In the present work, local radial basis function (RBF) collocation method is used to solve the Stokes problem numerically. Benefits of the local meshless method is its flexibility of handling complex computational domain and interface. Local meshless method produces sparse coefficient matrix, though its structure is depending on the placement of nodes, and type of boundary conditions. The Stokes equations

Smoothed particle hydrodynamics (SPH) is adopted to simulate the peak impact load, the water entry process and the water entry characteristics of a re-entry capsule with the complex capsule motions modelled by a developed six degrees of freedom fluid-solid coupling model. Diffused particle distribution is developed and used in the simulations to decrease memory and computational cost. The results show

In order to solve multi-medium nonlinear transient heat conduction problems, based on interface integration boundary element method, a new approach, which can convert the multi-domain integrals to the boundary integrals with high precision, is firstly proposed in this paper. The boundary element method with the internal and exterior source is used to establish the interface integral equation of the

In this paper, some steady infiltration problems from periodic channels into two-layered soils are considered. The problems are governed by a system of Richards’ equations with boundary interface conditions. To solve the problems, the system of Richards’ equations with respect to some boundary conditions are transformed into a system of steady diffusion-convection equations with respect to transformed

The collocation-based impedance-to-scattering matrix method recently developed in conjunction with the boundary element method (BEM) for large silencer analysis is reformulated by using the reciprocal identity integral. The reciprocal identity integral also forms the foundation of the classical theory of acoustic reciprocity for silencers. Contrary to the conventional wisdom, when the inlet and the

The Contact Theory proposed by Shi in 2015 is expected to solve the contact detection problem of discrete blocks in a perfect and universal manner. In the present paper, a contact detection algorithm for arbitrary polygonal blocks based on the Contact Theory is proposed and coupled into the two-dimensional DDA (2D-DDA). Four different methods to determine the contact entrance lines are presented, and

The numerical solutions of boundary integral equations by the Boundary Element Method (BEM) have been applied in several areas of computational engineering and science such as elasticity and fracture mechanics. The BEM formulations often require the evaluation of complex singular and hypersingular integrals. Therefore, BEM requires special integration schemes for singular elements. The Subtraction

Nonlinear water waves are common physical phenomena in the field of coastal and ocean engineering, which plays a critical role in the investigation of hydrodynamics regarding offshore and deep-water structures. In the present study, a three-dimensional (3D) numerical wave flume (NWF) is constructed to simulate the propagation of nonlinear water waves. On the basis of potential flow theory, the second-order

The recently developed edge-based smoothed finite element method (ES-FEM) is an efficiency method for solving frequency response of structural-acoustic systems with nominally deterministic parameters. In order to further dealing with the unavoidable uncertainties, both the interval perturbation techniques and the subinterval perturbation techniques are introduced and embedded into the hybrid edge-based

We propose a novel approach for two-way coupled simulations of multiphase flows within an Eulerian-Lagrange framework. Lagrangian particles are commonly approximated as point sources of either energy, mass or momentum. To introduce them into the Eulerian computation of the fluid flow, an approximation of the Dirac delta function has to be made. By resorting to the Boundary Element Method (BEM) based

Based on the Erdogan fundamental solutions for infinite cracked plates, a new hybrid boundary node method for linear fracture problems is proposed in this paper. The origin singular intensity factor for the Erdogan fundamental solutions is developed to overcome the singular when the field points are coincided with the source points, and no virtual source points are needed, a new scheme for calculating

A mixed analytical-numerical method is proposed to evaluate the acoustic radiation of a double elastic spherical shell in finite-depth water by combining the analytical method with the numerical Wave Based Method (WBM) [or Wave Superposition Method, WSM]. The effects of reflection from both the free surface and the seabed are considered. The correctness of this method is verified through several numerical

The current paper describes a rapid and impressive numerical technique to simulate the flows with multiple phases and components based upon the Shan-Chen model. The Shan-Chen model is a generalization of the incompressible Navier-Stokes equation with the variable density. The local radial basis function-generated finite difference method or local RBF-FD approach has been developed to solve the considered

In this paper, a localized meshless collocation method, the generalized finite difference method (GFDM), is first applied to calculate the bandgaps of anti-plane transverse elastic waves in 2D solid phononic crystals with square and triangular lattice. The corresponding theoretical consistency analysis of the GFDM is given. The universal algorithm for the uniform/scattered node generation in the GFDM

A boundary element method (BEM) for the solution of lubrication problems on finite bearings is presented. The formulation requires the Reynolds equation to be transformed into a constant coefficient equation. Several film shapes that make the transformation possible are systematically obtained. Noticeably, they cover most practical cases. As an example of application, a numerical solution that only

