Finite Element Method Region Research Articles

A coupled Meshless-FEM method based on strong form of Radial Point Interpolation Method (RPIM)

In this present work, we are implementing a novel hybrid method based on the coupling of RPIM in strong form and Finite Element Method (FEM). The basic idea is to ensure the coupling between the two methods through the collocation technique based on RPIM interpolation. This technique is used to evaluate the local equations of the problem at the interface between FEM and RPIM regions. We can avoid numerical integrations of a big part of nodes using the strong form of RPIM. Numerical studies show that this method gives reasonably accurate results consistent with the theory.

A coupling method of non-ordinary state-based peridynamics and finite element method

Non-ordinary state-based peridynamics (NOSBPD) and finite element method (FEM) are coupled to study the discontinuous problems, in which the damage criteria can be adopted from the viewpoint of strain and stress tensors. The coupling method takes full use of advantages of NOSBPD in dealing with discontinuous issues and the high efficiency of FEM, which also can eliminate the surface effect in PD. The computation domain for the coupling method includes the NOSBPD region and the FEM region, but no coupling region between the above two regions. Several numerical examples are used to validate the accuracy and efficiency of the coupling method in solving the one-dimensional, two-dimensional and three-dimensional static and dynamic discontinuous problems.

Study of composite material damage problem using coupled peridynamics and finite element method

<p indent=0mm>A new method is proposed to study damage problems of fiber reinforced composite material by using coupled peridynamics (PD) and finite element method (FEM). This method has both the advantage of the computational efficiency of FEM and the advantage of PD solving discontinuous problems. The computational domain can be partitioned into PD region and FEM region and coupling region. The region containing crack is modeled by PD, the other region is modeled by FEM, and the coupling region is between the above two regions. Application of the coupling scheme proposed in this paper is simple and convenient, and there is no need to introduce an overlapping region between PD particles and FE nodes. The PD particle is connected non-locally to all particles (PD particles and FE nodes) within its horizon, whereas the FE node interacts with other nodes in the finite element manner. The damage states obtained by the coupling method are good in agreement with that obtained pure PD method, while this coupling method has the high computation efficiency.

A method to couple state-based peridynamics and finite element method for crack propagation problem

A coupling method of the state-based Peridynamics and the finite element method (FEM) is proposed here to solve the problem of crack propagation. It has both the advantage of Peridynamics in solving discontinuous problems and the computational efficiency of FEM. The solution domain is partitioned into three regions: Peridynamic region, FEM region and coupling region. Crack propagation happens in the Peridynamic region. The remaining region is discretized by FEM. The coupling method is achieved in the following way: the Peridynamic particle is connected non-locally to all particles, i.e., Peridynamic particles and finite element nodes within its horizon, and the finite element node applies force upon all nodes around it. The accuracy and efficiency of the proposed method are verified in solving crack propagation problems.

Improved hybrid FEM/MOM combining MLFMA for composite electromagnetic scattering

ABSTRACTA generalized hybrid scheme combining finite element method (FEM) and the method of moments (MOM) is first presented to investigate scattering from a 3-D dielectric object above a 2-D dielectric rough surface. The hybrid FEM/MOM scheme is divided into the FEM region for the object based on Helmholtz’s equation and the MOM region for the rough surface based on coupled integral function, which can greatly reduce the computed region. With the rough surface getting larger, the unknowns of the rough surface get more. So MLFMA is employed to reduce computation complexity of MOM region itself and coupling interaction matrices between MOM region and FEM region. Consequently, the iterative process can be greatly accelerated. This generalized hybrid FEM/MOM is very suitable for investigating scattering from composite model of a complex material object and electrically large dielectric rough surface. Some examples verify this generalized hybrid FEM/MOM in high efficiency, low storage requirement, high precision and generality.

A Hybrid FEM/MoM Technique for 3-D Electromagnetic Scattering From a Dielectric Object Above a Conductive Rough Surface

A hybrid approach combining the edge-based vector finite-element method (FEM) and the method of moments (MoM) is first extended to study 3-D scattering from a dielectric object above a conductive rough surface. The hybrid FEM/MoM technique is based on the electric field vector Helmholtz's equation. To reduce the calculational domain, the solution region is divided into the FEM region containing the object and the MoM region containing the rough surface. In our hybrid method, tetrahedral elements are applied to handle the object region based on vector basis functions, whereas triangular elements are used to deal with the rough surface based on Rao–Wilton–Glisson basis functions. The electromagnetic coupling between the object and the rough surface is considered by the surface integral equation with the Green's function. The hybrid technique presented here combines advantages between FEM and MoM, which is highly efficient in terms of computing memory, time consumed, and versatility.

