Showing papers on "Smoothed finite element method published in 2014"

Finite Element Solution of Boundary Value Problems: Theory and Computation

Abstract: Finite Element Solution of Boundary Value Problems: Theory and Computation provides a thorough, balanced introduction to both the theoretical and the computational aspects of the finite element method for solving boundary value problems for partial differential equations. Although significant advances have been made in the finite element method since this book first appeared in 1984, the basics have remained the same, and this classic, well-written text explains these basics and prepares the reader for more advanced study. Useful as both a reference and a textbook, complete with examples and exercies, it remains as relevant today as it was when originally published. This book is written for advanced undergraduate and graduate students in the areas of numerical analysis, mathematics, and computer science, as well as for theoretically inclined practitioners in engineering and the physical science.

A Simple Introduction to the Mixed Finite Element Method

Abstract: Introduction.- The Babuska-Brezzi Theory.- Raviart-Thomas Spaces.- Mixed Finite Element Methods.

A Simple Introduction to the Mixed Finite Element Method: Theory and Applications

Abstract: Introduction.- The Babuska-Brezzi Theory.- Raviart-Thomas Spaces.- Mixed Finite Element Methods.

Understanding the Discrete Element Method: Simulation of Non-Spherical Particles for Granular and Multi-body Systems

Abstract: Understanding the Discrete Element Method: Simulation of ... Understanding the Discrete Element Method: Simulation of ... Understanding the Discrete Element Method: Simulation of ... Understanding the Discrete Element Method eBook by Hans ... Understanding the Discrete Element Method : Simulation of ... Pharmaceutical Powder Process Modeling using DEM Discrete element method Wikipedia Understanding the Discrete Element Method: Simulation of ... Understanding The Discrete Element Method Modelling Complex Particle–Fluid Flow with a Discrete ... Understanding the Discrete Element Method | Wiley Online Books (PDF) Understanding the Discrete Element Method ... Understanding the discrete element method : simulation of ...

The Extended Finite Element Method

Abstract: This chapter discusses level-set topology optimization methods where the governing state equations are discretized by the Extended Finite Element Method (XFEM). In contrast to conventional methods that map the level-set function into a density distribution of a fictitious material, the XFEM allow preserving the crisp geometry information of level-sets in the mechanical model. A brief introduction into the XFEM will be provided and its application to topology optimization will be illustrated with problems in fluid mechanics.

Analysis of coupled structural-acoustic problems based on the smoothed finite element method (S-FEM)

Abstract: The smoothed finite element method (S-FEM) developed recently shows great efficiency in solving solid mechanics and acoustics problems. In this paper, coupled structural-acoustic problems are studied using the S-FEM method. Three-node triangular elements and four-node tetrahedral elements are used to discretize the two-dimensional and three-dimensional domains, respectively. The gradient field of the problem is smoothed using gradient smoothing operations over the edge-based and face-based smoothing domains in two-dimensional plate and three-dimensional fluid, respectively. Because the gradient smoothing technique can provide a proper softening effect to the “overly-stiff” FEM model, significant improvements are achieved on the accuracy of solution for the coupled systems. Typical numerical examples have been conducted to verify the effectiveness of the S-FEM for coupled structural-acoustic problems.

Three-Dimensional Solid Brick Element Using Slopes in the Absolute Nodal Coordinate Formulation

Abstract: The present paper contributes to the field of flexible multibody systems dynamics. Two new solid finite elements employing the absolute nodal coordinate formulation are presented. In this formulation, the equations of motion contain a constant mass matrix and a vector of generalized gravity forces, but the vector of elastic forces is highly nonlinear. The proposed solid eight node brick element with 96 degrees of freedom uses translations of nodes and finite slopes as sets of nodal coordinates. The displacement field is interpolated using incomplete cubic polynomials providing the absence of shear locking effect. The use of finite slopes describes the deformed shape of the finite element more exactly and, therefore, minimizes the number of finite elements required for accurate simulations. Accuracy and convergence of the finite element is demonstrated in nonlinear test problems of statics and dynamics. [DOI: 10.1115/1.4024910]

Finite Elements Methods in Mechanics

Abstract: This book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams and elasticity with detailed derivations for the mass, stiffness and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poissons equation. The second computer program handles the two dimensional elasticity problems and the third one presents the three dimensional transient heat conduction problems. The programs are written in C++ environment.

