Showing papers on "Smoothed finite element method published in 2017"
06 Sep 2017
TL;DR: In this paper, the first two parts -the foundations of solid mechanics and variational methods and the third part -explore the applicability of the finite element method to structural mechanics.
Abstract: The first two parts - ''Foundations of Solid Mechanics and Variational Methods'' and ''Structural Mechanics'' - develop a foundation in variational calculus and energy methods before progressing to the third section, which examines the finite element method and its application to stress, plate, torsion, stability, and dynamics problems. Throughout, the book makes finite elements more understandable in terms of fundamentals; provides the background needed to extrapolate the finite element method to areas of study other than solid mechanics; and shows how to derive working equations of structural mechanics through variational principles and to understand the limits of validity of these equations. New to the Second Edition are chapters on matrix methods for trusses, finite element methods for plane stress problems, and finite element methods for plates and elastic stability.
417 citations
01 Jan 2017
TL;DR: Finite elements theory fast solvers and applications in solid mechanics, but end up in infectious downloads because people juggled with some harmful bugs inside their computer.
Abstract: Thank you for downloading finite elements theory fast solvers and applications in solid mechanics. Maybe you have knowledge that, people have search numerous times for their chosen readings like this finite elements theory fast solvers and applications in solid mechanics, but end up in infectious downloads. Rather than enjoying a good book with a cup of tea in the afternoon, instead they juggled with some harmful bugs inside their computer.
228 citations
TL;DR: In this article, the development and application of the scaled boundary finite element method for fracture analysis is reviewed, with the only limitation that the whole boundary is directly visible from the scaling centre.
120 citations
TL;DR: Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes able to deliver the same optimal convergence rate as traditional quadrilateral and hexahedral approximations.
Abstract: The strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method. In this work, we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes. The main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain. This new strain is then used in the computation of the stiffness matrix. The convergence properties and accuracy of the proposed scheme are discussed by solving a few benchmark problems. Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes able to deliver the same optimal convergence rate as traditional quadrilateral and hexahedral approximations. The accuracy is also improved, and all the methods tested pass the patch test to machine precision.
87 citations
TL;DR: In this paper, the smoothed finite element method using four-node quadrilateral elements (SFEM-Q4) is employed to resolve underwater acoustic radiation problems, which can be regarded as a com...
Abstract: In this work, the smoothed finite element method using four-node quadrilateral elements (SFEM-Q4) is employed to resolve underwater acoustic radiation problems. The SFEM-Q4 can be regarded as a com...
73 citations
TL;DR: In this paper, a novel nonlinear algorithm is developed by introducing internal Gaussian points over a subdomain, and the response of nonlinearity for a concrete-faced rockfill dam is modeled.
60 citations
01 Jan 2017
TL;DR: In this paper, the authors consider a class of finite element methods for discretization of partial differential equations on surfaces, known as the trace finite element method (TraceFEM), where restrictions or traces of background surface independent finite element functions are used to approximate the solution of a PDE on a surface.
Abstract: In this paper we consider a class of unfitted finite element methods for discretization of partial differential equations on surfaces. In this class of methods known as the Trace Finite Element Method (TraceFEM), restrictions or traces of background surface-independent finite element functions are used to approximate the solution of a PDE on a surface. We treat equations on steady and time-dependent (evolving) surfaces. Higher order TraceFEM is explained in detail. We review the error analysis and algebraic properties of the method. The paper navigates through the known variants of the TraceFEM and the literature on the subject.
59 citations
TL;DR: In this paper, the authors used a non-residual penalty term from strain smoothing as a means of stabilizing the mesh-free nodal integration method under the Galerkin framework.
55 citations
TL;DR: In this article, a global numerical approach for lightweight design optimization of laminated composite plates subjected to frequency constraints is presented, in which fiber volume fractions and thicknesses of the layers are continuous variables and the thickness of layers are discrete variables.
53 citations
TL;DR: In this article, the edge-based smoothed finite element (ES/GW-FEM) method was used for the flexible shell and the gradient-weighted finite element method for the acoustic fluid field.
52 citations
TL;DR: In this paper, a band of finite elements is proposed for the buckling analysis of thin-walled members, where the trigonometric longitudinal shape functions of the finite strip method are replaced by polynomial longitudinal shape function, and longitudinal discretization is used, which can readily be termed as constrained (shell) finite element method.
Abstract: In this paper a novel method is employed for the buckling analysis of thin-walled members. The method is basically a shell finite element method, but constraints are applied which enforce the thin-walled member to deform in accordance with specific mechanical criteria, e.g., to force the member to buckle in flexural, or lateral-torsional or distortional mode. The method is essentially similar to the constrained finite strip method, but the trigonometric longitudinal shape functions of the finite strip method are replaced by polynomial longitudinal shape functions, and longitudinal discretization is used, which transform the finite strip into multiple finite elements, that is why the new method can readily be termed as constrained (shell) finite element method. In the companion to this paper a band of finite elements is discussed in detail, where ‘band’ is a segment of the member with one single finite element longitudinally. In this paper the constraining procedure is applied on thin-walled members discretized both in the transverse and longitudinal direction. The possible base systems for the various deformation spaces are demonstrated here, as well as numerous buckling examples are provided to illustrate the potential of the proposed method.
