Liu extended the strain smoothing technique in meshless method to the finite element method and named the resulting method the smoothed finite element method sfem 15, 16. Structural topology optimization based on the smoothed. However this complicates the numerical integration of. The element is a combination of a plate bending and membrane element. The smoothing techniquebased method was originally proposed in the mechanical field. Smoothed finite element methods with tetrahedral elements in large deformation elastoplastic analysis yuki onishi tokyo institute of technology, japan p.
For simplicity, a piecewise constant function is applied here, which is assumed to be constant within c and vanish somewhere else, as given. Finite this is the origin of the name, finite element. Generating a quality finite element mesh is difficult and often very timeconsuming. A modified smoothed finite element method msfem for. The salient feature of the csfem is that it does not require an explicit form of the derivative of the shape functions and there is no isoparametric mapping. An edgebased smoothed finite element method for analysis. A gradient stable nodebased smoothed finite element method. In the cellbased smoothed finite element method, the total design domain w is first divided into ne elements as in the finite element method. This thesis herein proposes a stochastic stable nodebased smoothed finite element method for uncertainty and reliability analysis of thermomechanica. Smoothed finite element method sfem for elastic problems zenan huoa, gang mei a, nengxiong xu aschool of engineering and technology, china university of geosciences beijing, 83, beijing, china abstract the smoothed finite element method sfem proposed by liu g.
Developed by the authors and their colleagues, the smoothed finite element method sfem only re. This paper presents a gradient stable nodebased smoothed finite element method gsfem which resolves the temporal instability of the nodebased smoothed finite element method nsfem while significantly improving its accuracy. In this paper, a hybrid smoothed finite element method hsfem is developed for solid mechanics problems by combining techniques of finite element method fem and nodebased smoothed finite element method nsfem using a triangular mesh. Highorder curvilinear finite element methods for lagrangian. Pdf download smoothed finite element methods free unquote. On smoothed finite element methods asme international. Extended finite element and meshfree methods timon rabczuk. The smoothed finite element method sfem proposed recently is more accurate and has higher convergence rate compared with standard fournode isoparametric finite element method fem. Smoothed finite element method sfem is a relatively new fe formulation proposed by g. Facebased smoothed finite element method for realtime.
In the early 1960s, engineers used the method for approximate solutions of problems. Smoothed finite element methods request pdf researchgate. A quadrilateral element with smoothed curvatures for mindlinreissner plates is proposed. Stochastic stable nodebased smoothed finite element. In this paper, we implement the strain projection idea to formulate and code a novel method, smoothed finite element method sfem 4, 5, which combines the existing fem technology with the strain smoothing technique. Index terms finite element method fem, gauss quadrature. In the gsfem, the strain is expanded at the first order by taylor expansion in a nodesupported domain, and the strain gradient is then smoothed within each. In this paper, the smoothed finite element methods sfems are developed to analyse the effective mechanical properties of composite materials. Fem using triangular type of elements has been found capable to produce upper bound solutions to the exact solutions for force driving static solid mechanics problems due to its monotonic soft behavior. In this paper, transient heat transfer problems are analyzed using the smoothed finite element methods sfems with explicit time integration. It indicates that the smooth technique can effectively soften the overly stiff fem model. Pdf the smoothed finite element methods sfem are a family of methods formulated through carefully designed combinations of the. The curvature at each point is obtained by a nonlocal approximation via a smoothing function.
Many smoothing approaches have been developed, such as the cellbased 65, nodalbased 66, edgebased 67 and facebased 68 sfem. A smoothed finite element method for plate analysis. The sfem, smoothed finite element methods, are a particular class of numerical simulation algorithms for the simulation of physical phenomena. Paulus, igor peterlik a, and st ephane cotin ainria nancy grand est, 54603 villerslesnancy, france. Galerkin meshfree method which shows higher efficiency, desired accuracy and convergent properties 3. A combined scheme of edgebased and nodebased smoothed. The first is an arbitrary lagrangianeulerian alebased fluid model coupled to a structural finite element fe method alefefe, and the second is a smoothed particle hydrodynamics sph method coupled to the same structural fe code sphfe. Selective cellbased smoothed finite element method using. Jul 24, 2014 download smoothed finite element methods generating a quality finite element mesh is difficult and often very timeconsuming. One possibility to improve the modeling of brittle faulting within the context of the finite element method fem method is the use of split nodes as demonstrated.
