, an adaptive element free Galerkin (EFG) method is presented to solve Poisson equation. In general, element free Galerkin method using moving least square (MLS) approximation needs a background mesh for integration. With the arbitrary polygonal influence domain technique, the shape function of MLS has almost interpolation property, and the Gaussian quadrature points in the background

This paper presents a hybrid plane wave expansion/edge-based smoothed finite element method (PWE/ES-FEM) for band structures simulation of semi-infinite beam-like phononic crystals (PCs). The field variables are first approximated using linear shape functions in conjunction with the spatial Fourier series. Within the further formed edge-based smoothing domains, the gradient smoothing technique (GST)

Block Toeplitz matrices are a special class of matrices that exhibit reduced memory requirements and a reduced complexity of matrix-vector multiplications. We herein present an efficient computational approach to solve a sequence of block Toeplitz systems arising from a block Toeplitz system with multiple right-hand sides. Two different numerical schemes are implemented for the solution of the sequence

A moderated thick double curved shallow shell with functionally graded materials subjected to static and dynamic loads are investigated by the meshless methods. Shear deformable plate theory is applied and the governing equation with respect to the middle surface is formulated in the Cartesian coordinate system with five degrees of freedom. The numerical solutions of the partial differential equations

In this research, free and forced vibrations of the functionally graded material (FGM) sandwich beams are investigated by using the scaled boundary finite element method (SBFEM). The innovation of this method is that the discretization only exists in the axial direction of the beam, which reduces the spatial dimension of problem by one, the time-consuming mesh generation processes are greatly reduced

In the numerical discretization for the models of multilayer thin structures, the elements with narrow strip shape may be appeared. When using the previous methods to integrate these elements, the potentially near singularity will arise in the circumferential direction. In this paper, a weak singularity elimination method for multilayer structures of 3D boundary element method is presented to accurately

Pre-stressed cables were found to be a viable approach of reinforcing anti-dip bedding rock slopes (ABRSs) in the Wenchuan earthquake. However, the dynamic response law and failure mechanism of reinforced ABRSs are still unclear, which was studied using the Universal Distinct Element Code (UDEC) method in this work. A numerical model of a typical ABRS was first built up using UDEC. Then, a comparison

The present paper deals with the development of a Galerkin Boundary Element Method (Galerkin-BEM) approach applied to the numerical simulation of plane and half-plane quasi-static viscoelastic problems. This approach makes use of a half-plane viscoelastic fundamental solution, thus avoiding the full discretization of the half-plane and consequently reducing the computational requirements of the proposed

In this study, we focus on space-time mesh-free numerical techniques for efficiently solving the Richards equation which is often used to model unsaturated flow through porous media. We propose an efficient approach which combines the use of local multiquadric (MQ) radial basis function (RBF) methods and space-time techniques. The localized MQ-RBFs meshless methods allow to avoid mesh generation and

This study presents an upgraded Ritz method capable of providing solutions to thin polygonal plates of regular and irregular shapes with various boundary conditions. The method presented herein is called the Boundary-Type Ritz (BTR) Method and it circumvents the complexity of the involved domains by transforming the encountered integrals to other forms that need to be evaluated only at corners. This

We investigate the nonlinear bending behavior of nanoporous metal foam plates within the framework of isogeometric analysis (IGA) and higher-order plate theory. The nonlocal strain gradient theory (NSGT) taking into account the length scale and nonlocal parameters has been adopted to establish a scale dependent model of metal foam nanoscale plates. Von Karman nonlinear strains are then used to take

In this paper, we propose a new geometric model that includes a fourth-order partial differential equation (PDE) for reconstructing 2D curves. For instance, we use this model to reproduce letters in Time Roman font. The method of fundamental solutions (MFS), which is a simple and easily implemented meshless method, is employed for solving the proposed PDEs. In addition, no fictitious boundary is required

In this study, a strategy was proposed to determine the interval of the variable shape parameter for the ghost point method using radial basis functions. The determination of a suitable interval for the variable shape parameter remains a challenge. The modified Franke formula was used as an initial predictor of the center of the interval of the variable shape parameter in this study. After extensive

The article deals with the possibilities of using local meshless methods for modeling the movement of avalanches and rapid slopes movements. These are dangerous phenomena that can cause extensive damage to the infrastructure of mountainous areas and numerical models are therefore an important tool in their prediction. Today, meshless methods are increasingly developed in many different areas for their

In this paper, we analyze the hygro-thermo-electro-mechanical (HTEM) coupling problem of functionally graded piezoelectric (FGPE) structure based on edge-based smoothed point interpolation method (ES-PIM). The basic equations for FGPE structure are derived in the multi-physical field. Triangular elements adopted in ES-PIM can be generated automatically and suitable for complicated structures. The responses