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

This paper presents an isogeometric analysis with adaptivity using locally refined B-splines (LR B-splines) for steady-state heat conduction simulations in solids. Within this framework, the LR B-splines, which have an efficient and simple local refinement algorithm, are used to represent the geometry, and are also employed for spatial discretization, thus providing a seamless interaction between the

A dual boundary element method formulation for elastoplastic fracture mechanics of shear deformable plate is reported in this work. The formulation can be viewed as an extension to the two-dimensional problem. The boundaries of crack surfaces are modeled using discontinuous elements of quadratic elements to fulfill the continuity requirements of displacements and tractions at collocation points for

Oblique water entry of a rigid paraboloid is investigated by fully nonlinear boundary element method. The deadrise angle of the paraboloid increases gradually from zero at the bottom tip and a slenderness coefficient is introduced to symbolize the shape of the paraboloid. Convergence study with respect to time step and element size is carried on to assure the numerical procedure. The free surface elevation

In this paper, a meshless generalized finite difference (FD) method is developed and presented for solving 2D elasticity problems. Different with other types of generalized FD method (GFDM) commonly constructed with moving least square (MLS) or radial basis function (RBF) shape functions, the present method is developed based upon B-spline based shape function. The method is a truly meshless approach

A higher-order stress point method for non-ordinary state-based peridynamic (NOSB-PD) is presented. The stress point is interpolated by its adjacent original nodes, where the second-order peridynamic derivatives are determined according to the peridynamic differential operator. By introducing the higher-order derivatives, the proposed stress point method could efficiently suppress the zero-energy mode

In this paper, a new single interface integral equation method is established for solving non-linear multi-medium heat transfer problems with temperature- dependent thermal conductivity. At first, the boundary-domain integral equation for nonlinear heat transfer in single medium is established based on the fundamental solution of Laplace equation. Then, based on the variation feature of the material

A damaged-based numerical manifold method is proposed in this paper to investigate the micro- and macro- mechanical properties of rocks. This model accounts for material heterogeneity and local material degradation using an exponential material softening law. The Mohr-Coulomb criterion with a tension cut-off is chosen as the strength criterion to capture the rock damage and fracture modes. Once the

A Boundary Element Method formulation is developed for the solution of the two-dimensional diffusion-wave problem, which is governed by a partial differential equation presenting a time fractional derivative of order α, with 1.0 < α < 2.0. In the proposed formulation, the fractional derivative is transferred to the Laplacian through the Riemann–Liouville integro-differential operator; then, the basic

The present study deals with the hydrodynamic performance of an OWC (oscillating water column) wave energy converter device placed on an undulated bed. The bed undulation is finitely extended and beyond that, the water bed is uniform in nature. The mathematical problem is studied in the two-dimensional Cartesian coordinate system under the linearized water wave theory. To solve the associated boundary

Accurate and efficient evaluation of singular integrals is of crucial importance for the successful implementation of the boundary element method (BEM). In most traditional methods, complex mathematical operations or expensive computation cost is required to achieve high accuracy of singular integral. To solve this problem, a new machine learning-based prediction framework is proposed in this paper

Transcranial magnetic stimulation is a promising tool in neuroscience of which successful development is affected by the loud click noise originated when the stimulating coil is energized. This undesired sound is produced by the coil winding deformations generated by the Lorentz self-forces in the TMS device. Addressing the need for TMS systems that produce less noise, a quiet coil design technique

This paper proposes an enhancement of the treatment of non-homogeneous boundary conditions to improve the boundary element method (BEM) formulation. The standard formulation is modified by introducing the boundary conditions in the integral kernels. The boundary conditions are implicitly defined through known parameters depending on the geometry, rather than by prescribing nodal values as is done in

This paper presents a meshfree collocation method for solving high order partial differential equations (PDEs). The leading numerical difficulty is the approximation of high order derivatives. To make the approximation simple and efficient, a moving Taylor polynomial (MTP) approximation is presented by using movable expansion point for each sub-domain. Derivatives can be derived straightforward from

An improved NMM (Numerical Manifold Method) with mathematical cover refinement (RNMM) is adopted to investigate the stability of a SRM (soil-rock-mixture) slope. In the RNMM, refined mathematical meshes are deployed at specified domains where stress concentration may occur. Compared to the TNMM (Traditional NMM), the computational efficiency of the RNMM is better for slope stability problems. Besides

This paper explores, for the first time, the application of the novel mesh-free local radial basis function collocation method (LRBFCM) to the solution of a multi-physics problem in three dimensions. A related benchmark problem is solved by considering the natural convection of an incompressible Newtonian fluid in a differentially heated cubic cavity with and without the application of a magnetic field

A novel element subdivision method based on the binary tree has been proposed for evaluation of singular domain integrals in BEM. In this paper, this element subdivision technique is called the Binary-Tree Subdivision Method (BTSM), which is applicable to arbitrary shape linear and curved volume elements with arbitrary locations of the source point. Compared to the Conventional Subdivision Method (CSM)

This paper attempts to develop a novel hybrid method to address the dynamic impedance functions of a rigid strip-foundation resting on a non-homogeneous poroelastic soil profile. The rigid footing is perfectly bonded to the soil profile and is subjected to time-harmonic loadings. The soil profile under consideration comprises several horizontal layers with different thicknesses and an underlying half-space

