Showing papers on "Smoothed finite element method published in 2018"
TL;DR: The smoothed finite element methods (S-FEM) as discussed by the authors are a family of methods formulated through carefully designed combinations of the standard FEM and some of the techniques from the mesh free methods.
Abstract: The smoothed finite element methods (S-FEM) are a family of methods formulated through carefully designed combinations of the standard FEM and some of the techniques from the meshfree methods. Studies have proven that S-FEM models behave softer than the FEM counterparts using the same mesh structure, often produce more accurate solutions, higher convergence rates, and much less sensitivity to mesh distortion. They work well with triangular or tetrahedral mesh that can be automatically generated, and hence are ideal for automated computations and adaptive analyses. Some S-FEM models can also produce upper bound solution for force driving problems, which is an excellent unique complementary feature to FEM. Because of these attractive properties, S-FEM has been applied to numerous problems in the disciplines of material mechanics, biomechanics, fracture mechanics, plates and shells, dynamics, acoustics, heat transfer and fluid–structure interactions. This paper reviews the developments and applications of the S-FEM in the past ten years. We hope this review can shed light on further theoretical development of S-FEM and more complex practical applications in future.
204 citations
TL;DR: In this paper, a novel approach to couple ordinary state-based peridynamics (OSPD) with node-based smoothed finite element method (NS-FEM) is proposed, where the physical information is transmitted mutually from local to non-local regions, which is governed by the unified coupling equations of motion.
88 citations
TL;DR: In this paper, a high-order finite element method for the discretization of partial differential equations on stationary smooth surfaces which are implicitly described as the zero level of a level set function is presented.
Abstract: We present a new high-order finite element method for the discretization of partial differential equations on stationary smooth surfaces which are implicitly described as the zero level of a level set function. The discretization is based on a trace finite element technique. The higher discretization accuracy is obtained by using an isoparametric mapping of the volume mesh, based on the level set function, as introduced in [C. Lehrenfeld, Comp. Meth. Appl. Mech. Engrg., 300 (2016), pp. 716--733]. The resulting trace finite element method is easy to implement. We present an error analysis of this method and derive optimal order $H^1(\Gamma)$-norm error bounds. A second topic of this paper is a unified analysis of several stabilization methods for trace finite element methods. Only a stabilization method which is based on adding an anisotropic diffusion in the volume mesh is able to control the condition number of the stiffness matrix also for the case of higher-order discretizations. Results of numerical e...
54 citations
TL;DR: In this paper, the authors proposed a cell-based Smoothed Finite Element Method (CS-FEM) with the semi-implicit Characteristic-Based Split (CBS) scheme for computational fluid dynamics (CFD).
Abstract: Summary
In this paper, the cell-based Smoothed Finite Element Method (CS-FEM) with the semi-implicit Characteristic-Based Split (CBS) scheme (CBS/CS-FEM) is proposed for computational fluid dynamics (CFD). The 3-node triangular (T3) element and 4-node quadrilateral (Q4) element are employed for present CBS/CS-FEM for two-dimensional flows. The 8-node hexahedral element (H8) is used for three-dimensional flows. Two types of CS-FEM are implemented in this paper. One is standard CS-FEM with quadrilateral gradient smoothing cells for Q4 element and hexahedron cells for H8 element. Another is called as n-sided CS-FEM (nCS-FEM) whose gradient smoothing cells are triangles for Q4 element and pyramids for H8 element. To verify the proposed methods, benchmarking problems are tested for two-dimensional and three-dimensional flows. The benchmarks show that CBS/CS-FEM and CBS/nCS-FEM are capable to solve incompressible laminar flow, and can produce reliable results for both steady and unsteady flows. The proposed CBS/CS-FEM method has merits on better robustness against distorted mesh with only slight more computation time and without losing accuracy, which is important for problems with heavy mesh distortion. The blood flow in carotid bifurcation is also simulated to show capabilities of proposed methods for realistic and complicated flow problems.
47 citations
TL;DR: In this article, a phase field model in the framework of cell-based smoothed finite element method (CS-FEM) aiming to solve problems of brittle fracture in solids is developed.
42 citations
TL;DR: With the improvement of local velocity reconstruction, advanced searching algorithms and code parallelization, the proposed Sharp-ISFEM method has shown great promises for complex engineering flows with higher Reynolds number.
