Showing papers on "Smoothed finite element method published in 2015"
TL;DR: Recent advances on robust unfitted finite element methods on cut meshes designed to facilitate computations on complex geometries obtained from computer‐aided design or image data from applied sciences are discussed and illustrated numerically.
Abstract: We discuss recent advances on robust unfitted finite element methods on cut meshes. These methods are designed to facilitate computations on complex geometries obtained, for example, from computer- ...
636 citations
Book•
17 Dec 2015
TL;DR: This paper focuses on theoretical and practical aspects of least-square finite element methods and includes discussions of what issues enter into their construction, analysis, and performance.
Abstract: Least-squares finite element methods are an attractive class of methods for the numerical
solution of partial differential equations. They are motivated by the desire to recover, in
general settings, the advantageous features of Rayleigh�Ritz methods such as the avoidance of
discrete compatibility conditions and the production of symmetric and positive definite discrete
systems. The methods are based on the minimization of convex functionals that are constructed
from equation residuals. This paper focuses on theoretical and practical aspects of least-square
finite element methods and includes discussions of what issues enter into their construction,
analysis, and performance. It also includes a discussion of some open problems.
422 citations
387 citations
01 Jan 2015
TL;DR: In this paper, the authors propose a finite element analysis procedure for nonlinear elastic systems, including contact problems, and finite element analyses for elastoplastic problems, such as contact failure.
Abstract: Preliminary concepts.- Nonlinear Finite Element Analysis Procedure.- Finite Element Analysis for Nonlinear Elastic Systems.- Finite Element Analysis for Elastoplastic Problems.- Finite Element Analysis for Contact Problems.
346 citations
Book•
23 Feb 2015
TL;DR: In this article, the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics are introduced.
Abstract: Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics • Explores the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. • Covers numerous applications of XFEM including fracture mechanics, large deformation, plasticity, multiphase flow, hydraulic fracturing and contact problems • Accompanied by a website hosting source code and examples
222 citations
Book•
06 Jan 2015
TL;DR: Weak-Form Finite Element Models of Flows of Viscous Incompressible Fluids (FFFLs) as discussed by the authors are a generalization of the finite element method.
Abstract: 1. General Introduction and Mathematical Preliminaries 2. Elements of Nonlinear Continuum Mechanics 3. The Finite Element Method: A Review 4. One-Dimensional Problems Involving a Single Variable 5. Nonlinear Bending of Straight Beams 6. Two-Dimensional Problems Involving a Single Variable 7. Nonlinear Bending of Elastic Plates 8. Nonlinear Bending of Elastic Shells 9. Finite Element Formulations of Solid Continua 10. Weak-Form Finite Element Models of Flows of Viscous Incompressible Fluids 11. Least-Squares Finite Element Models of Flows of Viscous Incompressible Fluids Appendix 1: Solution Procedures for Linear Equations Appendix 2: Solution Procedures for Nonlinear Equations
215 citations
TL;DR: This approach allows the use of general and unstructured space-time finite elements which do not require any tensor product structure and the stability of the numerical scheme is based on a stability condition which holds for standard finite element spaces.
Abstract: Abstract We propose and analyze a space-time finite element method for the numerical solution of parabolic evolution equations. This approach allows the use of general and unstructured space-time finite elements which do not require any tensor product structure. The stability of the numerical scheme is based on a stability condition which holds for standard finite element spaces. We also provide related a priori error estimates which are confirmed by numerical experiments.
112 citations
TL;DR: In this article, the hybrid smoothed finite element method (HS-FEM) using triangular (2D) and tetrahedron (3D) elements that can be generated automatically for any complicated domain is formulated to solve acoustic problems.
86 citations
TL;DR: It is proved that exponential type of convergence can be obtained by the finite cell method for Laplace and Lamé problems in one, two as well as three dimensions.
Abstract: We present a detailed analysis of the convergence properties of the finite cell method which is a fictitious domain approach based on high order finite elements. It is proved that exponential type of convergence can be obtained by the finite cell method for Laplace and Lame problems in one, two as well as three dimensions. Several numerical examples in one and two dimensions including a well-known benchmark problem from linear elasticity confirm the results of the mathematical analysis of the finite cell method.
82 citations
TL;DR: In this paper, a stable node-based smoothed finite element method (SNS-FEM) is proposed for analyzing acoustic problems using linear triangular and tetrahedral elements that can be generated automatically for any complicated configurations.
