Meshfree methods operations can also be complicated and. 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. Smoothed finite element method sfem is a relatively new fe formulation proposed by g. The 2d and 3d demonstrative examples are shown in section 4 to verify the applicability of smoothed finite element method. Smoothed finite element methods sfem are a particular class of numerical simulation algorithms for the simulation of physical phenomena. Request pdf smoothed finite element methods generating a quality finite element mesh is difficult and often very timeconsuming. Developed by the authors and their colleagues, the smoothed finite element method sfem only re. A hybrid smoothed finite element method for predicting the. 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. It was developed by combining meshfree methods with the finite element method. Smoothed finite element approach for kinematic limit analysis.
Theory, implementation, and practice november 9, 2010 springer. A novel coupling approach of smoothed finite element. A gradient stable nodebased smoothed finite element method. The curvature at each point is obtained by a nonlocal approximation via a smoothing function. Largedeformation plasticity analysis using the edgebased. Finite element and smoothed particle hydrodynamics. In the early 1960s, engineers used the method for approximate solutions of problems. 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. Abstract this paper examines the theoretical bases for the smoothed finite element method sfem, which was formulated by incorporating. Apr 19, 2016 smoothed finite element methods ebook written by g.
Smoothed finite element method sfem was introduced by application of the stabilized conforming nodal integration in the conventional finite element method. 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. 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. Spectral element methods combine the geometric flexibility of finite elements and the acute. Download smoothed finite element methods in pdf and epub formats for free. The field is the domain of interest and most often represents a physical structure.
Homogenization for composite material properties using. Logan pdf, a first course in the finite element method, fourth edition by daryl l. Extended finite element and meshfree methods timon rabczuk. For the quadrilateral elements, when the number of sc of the. This implementation is accomplished by employing the user element subroutine uel. 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. Introduction to finite element analysis fea or finite. Finite element and smoothed particle hydrodynamics modeling.
Pdf a smoothed finite element method for shell analysis. 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. 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. Facebased smoothed finite element method for realtime simulation of soft tissue andrea mendizabal a, r emi bessard duparc, huu phuoc buib, christoph j. Smoothed adaptive finite element methods candidate. A quadrilateral element with smoothed curvatures for mindlinreissner plates is proposed. 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. Meshless numerical modeling of brittleviscous deformation. Index terms finite element method fem, gauss quadrature. The 2d and 3d demonstrative examples are shown in section 4 to verify the applicability of smoothed finite element method in numerical homogenization.
We will demonstrate through intensive case studies the significant. Pdf smoothed extended finite element method for continua. 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. The present method, named edgenodebased sfem ensfem, uses a gradient smoothing technique over smoothing domains based on a combination of es. Download for offline reading, highlight, bookmark or take notes while you read smoothed finite element methods. 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. 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. We discretize the kinematic variables of position and. An edgebased smoothed finite element method for wave scattering by an obstacle in elastic media. 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. Extended finite element and meshfree methods 1st edition. 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. 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. In the cellbased smoothed finite element method, the total design domain w is first divided into ne elements as in the finite element method.
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. The field is the domain of interest and most often represents a. The smoothed finite element method sfem proposed by liu et al. An adaptive finite element pml method for the acoustic. Selective smoothed finite element methods for extremely large. The sfem, smoothed finite element methods, are a particular class of numerical simulation algorithms for the simulation of physical phenomena. Many smoothing approaches have been developed, such as the cellbased 65, nodalbased 66, edgebased 67 and facebased 68 sfem. In this paper, transient heat transfer problems are analyzed using the smoothed finite element methods sfems with explicit time integration. Smoothed finite element methods with tetrahedral elements in large deformation elastoplastic analysis yuki onishi tokyo institute of technology, japan p. Jul 24, 2014 download smoothed finite element methods generating a quality finite element mesh is difficult and often very timeconsuming. Paulus, igor peterlik a, and st ephane cotin ainria nancy grand est, 54603 villerslesnancy, france.