Analysis of functionally graded material plates using triangular elements with cell-based smoothed discrete shear gap method

Abstract: A cell-based smoothed finite element method with discrete shear gap technique is employed to study the static bending, free vibration, and mechanical and thermal buckling behaviour of functionally graded material (FGM) plates. The plate kinematics is based on the first-order shear deformation theory and the shear locking is suppressed by the discrete shear gap method. The shear correction factors are evaluated by employing the energy equivalence principle. The material property is assumed to be temperature dependent and graded only in the thickness direction. The effective properties are computed by using the Mori-Tanaka homogenization method. The accuracy of the present formulation is validated against available solutions. A systematic parametric study is carried out to examine the influence of the gradient index, the plate aspect ratio, skewness of the plate, and the boundary conditions on the global response of the FGM plates. The effect of a centrally located circular cutout on the global response is also studied.

A stabilized finite element method for advection-diffusion equations on surfaces

Abstract: A recently developed Eulerian finite element method is applied to solve advectiondiffusion equations posed on hypersurfaces. When transport processes on a surface dominate over diffusion, finite element methods tend to be unstable unless the mesh is sufficiently fine. The paper introduces a stabilized finite element formulation based on the SUPG technique. An error analysis of the method is given. Results of numerical experiments are presented that illustrate the performance of the stabilized method.

A cell-based smoothed finite element method using three-node shear-locking free Mindlin plate element (CS-FEM-MIN3) for dynamic response of laminated composite plates on viscoelastic foundation

Abstract: A cell-based smoothed finite element method using three-node Mindlin plate element (CS-FEM-MIN3) based on the first-order shear deformation theory (FSDT) was recently proposed for static and dynamic analyses of Mindlin plates. In this paper, the CS-FEM-MIN3 is extended and incorporated with damping-spring systems for dynamic responses of sandwich and laminated composite plates resting on viscoelastic foundation subjected to a moving mass. The plate-foundation system is modeled as a discretization of three-node triangular plate elements supported by discrete springs and dashpots at the nodal points representing the viscoelastic foundation. The position of the moving mass with specified velocity on triangular elements at any time is defined, and then the moving mass is transformed into loads at nodes of elements. The accuracy and reliability of the proposed method is verified by comparing its numerical solutions with those of others available numerical results. A parametric examination is also conducted to determine the effects of various parameters on the dynamic response of the plates on the viscoelastic foundation subjected to a moving mass.

A Review on Recent Contribution of Meshfree Methods to Structure and Fracture Mechanics Applications

Abstract: Meshfree methods are viewed as next generation computational techniques. With evident limitations of conventional grid based methods, like FEM, in dealing with problems of fracture mechanics, large deformation, and simulation of manufacturing processes, meshfree methods have gained much attention by researchers. A number of meshfree methods have been proposed till now for analyzing complex problems in various fields of engineering. Present work attempts to review recent developments and some earlier applications of well-known meshfree methods like EFG and MLPG to various types of structure mechanics and fracture mechanics applications like bending, buckling, free vibration analysis, sensitivity analysis and topology optimization, single and mixed mode crack problems, fatigue crack growth, and dynamic crack analysis and some typical applications like vibration of cracked structures, thermoelastic crack problems, and failure transition in impact problems. Due to complex nature of meshfree shape functions and evaluation of integrals in domain, meshless methods are computationally expensive as compared to conventional mesh based methods. Some improved versions of original meshfree methods and other techniques suggested by researchers to improve computational efficiency of meshfree methods are also reviewed here.

Finite Element Modeling

Abstract: This chapter primarily conducted the finite element analysis of the dynamic response of soil around the tunnel under dynamic load induced by the subway train; the main work and conclusions are summarized as below: 1. This chapter analyzed the mechanism of the generation of dynamic load induced by subway train and simulated it by programming in ANSYS. 2. According to the field investigation and data from the boreholes, we developed a 3D finite element numerical model by inputting the relevant data. 3. For obtaining accurate results without too large computational domain, artificial boundary was applied to simulate the soil body in the discretization of this model. 4. The dynamic response of the soil in the model was consistent to the data obtained from the field test. And the results were proved effective and reliable. 5. According to the calculation results, σ z ′ propagates further in vertical direction, while σ x ′ propagates further in the horizontal direction. Furthermore, the influence range of the dynamic load was determined by this model.