Finite element-least squares point interpolation method (FE-LSPIM) developed recently shows some excellent features to improve the calculation accuracy of mechanical problems. In this paper, a coupled finite element-least squares point interpolation method/ boundary element method (FE-LSPIM/BEM) is proposed to analyze plate-like structural-acoustic coupled system. Here, the FE-LSPIM is used to model

Consider a two dimensional steady low Reynolds number flow past a circular cylinder. A boundary integral representation that matches an outer Oseen flow and inner Stokes flow is given, and the matching error is shown to be smallest when the outer domain is as close as possible to the body. Also, it is shown that as the Greenâs function is approached, the oseenlet becomes the stokeslet to leading order

In this study, a symmetric method of approximate particular solutions (MAPS) is proposed for solving certain partial differential equations (PDEs). Inspired by the unsymmetric MAPS and symmetric radial basis function collocation method (RBFCM), the symmetric MAPS is developed by using the bi-particular solutions of the multiquadrics (MQ). Similar to the unsymmetric MAPS, the right-hand-side of the

The augmented moving least squares (AMLS) approximation is a meshless scheme to construct continuous functions by using fundamental solutions as basis functions. By incorporating the AMLS approximation into the method of fundamental solutions (MFS), the localized MFS can significantly reduce the computational load and accelerate the solution progress of the MFS. In this paper, error estimates of the

An equivalent linear BEM-FEM model for the approximate analysis of the time harmonic lateral response of piles considering soil degradation along the soil-pile interface is proposed. The non-degraded soil around the foundation is modelled with boundary elements as a continuum, semi-infinite, isotropic, homogeneous or zoned homogeneous, linear, viscoelastic medium. Piles are modelled with finite elements

The paper takes advantage of the digital images exported from the digital visualization models of geotechnical engineering and the meshless method based on Shepard function and Partition of Unity (MSPU) to develop a new solution for the automatic digital-numerical integrated analysis. The proposed method fully utilizes the information of pixels to substitute geometric models with digital images, which

In this paper, a novel space-time generalized finite difference method (GFDM) is proposed for solving transient heat conduction problems by integrating a direct space-time discretization technique into the meshless GFDM. The spatial and temporal dimensions are simultaneously discretized by randomly distributed nodes in the coupled space-time continuum. Transient heat conduction in homogenous and heterogeneous

A full coupled multi-scale modelling using the Boundary Element Method for analysing the 2D problem of stretched plates composed of heterogeneous materials, where dissipative phenomena can be considered, is presented. Both the macro-scale and the micro-scale are modelled by BEM formulations where the consistent tangent operator (CTO) is used to achieve the equilibrium of the iterative procedures. The

This paper proposes the topology optimization for steady-state heat conduction structures by incorporating the meshless-based generalized finite difference method (GFDM) and the solid isotropic microstructures with penalization interpolation model. In the meshless GFDM numerical scheme, the explicit formulae of the partial differential equation are expressed by the Taylor series expansions and the

The main aim of this study is presenting a semi-discretization scheme to find the numerical solution of two dimensional (2D) stochastic time fractional diffusion-wave equation, which obtains from classical 2D diffusion-wave equation by replacing integer time derivative with Caputo fractional time derivative of order α (1 < α ≤ 2) and inserting some stochastic factors. In this scheme, first Crank-Nicolson

In this paper both of the elastic-viscoelastic correspondence principle and time stepping method, which can convert viscoelasticity to elasticity, are employed to the boundary element method (BEM) to solve the contact problems between multiple rigid punches and anisotropic viscoelastic foundation. The one based upon the correspondence principle has the restriction on time-invariant boundaries, and

An easy implemented and effective pure meshfree method is first developed to solve the 1D/2D constant/variable-order time fractional convection-diffusion equation (TF-CDE) on non-regular domain with two boundary conditions in this paper. The proposed method (CSPH-FDM) is derived from that the finite difference scheme (FDM) for Caputo time fractional derivative and a corrected smoothed particle hydrodynamics

In this paper we present an approach which predicts directly without search the optimal choice of the shape parameter c contained in the multiquadrics (−1)⌈β2⌉(c2+∥x∥2)β2,β>0, and the inverse multiquadrics (c2+∥x∥2)β2,β<0. Unlike the simplex scheme where the data points are required to be evenly spaced, as in a recent paper of the author, here we allow them to be arbitrarily scattered in the simplex

A new nested complex source beam (NCSB) method based on the volume-surface integral equation (VSIE) is proposed for fast electromagnetic scattering analysis of composite conducting-dielectric objects. This scheme is based on the nested equivalent structure of the complex source beams to approximate the far-field interactions of both the RWG basis functions and SWG basis functions with an acceptable

This work presents a novel formulation of the Boundary Element Method (BEM) with the Radial Integration Method (RIM) to calculate the critical loads of the plate buckling problem with shear deformation. An alternative formulation is adopted where the effect of the geometric non-linearity is described by using the first derivative of the function for the out-of-plane displacements. The RIM is developed