36 citations
TL;DR: In this article, a generalized stochastic edge-based smoothed finite element method is proposed for Reissner-Mindlin plate problems, which improves the numerical accuracy of deterministic output quantities with respect to a given random variable, but also overcomes the inherent drawbacks of conventional second-order perturbation approach.
24 citations
TL;DR: The cell-based smoothed finite element method (CS-FEM) is introduced into two mainstream aspects of computational fluid dynamics: incompressible flows and fluid–structure interaction (FSI).
Abstract: In this paper the cell-based smoothed finite element method (CS-FEM) is introduced into two mainstream aspects of computational fluid dynamics: incompressible flows and fluid–structure interaction (FSI). The emphasis is placed on the fluid gradient smoothing which simply requires equal numbers of Gaussian points and smoothing cells in each four-node quadrilateral element. The second-order, smoothed characteristic-based split scheme in conjunction with a pressure stabilization is then presented to settle the incompressible Navier–Stokes equations. As for FSI, CS-FEM is applied to the geometrically nonlinear solid as usual. Following an efficient mesh deformation strategy, block-Gauss–Seidel procedure is adopted to couple all individual fields under the arbitrary Lagriangian–Eulerian description. The proposed solvers are carefully validated against the previously published data for several benchmarks, revealing visible improvements in computed results.
23 citations
TL;DR: 2 simple but effective alternatives to improve the characteristic‐based split–based partitioned semi‐implicit coupling algorithm for fluid‐structure interaction by introducing the end‐of‐step velocity into the implicit stages of the 2 algorithms integrating different splits.
22 citations
TL;DR: In this paper, the cell-based smoothed finite element method (CS-FEM) was integrated with the phase-field technique to model brittle fracture in 3D elastic solids.
Abstract: The cell based smoothed finite element method (CS-FEM) was integrated with the phase-field technique to model brittle fracture in 3D elastic solids. The CS-FEM was used to model the mechanics behavior and the phase-field method was used for diffuse fracture modeling technique where the damage in a system was quantified by a scalar variable. The integrated CS-FEM phase-field approach provides an efficient technique to model complex crack topologies in three dimensions. The detailed formulation of our combined method is provided. It was implemented in the commercial software ABAQUS using its user-element (UEL) and user-material (UMAT) subroutines. The coupled system of equations were solved in a staggered fashion using the in-built non-linear Newton–Raphson solver in ABAQUS. Eight node hexahedral (H8) elements with eight smoothing domains were coded in CS-FEM. Several representative numerical examples are presented to demonstrate the capability of the method. We also discuss some of its limitations.
TL;DR: In this article, a semi-discrete Galerkin mixed finite element method was proposed to solve the Rosenau equation by employing splitting technique, and error estimates were established in one space dimension.
Abstract: Mixed finite element methods are applied to the Rosenau equation by employing splitting technique The semi-discrete methods are derived using $$C^0-$$
piecewise linear finite elements in spatial direction The existence of unique solutions of the semi-discrete and fully discrete Galerkin mixed finite element methods is proved, and error estimates are established in one space dimension An extension to problem in two space variables is also discussed It is shown that the Galerkin mixed finite finite element have the same rate of convergence as in the classical methods without requiring the LBB consistency condition At last numerical experiments are carried out to support the theoretical claims
TL;DR: In this paper, the cell-based smoothed finite element using quadrilateral elements (CS-FEM) is used for 2D contact problems which are converted into linear complementarity problems (LCPs), which can be solved efficiently using the Lemke method.
TL;DR: An efficient periodic mesh generation scheme for representative volume elements (RVEs) of inclusion-reinforced composites is proposed with the aid of an element-carving technique as discussed by the authors.
TL;DR: In this article, an edge-based smoothed finite element method (ES-FEM) is presented to solve electromagnetic field problems, where the analysis domain is discretized into a set of tetrahedron cells that can be easily generated automatically for complicated domains.
TL;DR: In this article, a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain is proposed, based on a quasi-Lagrangian formulation of the problem.
TL;DR: Results show that the present SNS-F EM can provide very high precision solution for thermo-elastic equations and is more efficient than original NS-FEM and the standard FEM.
TL;DR: A simple finite element method for solving first order hyperbolic equations with easy implementation and analysis designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra.