A temporal stable node-based smoothed finite element method for three-dimensional elasticity problems

Abstract: A stabilized node-based smoothed finite element method (sNS-FEM) is formulated for three-dimensional (3-D) elastic-static analysis and free vibration analysis In this method, shape functions are generated using finite element method by adopting four-node tetrahedron element The smoothed Galerkin weak form is employed to create discretized system equations, and the node-based smoothing domains are used to perform the smoothing operation and the numerical integration The stabilization term for 3-D problems is worked out, and then propose a strain energy based empirical rule to confirm the stabilization parameter in the formula The accuracy and stability of the sNS-FEM solution are studied through detailed analyses of benchmark cases and actual elastic problems In elastic-static analysis, it is found that sNS-FEM can provide higher accuracy in displacement and reach smoother stress results than the reference approaches do And in free vibration analysis, the spurious non-zero energy modes can be eliminated effectively owing to the fact that sNS-FEM solution strengths the original relatively soft node-based smoothed finite element method (NS-FEM), and the natural frequency values provided by sNS-FEM are confirmed to be far more accurate than results given by traditional methods Thus, the feasibility, accuracy and stability of sNS-FEM applied on 3-D solid are well represented and clarified

Selective smoothed finite element methods for extremely large deformation of anisotropic incompressible bio‐tissues

Abstract: Two dynamic selective smoothed FEM (selective S-FEM) are proposed for analysis of extremely large deformation of anisotropic incompressible bio-tissues using the simplest four-node tetrahedron elements. In the present two Selective S-FEMs, the method that consists of the face-based smoothed FEM (FS-FEM) used for the deviatoric part of deformation and the node-based smoothed FEM (NS-FEM) used for the volumetric part is called FS/NS-FEM; another method that replaces the deviatoric part of deformation in the first one by the edge-based smoothed FEM (3D-ES-FEM) is call 3D-ES/NS-FEM. Both selective S-FEMs can achieve outstanding accuracy, and stability of volumetric locking free. This is because the NS-FEM offers an ‘overly-soft’ feature (in contrast to the standard FEM ‘overly-stiff’ model), which can be used to effectively mitigate the volumetric locking, and on the other hand, the 3D-ES-FEM and FS-FEM produce close to exact stiffness for the discretized model leading to accurate solution. Numerical examples are presented to examine the performance of the selective S-FEM methods, including soft bio-tissues that may be isotropic, transversely isotropic, and anisotropic arterial layered materials. The present methods are found having good accuracy and performance. The examples also demonstrate that the proposed methods are very robust and possess remarkable capabilities of handling element distortion, which is very useful for simulating soft materials including bio-tissues. Copyright © 2014 John Wiley & Sons, Ltd.

A physically and geometrically nonlinear scaled‐boundary‐based finite element formulation for fracture in elastomers

Abstract: SUMMARY This paper is devoted to the formulation of a plane scaled boundary finite element with initially constant thickness for physically and geometrically nonlinear material behavior. Special two-dimensional element shape functions are derived by using the analytical displacement solution of the standard scaled boundary finite element method, which is originally based on linear material behavior and small strains. These 2D shape functions can be constructed for an arbitrary number of element nodes and allow to capture singularities (e.g., at a plane crack tip) analytically, without extensive mesh refinement. Mapping these proposed 2D shape functions to the 3D case, a formulation that is compatible with standard finite elements is obtained. The resulting physically and geometrically nonlinear scaled boundary finite element formulation is implemented into the framework of the finite element method for bounded plane domains with and without geometrical singularities. The numerical realization is shown in detail. To represent the physically and geometrically nonlinear material and structural behavior of elastomer specimens, the extended tube model and the Yeoh model are used. Numerical studies on the convergence behavior and comparisons with standard Q1P0 finite elements demonstrate the correct implementation and the advantages of the developed scaled boundary finite element. Copyright © 2014 John Wiley & Sons, Ltd.