In this paper, we develop a meshless method by using radial basis functions (RBFs) to solve time domain Maxwell’s equations resulting from simulating wave propagation in electromagnetic wave splitter and rotator devices. To simulate wave propagation in these devices, we introduce a perfectly matched layer (PML) to reduce the unbounded physical domain problem to a bounded domain problem. Using PML leads

We present a B-spline based semi-analytical technique for solving 2D convection-diffusion-reaction equations. The main feature of the presented technique is to separate the satisfaction of the conditions on the boundary and the elliptic partial differential equation inside. To be more precise, we transform the original equation into the problem with homogeneous boundary conditions and seek the approximate

In the paper, an inverse source problem for a 2D nonlinear elliptic partial differential equation is considered. With the over-specified boundary data given on two sides of a rectangle, we do not need the data on bottom and top sides to estimate an unknown 2D source function. As a consequence, we encounter a quite difficult inverse problem for solving the inverse source problem in an environment of

The meshless local technique is employed to simulate potential problems involving material anisotropy and also plane elastostatic equations of anisotropic functionally graded materials (PEE-AFGM). We utilize direct meshless local Petrov Galerkin (DMLPG) technique to discrete the spatial directions. The DMLPG5 (based on weak form) is applied to solve potential problems involving material anisotropy

Wave scattering of plane waves by irregularities in a transversely isotropic (TI) saturated half-space has been rarely studied. Based on Biot's theory, this paper used an indirect boundary element method (IBEM) to solve the two-dimensional (2D) wave scattering of incident plane qP1- and qSV-waves by irregularities in a layered TI saturated half-space. 2D dynamic Green's functions for uniformly distributed

In this paper, three meshless methods are proposed to solve boundary value problems. The special purpose Trefftz function method, the method of fundamental solutions and the symmetry method of fundamental solutions are compared. We considered six numerical examples for harmonic and biharmonic problems as a flow through the cylindrical fibers arranged in a regular square array, deflection of a uniformly

In this paper, an efficient numeric approach coupling smoothed particle hydrodynamics (SPH) with finite particle method (FPM) for fluid-solid interaction (FSI) problems is proposed and discussed. SPH is used for modeling fluid domains because of its ability to simulate free-surface flow. FPM is used to model solid domains as discretized particles to address motion, deformation, fracture and contact

In the present manuscript, we present an RBF based meshless method to investigate the time-fractional Tricomi-type equation, which has been arising in transonic flow. The unconditional stability of the proposed numerical scheme is discussed and theoretically proved. The time semi discretization has been done by using the finite difference method and for space discretization, we proposed an RBF based

In this paper, a particle refinement scheme with a hybrid particle interacting technique for SPH is proposed. The axis-aligned square refinement pattern is adopted to split coarse particles into fine ones and produces a new kind of particle named as “representative particles”. Representative particles have the same masses and initial particle spacings as the fine ones and are used to represent coarse

In this paper, out-of-core solution algorithms are used for analyzing large 3D soil problems. Such problems involve huge number of degrees of freedom. The soil continuum is modeled using 3D multi-region boundary element method. The overall stiffness matrix resulted from the multi-region boundary element problem is large, sparse and non-symmetric. The soil stiffness matrix is divided into series of

The previous papers by the author propose a new classification scheme of the boundary methods based on variational formulations. They contain initial numerical experiments conducted in order to compare nonsingular methods from the group generated by the original and inverse variational formulations. This paper is a continuation of that research and its aim is to apply one of the nonsingular Trefftz

In this paper, the technique of the Stable Generalized Finite Element Method (SGFEM) is applied to the numerically constructed functions of the Generalized Finite Element Method with Global-Local Enrichments (GFEMgl). The application of the resulting approach, named SGFEMgl, is expanded here to 2-D quasi-static crack propagation problems. Crack growth is performed by a two-scale strategy, using local

Fundamental solution for the time-harmonic vertical vibration of a rigid circular disc embedded in a transversely isotropic and layered poroelastic half-space is developed using a semi-analytical method. First, based on the Green's function of the time-harmonic vertical circular load embedded in the layered half-space, function of the corresponding annular ring load is determined via the method of

This paper focuses on near singularity in weakly singular integrals of three-dimensional boundary element method. In traditional methods, only one directional transformation is introduced to remove the weak singularity. However, near singularity is still existed. Thus in our paper, serval methods for removal of weak singularity are introduced firstly. Then, angular and sigmoidal transformations are

This study considers the fluid flow through a porous formation containing discontinuities (fault, fracture, crack, microcrack), which is usually much more conductive than the surrounding matrix. The discontinuity is mathematically represented by a 1D smooth function of curvilinear abscise and physically characterized by its aperture. Fluid flow is assumed to obey Poiseuille's law in the discontinuity