Using FEM–DEM coupling method to study three-body friction behavior

Three-body friction is a system of complex dry particles whose behavior is difficult to predict during sliding contact. To account for the interaction of first-body deformation and third-body rheology in a three-body interface, a multi-scale method based on coupling the finite element method (FEM) and discrete element method (DEM) is used to model the shear process of two parallel plates with solid particles between them. The model has two subregions: the FEM region (upper plate) and the DEM region (third-body and lower plate). The upper plate compresses the third-body at a certain pressure, and the lower plate shears it at a constant velocity. A stress–strain transmission mechanism is established to achieve the interaction of both subregions. The results of the coupling method are energy dissipation, particle contact state and stress transmission between the first and third bodies. Particle velocity changes with the energy transmitted between particles under low pressure. The global friction coefficient increases because of strong collisions among particles under low pressure. During shear processes, particle contact distributions in the third-body are regular. The stress profiles in the FEM regions correspond to the force chain distributions in the DEM regions.

An efficient hybrid method for scattering from arbitrary dielectric objects buried under a rough surface: TM case

A hybrid method combining the finite element method (FEM) with the boundary integral equation (BIE) is presented in this paper to investigate two-dimensional (2D) electromagnetic scattering properties of multiple dielectric objects buried beneath a dielectric rough ground for TM case. In traditional FEM simulation, the artificial boundaries, such as perfectly matched layer (PML) and the absorbing boundary conditions (ABC), are usually adopted as truncated boundaries to enclose the whole model. However, the enclosed computational domain increases quickly in size for a rough surface with a large scale, especially for the scattering model of objects away from the rough surface. In the hybrid FEM-BIE method, one boundary integral equation is adopt to depict the scattering above the rough surface based on Green's function. Based on the domain decomposition technique, the computational region below the rough ground is divided into multiple isolated interior regions containing each object and the exterior region. Finite element formulations are only applied inside interior regions to derive a set of linear systems, and another boundary integral formula is developed below the rough surface which also acts as the boundary constraint of the FEM region. Compared with traditional FEM, the hybrid technique presented here is highly efficient in terms of computational memory, time, and versatility. Numerical simulations are carried out based on hybrid FEM-BIE to study the scattering from multiple dielectric objects buried beneath a rough ground.

SGBEM–FEM coupling for analysis of cracks in 3D anisotropic media

AbstractA weakly singular symmetric Galerkin boundary element method (SGBEM) is coupled with the standard finite element method (FEM) in order to establish an accurate and efficient numerical technique for analysis of fractures in three‐dimensional, anisotropic, linearly elastic media. In the strategy, the weakly singular SGBEM developed by Rungamornrat and Mear (textitInt. J. Solids Struct. 2008; 45:1283–1301; Comput. Methods Appl. Mech. Engrg 2008; 197:4319–4332) is utilized to model a small‐scale region containing the crack while the (possibly large and complex) compliment region is treated by the FEM. The coupled technique exploits the positive features of both methods; the SGBEM proves to be a convenient and highly accurate method for obtaining mixed‐mode stress intensity factors along the crack front, whereas the FEM is very efficient for modeling large‐scale problems in the absence of cracks. An important aspect of the formulation and implementation of the technique is that continuity of displacement and traction across the interface between the SGBEM and FEM regions is enforced in a weak sense. This allows the two regions (one modeled by the SGBEM and the other by the FEM) to be discretized independently without the need for the resulting meshes to conform on the interface separating the regions, and this flexibility in the discretization process leads to a significant reduction in the modeling effort. To demonstrate the utility and accuracy of the technique, several boundary value problems involving both embedded and surface breaking cracks are treated, and it is shown that the coupled technique yields highly accurate stress intensity factors that exhibit only a slight dependence upon mesh refinement. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Multiscale simulation of nanoindentation on Ni (1 0 0) thin film

The multiscale simulations of nanoindentation by coupling molecular dynamics (MD) and finite element method (FEM) are performed on Ni (1 0 0) thin film. By means of the indentation curves and the deformation profiles induced by the tip, the coupling for the multiscale model, the indentation curve corresponding to atomic phases and the material properties are examined. The present results reveal that the indentation curve of multiscale simulations exhibits a trend agreement with the atomistic solution. The deformation profile of multiscale model passing from the MD region to the FEM region displays a consistent gradation. The strain energy of the thin film exerted by the tip is stored by the formation of the homogeneous nucleation, and is dissipated by the dislocation sliding of the {1 1 1} plane. As compared with the literature research, the pile-up pattern proves that the crystalline nickel also produces the pile-up phenomenon on the nanoscale. However, the material properties extracted from the indentation curve of multiscale simulations are still higher than the experimental values although a quantitative agreement with the atomistic results is achieved. By the use of multiscale simulations, the compensation of a large specimen for the limitation of MD simulations without significant increase in the problem size is meaningful.