Recent advances in smoothed finite element methods with. Then reconnects elements at nodes as if nodes were pins or drops of glue that hold elements together. It has a family of models carefully designed with innovative types of smoothing domains. We discretize the kinematic variables of position and. Finite element and smoothed particle hydrodynamics. Stability analysis of smoothed finite element methods with. Jan 26, 2018 finite element method pdf full book, finite element method daryl l. Boundary value problems are also called field problems.
Dispersion error reduction for acoustic problems using the. Extended finite element and meshfree methods 1st edition. Scientific article 3d finite element analysis of the modular prosthesis with tooth mechanism of the femoral shaft jianfeng zhang, md, phd1, yongcheng hu, md, phd2, baocang wang, md1, lei wang, md, phd3, hui wang, md1, yong li, md1, ming yan, md1, hongtao liu, md1 department of 1osteopathy and 3trauma surgery, the second hospital of tangshan, tangshan and 2department of orthopaedic. Finite element and smoothed particle hydrodynamics modeling. The field is the domain of interest and most often represents a physical structure. The paper presents an overview of the smoothed finite element methods sfem which are formulated by combining the existing standard fem with the strain smoothing techniques used in the meshfree methods.
Logan pdf, a first course in the finite element method, fourth edition by daryl l. Studies have proven that sfem models behave softer than the fem counterparts using the same mesh structure, often produce more accurate solutions. In this work, a modified sfem using fournode quadrilateral elements is proposed, which greatly reduces further the computation cost while maintaining the high. Smoothed finite element approach for kinematic limit analysis. Finite element method pdf full book finite element. Sfem are applicable to solid mechanics as well as fluid dynamics problems, although so far they have mainly been applied to the former. The smoothed finite element method sfem proposed by liu et al. In this paper, we discuss the implementation of a cell based smoothed finite element method csfem within the commercial finite element software abaqus. Pdf homogenization for composite material properties using. Logan, finite element simulations with ansys workbench 15 pdf download, finite element analysis pdf book title. The 2d and 3d demonstrative examples are shown in section 4 to verify the applicability of smoothed finite element method.
A novel coupling approach of smoothed finite element. Developed by the authors and their colleagues, the smoothed finite element method sfem. Pdf homogenization for composite material properties. A hybrid smoothed finite element method for predicting the. According to the smoothed theory, the exact solution is bounded by the results of the nsfem and fsfem.
These methods include the original extended finite element method, smoothed extended finite element method xfem, phantom node method, extended meshfree methods, numerical manifold method and extended isogeometric analysis. Selective cellbased smoothed finite element method using 10node tetrahedral elements for large deformation of nearly incompressible solids yuki onishi tokyo institute of technology, japan p. Download smoothed finite element methods in pdf and epub formats for free. Smoothed finite element methods book also available for read online, mobi, docx and mobile and kindle reading. However, the standard finite element method fem leads to an overlystiff model which gives poor accuracy especially using triangular elements in 2d or tetrahedral elements in 3d with coarse mesh. Abstract this paper examines the theoretical bases for the smoothed finite element method sfem, which was formulated by incorporating.
For the quadrilateral elements, when the number of sc of the. The finite element method fem, or finite element analysis fea, is a computational technique used to obtain approximate solutions of boundary value problems in engineering. Hence the wellknown issue of the shape distortion of isoparametric elements can be resolved. We will demonstrate through intensive case studies the significant. Smoothed finite element methods sfem are a particular class of numerical simulation algorithms for the simulation of physical phenomena. Meshless numerical modeling of brittleviscous deformation. Request pdf smoothed finite element methods generating a quality finite element mesh is difficult and often very timeconsuming. Dangtrung et al smoothed finite element methods sfem. As we prove mathematically and show numerically in a short communication to be published in computer methods in applied mechanics and engineering, in the context of continuum elements, the smoothed finite element method yields solutions comprised between the standard, displacement based fem and equilibrium, stress based elements. Meshfree methods operations can also be complicated and. Facebased smoothed finite element method for realtime simulation of soft tissue andrea mendizabal a, r emi bessard duparc, huu phuoc buib, christoph j. An abaqus uel implementation of the smoothed finite. In addition, a linear exactness can be guaranteed in the solution of galerkin weakform based meshfree methods.