Based on both the boundary element and spectral representation methods, an effective simulation method for multiple-station spatially correlated ground motions on both bedrock and surface is developed, incorporating the spectral density function, coherence function, and site transfer function that consider the wave scattering effect. The accuracy and feasibility of the present method is validated by

The paper presents the strategy for automatic generating a plastic region in the parametric integral equation system (PIES) and its spread during the incremental process of solving elastoplastic problems. Instead of some preliminary research on the not known a priori plastic zone, it is found automatically on the basis of stresses on the boundary and then it propagates considering the current stress

For boundary element analysis of the orthotropic potential problems in thin structures, the higher order elements are expected to discretize the boundary. However, the use of the higher order elements leads to more complex forms of the integrands in boundary integral equations. The resulting nearly singular integrals on the higher order elements are difficult to be evaluated when the source point is

This work presents a self-regularized scheme of the Direct Interpolation Boundary Element Technique with Radial Basis Functions (DIBEM) for the solution of Helmholtz problems. Said scheme avoids the singularity produced by the fundamental solution due to the coincidence between source points and the interpolation basis points, eliminating the necessity for regularization procedure. The mathematical

This paper presents numerical simulations of metal machining processes with Eulerian and Total Lagrangian Smoothed Particle Hydrodynamics (SPH). Being a mesh-free method, SPH can conveniently handle large deformation and material separation. However, the Eulerian SPH (ESPH) in which the kernel functions are computed based on the current particle positions suffers from the tensile instability. The original

The local boundary integral equation (LBIE) method is a pure meshless integral method proposed by Atluri and co-workers. Since the fundamental solutions are used as the test functions, the sub-domain can be very small and the LBIE method is a promising method for solving problems of elasticity with nonhomogeneous material properties. In this paper, the subtraction technique is introduced to remove

This paper investigates the flow behavior of a viscous, incompressible and electrically conducting fluid in a long channel subjected to a time-varied oblique magnetic field B0(t)=B0f(t). The time-dependent MHD equations are solved by using the dual reciprocity boundary element method (DRBEM). The transient level velocity and induced magnetic field profiles are presented for moderate Hartmann number

We present a numerical method that allows for the efficient solution of general linear water-wave problems with multiple arbitrarily shaped bodies and seabed geometry when the number of unknowns in the problem N is large. The problem domain is divided into an internal region that is modeled using a simple-source boundary integral equation and an outer domain of uniform water depth. The contribution

A novel wavelet multi-resolution formulation in which arbitrary specified nodal coefficients can be exactly the function values at the corresponding nodes is proposed to approximate field functions for solid mechanics problems. This wavelet approximation is explicitly constructed based only on properly scattered nodes without any matrix inversion or ad-hoc parameters. It allows easy and automatic node

In this research, a computational technique is developed for determining effective in-plane properties of hexagonal core honeycombs utilizing homogenization multi-scale technique based on averaging theorems. Purposely associated with engineering constants, specialized unit cells under appropriate boundary conditions are elaborated for two well-known configurations of uniform cell wall thickness and

In this study, the singular boundary method (SBM) is extended to solve 3D inhomogeneous elliptic boundary value problems. Before applying the SBM, the multiple reciprocity method (MRM) removes the inhomogeneous terms and establishes an equivalent high-order homogeneous problem, which is then solved by the SBM, a boundary-only fundamental-solution based collocation method. It is worth-noting that the

In this paper we will present a formulation for solving elastodynamic problems in 2D using the method of fundamental solutions (MFS). The governing equation for the displacement in the elastodynamic problem is expressed by the Navier equation with an additional non-homogeneous inertial term, which involves the second derivative of displacement with respect to time. The inertial term is approximated

Polycrystalline materials are widely utilized in engineering fields. In this study, peridynamic (PD) models are developed for the first time in the literature to investigate thermally-induced fracture phenomenon for cubic polycrystals and ceramic made of different materials. After validating the current model, the influences of the grain size, grain boundary strength and composition of the materials

The adaptive finite element material point method (AFEMP) takes advantages of both finite element method (FEM) and material point method (MPM), suitable for dealing with extreme deformation problems. Use AFEMP to simulate the penetration of steel spheres and bullets into ballistic gelatin at high velocities to better understand the damage effects caused by the projectiles to biological soft tissue

A dual interpolation Galerkin boundary face method (DiGBFM) is applied in this paper by combining the newly developed dual interpolation method with the Galerkin boundary face method (BFM). The dual interpolation method unifies the conforming and nonconforming elements in the BFM implementation. It classifies the nodes of a conventional conforming element into virtual nodes and source nodes. Potentials