Meshless methods based on infinitely smooth radial kernels have the potential to provide spectrally accurate function approximations with enormous geometric flexibility in any number of dimensions. The highest accuracy can often be obtained when the shape parameter in the basis function is small. But as the shape parameter goes to zero, the standard RBF interpolant matrix becomes severely ill-conditioned

This short communication documents the first attempt to apply the generalized finite difference method (GFDM) for inverse heat conduction analysis of functionally graded materials (FGMs). The fact that the GFDM is a meshless collocation method makes it particularly attractive in solving problems with complex geometries and high dimensions. By employing the Taylor series expansion and the moving least-squares

This paper presents a high-order node-based smoothed radial point interpolation method (NS-RPIM) with linear strain fields in smoothing domains. The linear smoothed strains are constructed by complete order of polynomial functions and normalized with reference to the central point of the smoothing region. The new NS-RPIM is one order higher than those of the existing methods which use piecewise constant

This thesis herein proposes a stochastic stable node-based smoothed finite element method for uncertainty and reliability analysis of thermo-mechanical problems. First, the deterministic ingredient of the thermo-mechanical solution is accurately solved by our proposed stable node-based smoothed finite element method (SNS-FEM); and the stochastic ingredient including the fourth-order moment and probability

Many authors have studied the numerical computation of conformal mappings (numerical conformal mapping), and there are nowadays several efficient numerical schemes. Among them, Amano’s method offers a straightforward numerical procedure for computing conformal mappings based on the method of fundamental solutions, and it has been applied to several regions with great success. However, there are some

User-defined element subroutines (UEL and VUEL) in Fortran are developed in ABAQUS, to implement the Scaled Boundary Finite Element Method (SBFEM), for general static and elastodynamic stress analyses of solids. The purposes are twofold: to increase the ease-of-use and acceptability of this relatively new numerical method; and to combine advantages of both the SBFEM and ABAQUS, namely, the former's

In the present work, the Fast Multipole Boundary Element Method (FMM / BEM) for solving three-dimensional incompressible fluid flow problems governed by the Navier–Stokes equations is proposed. With the velocity-vorticity formulation the pressure gradient is eliminated from the equations. The kinematics equation, related to the velocity field satisfies continuity and provides a direct boundary condition

This paper aims to study the seismic responses of a long lined tunnel embedded in a water-saturated poro-viscoelastic half-space, with focus on wave passage effects. The poro-viscoelastic half-space is modeled by the Biot's theory and the soil nonlinearity is considered via an equivalent linear approach. The seismic responses of the tunnel structure are simulated by a 2.5D hybrid FE-BE method. A total

The finite volume particle method (FVPM) is a meshless computational fluid dynamics (CFD) method, where the fluid domain is represented by a set of overlapping particles, and boundaries are defined as exact geometries. Particle-based CFD methods, such as smoothed particle hydrodynamics (SPH) and FVPM, are susceptible to non-uniform particle distributions, which result in errors. Particle regularisation

The generation of discrete elements into certain domain is the first step of DEM simulation. Geometric constructive methods are becoming increasingly popular because of their high efficiency, but the tangency problem between the generated particles and the boundaries has not been well solved yet. In this paper, the complete algorithm to achieve the boundary tangency is developed. Several packings are

The theory of boundary eigensolutions is developed for boundary value problems. It is general for boundary value problem. Steklov-Poincaré operator maps the values of a boundary condition of the solution of the Laplace equation in a domain to the values of another boundary condition. The eigenvalue is imbedded in the Dirichlet to Neumann (DtN) map. The DtN operator is called the Steklov operator. In

The NURBS basis is introduced into the boundary element method (BEM) for solving the liquid sloshing problem in the multiply connected domain. An ideal liquid assumed to be inviscid, incompressible is used to study the sloshing characteristics in the cylindrical tanks with barrels of the arbitrary shapes, dimensions and number. Considering the boundary conditions at the free surface and the tank bottom

In this paper, Laplace transform triple reciprocity boundary element method (LT-TRBEM) is employed to solve the three dimensional transient heat conduction problems. In order to improve the accuracy of the Laplace inversion using Gaver-Wynn-Rho (GWR) algorithm in non-multi-precision computational environment, a precision controllable GWR (PCGWR) algorithm is proposed in the current study. The inversion

This paper presents an efficient and accurate boundary element method (BEM) for the elastic analysis of axisymmetric problems in vertically non-homogeneous solids without or with cavity. This BEM uses the fundamental solution of the elastic field in a multilayered elastic solid induced by the body force uniformly concentrated at a circular ring. This solution is also called Yue's solution. The effective

In the context of the adaptive finite element method (FEM), ZZ-error estimators named after Zienkiewicz and Zhu (1987) [52] are mathematically well-established and widely used in practice. In this work, we propose and analyze ZZ-type error estimators for the adaptive boundary element method (BEM). We consider weakly singular and hyper-singular integral equations and prove, in particular, convergence

Only very recently, Sayas [The validity of Johnson-Nédélec's BEM-FEM coupling on polygonal interfaces. SIAM J Numer Anal 2009;47:3451-63] proved that the Johnson-Nédélec one-equation approach from [On the coupling of boundary integral and finite element methods. Math Comput 1980;35:1063-79] provides a stable coupling of finite element method (FEM) and boundary element method (BEM). In our work, we

The paper provides boundary integral equations for solving the problem of viscous scattering of a pressure wave by a rigid body. By using this mathematical tool uniqueness and existence theorems are proved. Since the boundary conditions are written in terms of velocities, vector boundary integral equations are obtained for solving the problem. The paper introduces single-layer viscous potentials and