The field is the domain of interest and most often represents a. Homogenization for composite material properties using. This book also addresses their implementation and provides small matlab codes on each subtopic. Theory, implementation, and practice november 9, 2010 springer. This implementation is accomplished by employing the user element subroutine uel. Pdf a smoothed finite element method for shell analysis. The smoothed finite element method sfem, which was recently introduced for solving the mechanics and acoustic problems, uses the gradient smoothing technique to operate over the cell. We present a general formulation for the analysis of fluidstructure interaction problems using the particle finite element method pfem. Sep 15, 2015 in this paper, a combined scheme of edgebased smoothed finite element method esfem and nodebased smoothed finite element method nsfem for triangular reissnermindlin flat shells is developed to improve the accuracy of numerical results. Introduction to finite element analysis fea or finite. An adaptive finite element pml method for the acoustic. It is based on mixed interpolation where the bending and. In this paper, we implement the strain projection idea to formulate and code a novel method, smoothed finite element method.
Pdf application of smoothed finite element method in coupled. Apr 02, 2014 the paper presents an overview of the smoothed finite element methods sfem which are formulated by combining the existing standard fem with the strain smoothing techniques used in the meshfree methods. Selective smoothed finite element methods for extremely large. By employing different smoothed finite element sfe methods, the kinematic limit analysis approach has been presented by using three noded triangular elements to solve plane strain and plane stress stability problems on basis of the mohrcoulomb yield criterion. A modified smoothed finite element method for static and free. A hybrid smoothed finite element method for predicting the sound. Largedeformation plasticity analysis using the edgebased. Jun, 2018 the first is an arbitrary lagrangianeulerian alebased fluid model coupled to a structural finite element fe method alefefe, and the second is a smoothed particle hydrodynamics sph method coupled to the same structural fe code sphfe.
A gradient stable nodebased smoothed finite element. A fournode quadrilateral shell element with smoothed membranebending based on mindlinreissner theory is proposed. A smoothed finite element method for mechanics problems. Rong liu, selective smoothed finite element methods for extremely large deformation of anisotropic incompressible bio. Download for offline reading, highlight, bookmark or take notes while you read smoothed finite element methods. Smoothed finite element method sfem was introduced by application of the stabilized conforming nodal integration in the conventional finite element method. Smoothed adaptive finite element methods candidate. A smoothed finite element method sfem for linear and geometrically. When a constant smoothing function is chosen, area integration becomes line integration along cell boundaries and no derivative of shape functions is. In this paper, the smoothed finite element method sfem is proposed for 2d elastic problems by incorporation of the cellwise strain smoothing operation into the conventional finite elements. Section 3 presents the formulation of smoothed finite element methods in numerical homogenization. An edgebased smoothed finite element method for wave scattering by an obstacle in elastic media. It was developed by combining meshfree methods with the finite element method. Studies have proven that sfem 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.
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. The key feature of the pfem is the use of a lagrangian description to model the motion of nodes particles in both the fluid and the structure domains. Theoretical aspects of the smoothed finite element method sfem. Pdf smoothed extended finite element method for continua.
A hybrid smoothed finite element method hsfem to solid. Spectral element methods combine the geometric flexibility of finite elements and the acute. In this method, the traditional nodebased and facebased smoothed finite element methods are mixed to form a new smoothed model through constructing the mixed smoothing domains. The smoothed finite element methods sfem are a family of methods formulated through carefully designed combinations of the standard fem and some of the techniques from the meshfree methods. Performance of smoothed finite element methods with. A first course in the finite element method authors. The bending stiffness matrix is calculated by a boundary integral along the boundaries of the smoothing elements smoothing cells. For a numerical method with spatial discretization, the computational cost per time step in the explicit method is less than that in the implicit method, but the time step is much smaller in the. Abstractin this paper, the smoothe d finite element method sfem is proposed for 2d elastic problems by incorporation of the cellwise strain smoothing operation into the conventional finite elements.
There are several types of sfems depending on the location of strain smoothing. The present method, named edgenodebased sfem ensfem, uses a gradient smoothing technique over smoothing domains based on a combination of es. Nov 21, 2016 the smoothed finite element methods sfem are a family of methods formulated through carefully designed combinations of the standard fem and some of the techniques from the meshfree methods. These models are found having a number of important and theoretically profound properties. In this paper, we incorporate cellwise strain smoothing operations into conventional finite elements and propose the smoothed finite element method sfem for. The sfem uses cellbased smoothing domains created by further dividing the elements quadrilateral or nsided polygonal into one or more smoothing cells sc, as shown in fig. Moving load by a cellbased smoothed triangular plate element h. The smoothed finite element methods sfem are a family of methods formulated through carefully designed combinations of the standard. This process results in a set of simultaneous algebraic equations.
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