TL;DR: In this article, an inhomogeneous cell-based smoothed finite element method (ICS-FEM) was proposed to overcome the overstiffness and imprecise magnetoelectroelastic coupling effects of FEM.
Abstract: To overcome the overstiffness and imprecise magnetoelectroelastic coupling effects of finite element method (FEM), we present an inhomogeneous cell-based smoothed FEM (ICS-FEM) of functionally graded magnetoelectroelastic (FGMEE) structures. Then the ICS-FEM formulations for free vibration calculation of FGMEE structures were deduced. In FGMEE structures, the true parameters at the Gaussian integration point were adopted directly to replace the homogenization in an element. The ICS-FEM provides a continuous system with a close-to-exact stiffness, which could be automatically and more easily generated for complicated domains, thus significantly decreasing the numerical error. To verify the accuracy and trustworthiness of ICS-FEM, we investigated several numerical examples and found that ICS-FEM simulated more accurately than the standard FEM. Also the effects of various equivalent stiffness matrices and the gradient function on the inherent frequency of FGMEE beams were studied.
01 Jan 2018
TL;DR: Chapter 3 presents the fundamentals of the Stochastic Finite Element Method in the framework of the stochastic formulation of the virtual work principle, and the concept of the variability response function is developed and generalized for general stoChastic finite element systems.
Abstract: Chapter 3 presents the fundamentals of the Stochastic Finite Element Method in the framework of the stochastic formulation of the virtual work principle. The resulting stochastic partial differential equations are solved with either non-intrusive Monte Carlo simulation methods, or intrusive approaches such as the versatile spectral stochastic finite element method. Additional approximate methodologies such as the Neumann and Taylor series expansion methods are also presented together with some exact analytic solutions that are available for statically determinate stochastic structures. The concept of the variability response function is then developed and generalized for general stochastic finite element systems.
TL;DR: In this paper, the singular edge-based smoothed finite element method (sES-FEM) using triangular mesh with a special layer of five-noded singular elements (sT5) connected to the singular point was proposed to model fracture problems in solids.
Abstract: The singular edge-based smoothed finite element method (sES-FEM) using triangular (T3) mesh with a special layer of five-noded singular elements (sT5) connected to the singular point, was proposed to model fracture problems in solids. This paper aims to extend the previous studies on singular fields of any order from −0.5 to 0, by developing an analytical means for integration to obtain the smoothed strains. We provide a more efficient practical formulae to estimate the stress intensity factor(SIF) for singular fields of mentioned order. The sT5 element has an additional node at each of the two edges connected to the crack tip, and the displacements are enriched with necessary terms to simulate the singularity. A weakened weak (W2) formulation is used to avoid the differentiation to the assumed displacement functions. The stiffness matrix is computed by using the smoothed strains calculated analytically from the enriched shape functions. Furthermore, our analytical integration techniques reduces the dependency on the order of numerical integration during the computation of the smoothed strain matrix. Several examples have been presented to demonstrate the reliability of the proposed method, excellent agreement between numerical results and reference observations shows that sES-FEM is an efficient numerical tool for predicting the SIF for singular fields.
TL;DR: A treatment for dealing with moving boundaries in FSI problems with an immersed solid is proposed in the framework of local remeshing, and by adopting a surrounding cell around a submerged solid, ill-shaped meshes occurring due to solid motion is reconstructed effectively.
TL;DR: A straightforward implementation of cell-based smoothed finite element method (CS-FEM) into fluid-structure interaction from the arbitrary Lagriangian-Eulerian perspective, followed by partitioned implicit coupling scheme based upon fixed-point iterations is adopted to interconnect individual fields.
TL;DR: In this article, a new four-node hybrid stress element is proposed using a node-based smoothing technique of tetrahedral mesh, which is expressed by nodal displacements and no additional variables.
Abstract: Summary
In this paper, a new four-node hybrid stress element is proposed using a node-based smoothing technique of tetrahedral mesh. The conditions for hybrid stress field required are summarized and the field should be continuous for better performance of a constant-strain tetrahedral element. Nodal stress is approximated by the node-based smoothing technique and the stress field is interpolated with standard shape functions. This stress field is linear within each element and continuous across elements. The stress field is expressed by nodal displacements and no additional variables. The element stiffness matrix is calculated using the Hellinger-Reissner functional, which guarantees the strain field from displacement field to be equal to that from the stress field in a weak sense. The performance of the proposed element is verified by through several numerical examples.