TL;DR: In this paper, the authors studied a system of advection-diffusion equations in a bulk domain coupled to an advective diffusion equation on an embedded surface and gave a well-posedness analysis for the system of bulk-surface equations and introduced a finite element method for its numerical solution.
Abstract: In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling of transport and diffusion of surfactants in two-phase flows. The model considered here accounts for adsorption-desorption of the surfactants at a sharp interface between two fluids and their transport and diffusion in both fluid phases and along the interface. The paper gives a well-posedness analysis for the system of bulk-surface equations and introduces a finite element method for its numerical solution. The finite element method is unfitted, i.e. , the mesh is not aligned to the interface. The method is based on taking traces of a standard finite element space both on the bulk domains and the embedded surface. The numerical approach allows an implicit definition of the surface as the zero level of a level-set function. Optimal order error estimates are proved for the finite element method both in the bulk-surface energy norm and the L 2 -norm. The analysis is not restricted to linear finite elements and a piecewise planar reconstruction of the surface, but also covers the discretization with higher order elements and a higher order surface reconstruction.
01 Jan 2015
TL;DR: In this article, the numerical modeling of carbon nanotubes based on the finite element method is presented, where the bonds between carbon atoms are considered as connecting load-carrying generalized beam members, while the carbon atoms act as joints of the members.
Abstract: This chapter covers the numerical modeling of carbon nanotubes based on the finite element method. The approach based on a three-dimensional space-frame structure where the bonds between carbon atoms are considered as connecting load-carrying generalized beam members, while the carbon atoms act as joints of the members, is introduced. The assignment of corresponding material and geometric properties is explained in detail.
TL;DR: In this paper, a connection between the smoothed finite element method (SFEM) and the virtual element method was made and a new stable approach to strain smoothing for polygonal/polyhedral elements was proposed.
Abstract: Summary
We show both theoretically and numerically a connection between the smoothed finite element method (SFEM) and the virtual element method and use this approach to derive stable, cheap and optimally convergent polyhedral FEM. We show that the stiffness matrix computed with one subcell SFEM is identical to the consistency term of the virtual element method, irrespective of the topology of the element, as long as the shape functions vary linearly on the boundary. Using this connection, we propose a new stable approach to strain smoothing for polygonal/polyhedral elements where, instead of using sub-triangulations, we are able to use one single polygonal/polyhedral subcell for each element while maintaining stability. For a similar number of degrees of freedom, the proposed approach is more accurate than the conventional SFEM with triangular subcells. The time to compute the stiffness matrix scales with the O(dofs)1.1 in case of the conventional polygonal FEM, while it scales as O(dofs)0.7 in the proposed approach. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. Copyright © 2015 John Wiley & Sons, Ltd.
TL;DR: Three-dimensional selective smoothed finite element method with edge-based and node-based strain smoothing techniques for nonlinear anisotropic large deformation analyses of nearly incompressible cardiovascular tissues and outperforms the standard FEM and other S-FEMs.
Abstract: This paper presents a three-dimensional selective smoothed finite element method with edge-based and node-based strain smoothing techniques (3D-ES/NS-FEM) for nonlinear anisotropic large deformation analyses of nearly incompressible cardiovascular tissues. 3D-ES/NS-FEM owns several superior advantages, such as the robustness against the element distortions and superior computational efficiency, etc. To simulate the large deformation experienced by cardiovascular tissues, the static and explicit dynamic 3D-ES/NS-FEMs are derived correspondingly. Performance contest results show that 3D-ES/NS-FEM-T4 outperforms the standard FEM and other S-FEMs. Furthermore, this 3D-ES/NS-FEM-T4 is applied to analyze intact common carotid artery undergo mean blood pressure and passive inflation of anatomical rabbit bi-ventricles. The results are validated with the reference solutions, and also demonstrate that present 3D-ES/NS-FEM-T4 is a powerful and efficient numerical tool to simulate the large deformation of anisotropic tissues in cardiovascular systems.
TL;DR: In this paper, a finite element method for convection-diffusion problems on a given time dependent surface, for instance modeling the evolution of a surfactant, is presented.
TL;DR: In this paper, a coupled smoothed finite element method (S-FEM) is developed to deal with the structural-acoustic problems consisting of a shell configuration interacting with the fluid medium.