A hybrid smoothed finite element method for predicting the sound. Pdf application of smoothed finite element method in coupled. When a constant smoothing function is chosen, area integration becomes line integration along cell boundaries and no derivative of shape functions is. In addition, a linear exactness can be guaranteed in the solution of galerkin weakform based meshfree methods. A smoothed finite element method for mechanics problems. 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. It indicates that the smooth technique can effectively soften the overly stiff fem model. Then reconnects elements at nodes as if nodes were pins or drops of glue that hold elements together. Pdf the smoothed finite element methods sfem are a family of methods formulated through carefully designed combinations of the. Jan 26, 2018 finite element method pdf full book, finite element method daryl l. Facebased smoothed finite element method for realtime. Pdf download smoothed finite element methods free unquote. Logan, finite element simulations with ansys workbench 15 pdf download, finite element analysis pdf book title.
For simplicity, a piecewise constant function is applied here, which is assumed to be constant within c and vanish somewhere else, as given. 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. 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. In this paper, we implement the strain projection idea to formulate and code a novel method, smoothed finite element method. In this paper, we incorporate cellwise strain smoothing operations into conventional finite elements and propose the smoothed finite element method sfem for. Pdf homogenization for composite material properties. Recent advances in smoothed finite element methods with. Sfem are applicable to solid mechanics as well as fluid dynamics problems, although so far they have mainly been applied to the former. An edgebased smoothed finite element method for analysis. Galerkin meshfree method which shows higher efficiency, desired accuracy and convergent properties 3. 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. However this complicates the numerical integration of. Developed by the authors and their colleagues, the smoothed finite element method sfem.
In this paper, the smoothed finite element methods sfems are developed to analyse the effective mechanical properties of composite materials. This book also addresses their implementation and provides small matlab codes on each subtopic. Section 3 presents the formulation of smoothed finite element methods in numerical homogenization. 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. Generating a quality finite element mesh is difficult and often very timeconsuming. 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. A modified smoothed finite element method msfem for. 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. Structural topology optimization based on the smoothed. This process results in a set of simultaneous algebraic equations. Meshfree methods operations can also be complicated and quite costly in terms of computational effort and resources. On smoothed finite element methods asme international.
Selective cellbased smoothed finite element method using. The bending stiffness matrix is calculated by a boundary integral along the boundaries of the smoothing elements smoothing cells. A gradient stable nodebased smoothed finite element. 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. 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. A modified smoothed finite element method for static and free. Highorder curvilinear finite element methods for lagrangian. Stochastic stable nodebased smoothed finite element. Finite this is the origin of the name, finite element. In this work, a modified sfem using fournode quadrilateral elements is proposed, which greatly reduces further the computation cost while maintaining the high. There are several types of sfems depending on the location of strain smoothing. An abaqus uel implementation of the smoothed finite.
In this paper, we discuss the implementation of a cell based smoothed finite element method csfem within the commercial finite element software abaqus. Theoretical aspects of the smoothed finite element method sfem. 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. Dangtrung et al smoothed finite element methods sfem. Finite element method pdf full book finite element. Performance of smoothed finite element methods with. Stability analysis of smoothed finite element methods with. Smoothed finite element methods book also available for read online, mobi, docx and mobile and kindle reading.
We present a general formulation for the analysis of fluidstructure interaction problems using the particle finite element method pfem. Hence the wellknown issue of the shape distortion of isoparametric elements can be resolved. These models are found having a number of important and theoretically profound properties. Boundary value problems are also called field problems. This thesis herein proposes a stochastic stable nodebased smoothed finite element method for uncertainty and reliability analysis of thermomechanica. 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. Smoothed finite element methods request pdf researchgate. Studies have proven that sfem models behave softer than the fem counterparts using the same mesh structure, often produce more accurate solutions.
The smoothed finite element methods sfem are a family of methods formulated through carefully designed combinations of the standard. It has a family of models carefully designed with innovative types of smoothing domains. A first course in the finite element method authors. 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. Pdf homogenization for composite material properties using. 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. The element is a combination of a plate bending and membrane element. A smoothed finite element method for plate analysis. It is based on mixed interpolation where the bending and. 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. A hybrid smoothed finite element method hsfem to solid. A combined scheme of edgebased and nodebased smoothed. Dispersion error reduction for acoustic problems using the.
A smoothed finite element method sfem for linear and geometrically. 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. 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. Liuthis content was downloaded from ip address 157. The smoothing techniquebased method was originally proposed in the mechanical field. According to the smoothed theory, the exact solution is bounded by the results of the nsfem and fsfem.
153 1446 227 1138 89 925 1022 272 1184 474 1450 851 1426 1344 707 1209 962 534 1398 1619 20 1479 546 471 1230 1309 1175 574 549 1495 178 581