Finite cell method compared to h-version finite element method for elasto-plastic problems

Abstract: The finite cell method (FCM) combines the high-order finite element method (FEM) with the fictitious domain approach for the purpose of simple meshing. In the present study, the FCM is used to the Prandtl-Reuss flow theory of plasticity, and the results are compared with the h-version finite element method (h-FEM). The numerical results show that the FCM is more efficient compared to the h-FEM for elasto-plastic problems, although the mesh does not conform to the boundary. It is also demonstrated that the FCM performs well for elasto-plastic loading and unloading.

A new hybrid smoothed FEM for static and free vibration analyses of Reissner---Mindlin Plates

Abstract: A new smoothed finite element method (S-FEM) is proposed using hybrid smoothing operations based on nodes and edges of the mesh for static and free vibration analyses of plates governed by the Reissner---Mindlin plate theory. In the present approach, both the node-based smoothed finite element method (NS-FEM) and edge-based smoothed finite element method (ES-FEM) are utilized in a careful designed manner to overcome the shear locking. The formulations use 3-node triangular elements for easy automatic mesh creation, and linear interpolation functions are used for simplicity and robustness. The bending strains field are smoothed by the means of gradient smoothing technique over smoothing domains constructed by element edges, while the shear strains filed is smoothed based on the combination of NS-FEM and ES-FEM with a proper weightage controlled by a coefficient. A simple formula is developed for automatic selection of the coefficient by considering mesh size and thickness of the plate. For easy reference, the present technique is termed as NS+ES-FEM. The numerical examples demonstrate that the proposed method passes the shear-locking test and improves accuracy of the solution.

Modeling fluid injection in fractures with a reservoir simulator coupled to a boundary element method

Abstract: We describe an algorithm for modeling saturated fractures in a poroelastic domain in which the reservoir simulator is coupled with a boundary element method. A fixed stress splitting is used on the underlying fractured Biot system to iteratively couple fluid and solid mechanics systems. The fluid system consists of Darcy’s law in the reservoir and is computed with a multipoint flux mixed finite element method, and a Reynolds’ lubrication equation in the fracture solved with a mimetic finite difference method. The mechanics system consists of linear elasticity in the reservoir and is computed with a continuous Galerkin method, and linear elasticity in the fracture is solved with a weakly singular symmetric Galerkin boundary element method. This algorithm is able to compute both unknown fracture width and unknown fluid leakage rate. An interesting numerical example is presented with an injection well inside of a circular fracture.

The Partition of Unity Finite Element Method for the simulation of waves in air and poroelastic media

Abstract: Recently Chazot et al. [J. Sound Vib. 332, 1918–1929 (2013)] applied the Partition of Unity Finite Element Method for the analysis of interior sound fields with absorbing materials. The method was shown to allow a substantial reduction of the number of degrees of freedom compared to the standard Finite Element Method. The work is however restricted to a certain class of absorbing materials that react like an equivalent fluid. This paper presents an extension of the method to the numerical simulation of Biot's waves in poroelastic materials. The technique relies mainly on expanding the elastic displacement as well as the fluid phase pressure using sets of plane waves which are solutions to the governing partial differential equations. To show the interest of the method for tackling problems of practical interests, poroelastic-acoustic coupling conditions as well as fixed or sliding edge conditions are presented and numerically tested. It is shown that the technique is a good candidate for solving noise control problems at medium and high frequency.

Solution bound and nearly exact solution to nonlinear solid mechanics problems based on the smoothed FEM concept

Abstract: Node-based and edge-based smoothed FEM (NS-FEM and ES-FEM), and α -FEM are extended to solve nonlinear problems. The nonlinear strain field is smoothed using the gradient smoothing. The continuous scalar scaling factor α enables the α -FEM continuously transforming from overestimated model to underestimated model. Numerical examples reveal that ES-FEM is a robust and stable method with high accuracy and computational efficiency for nonlinear problems. The exact solution in strain energy of force driven problems can be bounded by NS-FEM and FEM. The α -FEM can also be “tuned” to find nearly exact solution to nonlinear mechanics problems of solids of complicated geometry.