Fully Coupled Hybrid FEM-UTD Method Using NURBS for the Analysis of Radiation Problems

A novel hybrid finite element method (FEM) -uniform theory of diffraction (UTD) method for the analysis of radiating structures in the presence of electrically large objects is presented. The hybridization is done in a fully coupled way taking into account mutual interactions between the FEM and UTD regions. The UTD objects are modeled using non-uniform rational B-spline (NURBS) surfaces. Ray acceleration techniques and simple clustering strategies are used to speed up the computation time. Numerical results are presented showing the validity of the method.

Electric and magnetic losses modeled by a stable hybrid with explicit–implicit time-stepping for Maxwell’s equations

A stable hybridization of the finite-element method (FEM) and the finite-difference time-domain (FDTD) scheme for Maxwell’s equations with electric and magnetic losses is presented for two-dimensional problems. The hybrid method combines the flexibility of the FEM with the efficiency of the FDTD scheme and it is based directly on Ampère’s and Faraday’s law. The electric and magnetic losses can be treated implicitly by the FEM on an unstructured mesh, which allows for local mesh refinement in order to resolve rapid variations in the material parameters and/or the electromagnetic field. It is also feasible to handle larger homogeneous regions with losses by the explicit FDTD scheme connected to an implicitly time-stepped and lossy FEM region. The hybrid method shows second-order convergence for smooth scatterers. The bistatic radar cross section (RCS) for a circular metal cylinder with a lossy coating converges to the analytical solution and an accuracy of 2% is achieved for about 20 points per wavelength. The monostatic RCS for an airfoil that features sharp corners yields a lower order of convergence and it is found to agree well with what can be expected for singular fields at the sharp corners. A careful convergence study with resolutions from 20 to 140 points per wavelength provides accurate extrapolated results for this non-trivial test case, which makes it possible to use as a reference problem for scattering codes that model both electric and magnetic losses.

Problems of Secondary Sources for Hybrid Ray Tracing and FEM Simulation

The indoor propagation simulation of hybrid methods are employed. Usually for microwave band the hybrid method is based on ray tracing. In this case for numerical field calculation in regions with a small obstacles is selected finite element method (FEM). This paper explains solution method for two - dimensional FEM region with a boundary integral mesh truncating. Solving the system of FEM equations and boundary conditions, the field and its normal derivatives on boundary of region are determined. This solution gives orientation and field intensity for secondary source. Ill 4, bibl. 5 (in English; summaries in Lithuanian, English, Russian).

Scattering from a cavity backed microstrip antenna on a bi-anisotropic substrate with a finite ground plane by a hybrid finite element method

A new extended finite element formulation for finding radiation patterns, radar cross section (RCS) and input impedance of planar integrated circuits on a very general bi-anisotropic grounded slab with finite size is presented. The approach is based on a hybrid finite element method (FEM) wherein the electromagnetic fields in the FEM region are coupled to the fields outside by a surface integral equation. Because of the local nature of the FEM, this formalism allows inclusion of the inhomogeneities in the problem domain. Numerical results are compared and agree well with existing published data for various conventional configurations.

Hybrid finite element-Trefftz method for open boundary analysis

Electromagnetic field computation often involves open boundary analysis. Discretization of the exterior region by the finite element method (FEM) is cumbersome and computationally inefficient. This paper discusses a new hybrid finite element-Trefftz (1926) formulation to solve open boundary potential problems with an economic number of degrees of freedom. After the overview of literature, the paper describes the most important theoretical features of the proposed hybrid FEM-TRM formulation which is based on the synthesis of several proposed methods. Then it demonstrates the application of the formulation on a simple example which clearly shows its convergence behavior and reasonable precision both within the FEM region and very far from it. The verification has been carried out by a commercially available general purpose FEM package.

A hybrid finite-element method for axisymmetric waveguide-fed horns

A new method for finding radiation patterns and the reflection coefficients associated with an axisymmetric waveguide fed horn is presented. The approach is based on a hybrid finite element method (FEM) wherein the electromagnetic fields in the FEM region are coupled to the fields outside by two surface integral equations. Because of the local nature of the FEM, this formalism allows for the presence of inhomogeneities to be included in the problem domain. The matrix equation which results from the application of this method is shown to be complex-symmetric. Comparisons of calculated and measured data for two different horns show good agreement.

Analysis of fast transient electromagnetic fields: a frequency dependent 2-D procedure

An automatic procedure for the analysis of 2-D fast transient electromagnetic fields is presented. The fields are analyzed in the frequency domain by means of a node-based finite-element-method (FEM) procedure and the transients are derived by the application of Fourier transforms. The FEM mesh is generated through an algorithm which selects the element size as a function of the wavelength. The conductive regions are automatically removed from the FEM region when the value of the penetration depth is very small, and impedance boundary conditions or perfect electric conductor approximations are imposed. Open boundary conditions are applied at a distance varying with the frequency where the mesh is truncated. The FEM implementation of the proposed procedure is discussed. Numerical results demonstrate the validity of the method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>