TL;DR: In this paper, a new finite element method is introduced to study the time-dependent wave nature of the electron in quantum resonance devices, where an inter-element matrix is formed to smooth the derivatives over the edges.
Abstract: In this paper, a new finite element method (FEM) is introduced to study the time-dependent wave nature of the electron in quantum resonance devices. Unlike the well-known FEM, the new method smooths the wave function derivatives over the edges. In this sense, the new method is termed “smoothed FEM” where an “inter-element” matrix is formed to smooth the derivatives over the edges. For the electron’s wave function propagation in time, the presented method exploits the time domain beam propagation method (TD-BPM). Based only on first order elements, our suggested SFETD-BPM has high accuracy levels comparable to second-order conventional FEM elements; thanks to the element smoothing. The proposed method numerical performance is tested through the analysis of a quantum resonance cavity and a quantum resonant tunneling device. It is clearly demonstrated that the presented method is not only accurate but also more time efficient than the conventional FEM approach.
01 Jan 2018
TL;DR: A simulation framework for the simulation of cable-driven parallel robots including dynamics of the cables is developed and presented, based on the modified rigid-finite element method using rigid bodies and spring-damper elements.
Abstract: Kinematics and dynamics of cable-driven parallel robots are affected by the cables used as force and motion transmitting elements. Flexural rigidity of these cables is of major interest to better understand dynamics of these systems and to improve their accuracy. The approach for modeling spatial cable dynamics, as presented in this paper, is based on the modified rigid-finite element method using rigid bodies and spring-damper elements. With this, a simulation of a planar 3 degrees of freedom cable-driven parallel robot is constructed as a multi-body dynamics model. Under consideration of holonomic constraints and Baumgarte stabilization, a simulation framework for the simulation of cable-driven parallel robots including dynamics of the cables is developed and presented.
TL;DR: By combining finite element method (FEM) and meshfree method, this Quad4-CNS synergizes the individual strengths of these two methods, which leads to higher accuracy, better convergence rate, as well as high tolerance to mesh distortion, which is attractive for geometrical nonlinear solid mechanic problems where excessive distorted meshes occur.
Abstract: In this paper, the performance of a hybrid ‘FE-Meshfree’ quadrilateral element with continuous nodal stress (Quad4-CNS) is investigated for geometrical nonlinear solid mechanic problems. By combining finite element method (FEM) and meshfree method, this Quad4-CNS synergizes the individual strengths of these two methods, which leads to higher accuracy, better convergence rate, as well as high tolerance to mesh distortion. Therefore, Quad4-CNS is attractive for geometrical nonlinear solid mechanic problems where excessive distorted meshes occur. For geometrical nonlinear analysis, numerical results show that the results of Quad4-CNS element are much better than those of four-node isoparametric quadrilateral element (Quad4), and are comparable to quadratic quadrilateral element (Quad8) and other hybrid ‘FE- Meshfree’ elements.
TL;DR: In this paper, the authors apply the mesh-free method to the numerical simulation of geophysical electromagnetic prospecting, taking the 2D magnetotelluric as an example and deduce the corresponding meshfree radial point interpolation method (RPIM) equivalent linear equations in detail.
Abstract: As an important supplement and development of traditional methods, the meshfree method has received a great deal of attention in the field of engineering calculation, and has been successfully used to solve many problems which traditional methods have difficulty in solving. However, the application of meshfree method is relatively less in the area of geophysics. In this paper, we apply the meshfree method to the numerical simulation of geophysical electromagnetic prospecting, taking the 2D magnetotelluric as an example and deduce the corresponding meshfree radial point interpolation method (RPIM) equivalent linear equations in detail. The high-efficiency and accurate solutions of large-scale sparse linear equations are solved by the quasi-minimal residual method based on Krylov subspace. The optimal values of the shape parameters are given by numerical experiments. The correctness of the meshfree method is verified by a layered model. The root mean square error of the calculation results is no more than 0...
TL;DR: The edge-based smoothed finite element method (ES-FEM) and reduced-basis method are combined to form an efficient on-line algorithm for the optimal design of multi-material structures under thermal loads.