Abstract: In this paper, a coupled smoothed finite element method (S-FEM) is developed to deal with the structural-acoustic problems consisting of a shell configuration interacting with the fluid medium. Three-node triangular elements and four-node tetrahedral elements that can be generated automatically for any complicated geometries are adopted to discretize the problem domain. A gradient smoothing technique (GST) is introduced to perform the strain smoothing operation. The discretized system equations are obtained using the smoothed Galerkin weakform, and the numerical integration is applied over the further formed edge-based and face-based smoothing domains, respectively. To extend the edge-based smoothing operation from plate structure to shell structure, an edge coordinate system is defined local on the edges of the triangular element. Numerical examples of a cylinder cavity attached to a flexible shell and an automobile passenger compartment have been conducted to illustrate the effectiveness and accuracy of the coupled S-FEM for structural-acoustic problems.
TL;DR: In this article, a novel selective smoothed finite element method (S-FEM) in multi-material domain using triangular and tetrahedral elements is proposed to overcome the locking problem in the numerical homogenization of incompressible materials.
TL;DR: FS/NS-FEM-TET4 is a promising alternative other than FEM in passive cardiac mechanics and is comparable with higher-order FEM, such as 10-node tetrahedral elements.
Abstract: Summary
The smoothed FEM (S-FEM) is firstly extended to explore the behavior of 3D anisotropic large deformation of rabbit ventricles during the passive filling process in diastole. Because of the incompressibility of myocardium, a special method called selective face-based/node-based S-FEM using four-node tetrahedral elements (FS/NS-FEM-TET4) is adopted in order to avoid volumetric locking. To validate the proposed algorithms of FS/NS-FEM-TET4, the 3D Lame problem is implemented. The performance contest results show that our FS/NS-FEM-TET4 is accurate, volumetric locking-free and insensitive to mesh distortion than standard linear FEM because of absence of isoparametric mapping. Actually, the efficiency of FS/NS-FEM-TET4 is comparable with higher-order FEM, such as 10-node tetrahedral elements. The proposed method for Holzapfel myocardium hyperelastic strain energy is also validated by simple shear tests through the comparison outcomes reported in available references. Finally, the FS/NS-FEM-TET4 is applied in the example of the passive filling of MRI-based rabbit ventricles with fiber architecture derived from rule-based algorithm to demonstrate its efficiency. Hence, we conclude that FS/NS-FEM-TET4 is a promising alternative other than FEM in passive cardiac mechanics. Copyright © 2015 John Wiley & Sons, Ltd.
Book•
01 Jan 2015
TL;DR: The control volume finite element method (CVFEM) as discussed by the authors was proposed to bridge the gap between finite difference and finite element methods, using the advantages of both methods for simulation of multiphysics problems in complex geometries.
Abstract: Control volume finite element methods (CVFEM) bridge the gap between finite difference and finite element methods, using the advantages of both methods for simulation of multi-physics problems in complex geometries. In Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method, CVFEM is covered in detail and applied to key areas of thermal engineering. Examples, exercises, and extensive references are used to show the use of the technique to model key engineering problems such as heat transfer in nanofluids (to enhance performance and compactness of energy systems), hydro-magnetic techniques in materials and bioengineering, and convective flow in fluid-saturated porous media. The topics are of practical interest to engineering, geothermal science, and medical and biomedical sciences. * Introduces a detailed explanation of Control Volume Finite Element Method (CVFEM) to provide for a complete understanding of the fundamentals* Demonstrates applications of this method in various fields, such as nanofluid flow and heat transfer, MHD, FHD, and porous media * Offers complete familiarity with the governing equations in which nanofluid is used as a working fluid* Discusses the governing equations of MHD and FHD* Provides a number of extensive examples throughout the book* Bonus appendix with sample computer code
17 Jul 2015
TL;DR: In this paper, a framework of smoothed finite element method (S-FEM) for modeling anisotropic crystalline plasticity is presented to simulate the mechanical behavior with rate-independence.
TL;DR: In this article, a low-order single-point quadrature finite element suitable for dynamic 3D analysis of saturated soils is presented, which uses a u-p formulation to consider the interaction of the pore fluid and solid skeleton.
TL;DR: In this article, a displacement-based Galerkin mesh-free method was proposed for the analysis of nearly-incompressible linear elastic solids, where low-order simplicial tessellations (i.e., 3-node triangular or 4-node tetrahedral meshes) were used as a background structure for numerical integration of the weak form integrals and to get the nodal information for the computation of the meshfree basis functions.
TL;DR: In this paper, a specific computational program SAFEM was developed based on semi-analytical finite element (FE) method for analysis of asphalt pavement structural responses under static loads, and the reliability and efficiency of this program was proved by comparison with the general commercial FE software ABAQUS.
Abstract: A specific computational program SAFEM was developed based on semi-analytical finite element (FE) method for analysis of asphalt pavement structural responses under static loads. The reliability and efficiency of this FE program was proved by comparison with the general commercial FE software ABAQUS. In order to further reduce the computational time without decrease of the accuracy, the infinite element was added to this program. The results of the finite-infinite element coupling analysis were compared with those of finite element analysis derived from the verified FE program. The study shows that finite-infinite element coupling analysis has higher reliability and efficiency.
TL;DR: In this paper, a rigorous theoretical framework is presented to show stability, convergence and accuracy of improved edge-based and face-based smoothed finite element methods (bES-FEM and bFS-FEMS) for nearly-incompressible elasticity problems.
TL;DR: In this paper, a higher-order 3D finite element method was proposed for the simulation of fully compositional, three-phase and multi-component flow. And the phase behavior was described by cubic or cubic-plus-association (CPA) equations of state.
Abstract: The formation and development of patterns in the unstable interface between an injected fluid and hydrocarbons or saline aqueous phase in a porous medium can be driven by viscous effects and gravity. Numerical simulation of the so-called fingering is a challenge, which requires rigorous representation of the fluid flow and thermodynamics as well as highresolution discretization in order to minimize numerical artifacts. To achieve such a high resolution, we present higherorder 3D finite element methods for the simulation of fully compositional, three-phase and multi-component flow. This is based on a combination of the mixed hybrid finite element (MHFE) method for total fluid velocity and discontinuous Galerkin (DG) method for the species transport. The phase behavior is described by cubic or cubic-plus-association (CPA) equations of state. We present challenging numerical examples of compositionally triggered fingering at both the core and the large scale. Four additional test cases illustrate the robustness and efficiency of the proposed methods, which demonstrate their power for problems of this complexity. Results reveal three orders of magnitude improvement in CPU time in our method compared with the lowest-order finite difference method for some of the examples. Comparison between 3D and 2D results highlights the significance of dimensionality in the flow simulation.
01 Jan 2015
TL;DR: Because of the highly nonlinear and discontinuous nature of contact problems, great care and trial-and-error are necessary to obtain solutions to practical problems.
Abstract: When two or more bodies collide, contact occurs between two surfaces of the bodies so that they cannot overlap in space. Metal formation, vehicle crash, projectile penetration, various seal designs, and bushing and gear systems are only a few examples of contact phenomena. This chapter is organized as follows. In Sect. 5.2, simple one-point contact examples are presented in order to show the characteristics of contact phenomena and possible solution strategies. In Sect. 5.3, a general formulation of contact is presented based on the variational formulation. Sect. 5.4 focuses on finite element discretization and numerical integration of the contact variational form. Three-dimensional contact formulation is presented in Sect. 5.5 . From the finite element point of view, all formulations involve use of some form of a constraint equation. Because of the highly nonlinear and discontinuous nature of contact problems, great care and trial-and-error are necessary to obtain solutions to practical problems. Section 5.6 presents modeling issues related to contact analysis, such as selecting slave and master bodies, removing rigid-body motions, etc.
TL;DR: In this paper, a finite element formulation for a non-local particle method is proposed for elasticity and fracture analysis of 2D solids, which is based on a new particle method which incorporates a nonlocal multi-body particle interaction into the conventional pair-wise particle interactions.
TL;DR: In this paper, the topology optimization design of the continuum structures under static load is formulated on the basis of node-based smoothed finite element method (NS-FEM).
Abstract: The node-based smoothed finite element method (NS-FEM) proposed recently has shown very good properties in solid mechanics, such as providing much better gradient solutions. In this paper, the topology optimization design of the continuum structures under static load is formulated on the basis of NS-FEM. As the node-based smoothing domain is the sub-unit of assembling stiffness matrix in the NS-FEM, the relative density of node-based smoothing domains serves as design variables. In this formulation, the compliance minimization is considered as an objective function, and the topology optimization model is developed using the solid isotropic material with penalization (SIMP) interpolation scheme. The topology optimization problem is then solved by the optimality criteria (OC) method. Finally, the feasibility and efficiency of the proposed method are illustrated with both 2D and 3D examples that are widely used in the topology optimization design.