TL;DR: In this article, the stable node-based smoothed finite element method (SNS-FEM) and the well-known Dirichlet-to-Neumann (DtN) boundary condition are coupled together to reduce the dispersion error in analyzing acoustic radiation problems.
Abstract: In this paper, the stable node-based smoothed finite element method (SNS-FEM) and the well-known Dirichlet-to-Neumann (DtN) boundary condition are coupled together to reduce the dispersion error in analyzing acoustic radiation problems. An artificial boundary is introduced to truncate the infinite domain and the DtN boundary condition is imposed on the artificial boundary to guarantee the uniqueness of the solution. In the SNS-FEM formulation, a stable item which contains the gradient variance items is constructed without any uncertain parameter to strengthen the system stiffness. Through this operation, a perfect balance between the stiffness and mass matrices is established and the dispersion error is reduced significantly. Two benchmark cases and two practical engineering problems are employed to investigate the performance of the SNS-FEM. The results demonstrate that the SNS-FEM achieves super accuracy and super convergence. Additionally, the SNS-FEM is less sensitive to the wave number and high-efficiency.
TL;DR: The constrained finite element method as mentioned in this paper is essentially similar to the constrained finite strip method, but the trigonometric longitudinal shape functions are replaced by polynomial longitudinal shape function, which transforms a finite strip into multiple finite elements, and carefully defined constraints are applied which enforce the thinwalled member to deform in accordance with specific mechanical criteria, e.g., to force local, global or distortional deformations.
Abstract: In this paper a novel method for the analysis of thin-walled members is presented: the constrained finite element method. The method is basically a shell finite element analysis, but carefully defined constraints are applied which enforce the thin-walled member to deform in accordance with specific mechanical criteria, e.g., to force local, global or distortional deformations. The constrained finite element method is essentially similar to the constrained finite strip method, but the trigonometric longitudinal shape functions of the finite strip method are replaced by polynomial longitudinal shape functions, which – together with longitudinal discretization – transforms a finite strip into multiple finite elements. This change in longitudinal interpolation makes the method applicable for a wide range of practical problems not yet handled by other modal decomposition methods. The new shell finite element is briefly presented here, but the main focus of this paper is on how the constraining criteria can be applied for a thin-walled member. More specifically, in this paper a band of finite elements is discussed in detail, where ‘band’ is a segment of the member with multiple elements along the cross-section, but with one single finite element longitudinally. The possible base systems for the various deformation spaces are demonstrated here. Members built up from multiple bands are discussed and presented in a companion paper, where various numerical examples are also provided to illustrate the potential of the proposed constrained finite element method.
TL;DR: In this paper, a nonlinear interval perturbation hybrid node-based smoothed finite element method (NIPH-NS/FEM) was proposed to predict the upper and lower bounds of mechanical response of locally resonant acoustic metamaterials with uncertainty parameters such as Young's modulus, Poisson's ratio and density.
Book•
20 Mar 2017
TL;DR: In this article, the authors present an up-to-date exposition on hybrid equilibrium finite elements, which are based on the direct approximation of the stress fields, and the focus is on their derivation and on the advantages that strong forms of equilibrium can have, either when used independently or together with the more conventional displacement based elements.
Abstract: Equilibrium Finite Element Formulations is an up to date exposition on hybrid equilibrium finite elements, which are based on the direct approximation of the stress fields. The focus is on their derivation and on the advantages that strong forms of equilibrium can have, either when used independently or together with the more conventional displacement based elements. These elements solve two important problems of concern to computational structural mechanics: a rational basis for error estimation, which leads to bounds on quantities of interest that are vital for verification of the output and provision of outputs immediately useful to the engineer for structural design and assessment.
Book•
30 Nov 2017
TL;DR: The introduction to finite difference and finite element methods is aimed at graduate students who need to solve differential equations as discussed by the authors, with a focus on numerical algorithms, related mathematical theory, and essential details in the implementation, while some useful packages are also introduced.
Abstract: This introduction to finite difference and finite element methods is aimed at graduate students who need to solve differential equations. The prerequisites are few (basic calculus, linear algebra, and ODEs) and so the book will be accessible and useful to readers from a range of disciplines across science and engineering. Part I begins with finite difference methods. Finite element methods are then introduced in Part II. In each part, the authors begin with a comprehensive discussion of one-dimensional problems, before proceeding to consider two or higher dimensions. An emphasis is placed on numerical algorithms, related mathematical theory, and essential details in the implementation, while some useful packages are also introduced. The authors also provide well-tested MATLAB® codes, all available online.
TL;DR: A robust and efficient form of the smoothed finite element method (S-FEM) is presented to simulate hyperelastic bodies with compressible and nearly-incompressible neo-Hookean behaviour and strain smoothing is at least as accurate and stable, as the MINI element, for an equivalent problem size.
TL;DR: A new convergence analysis is developed that is applicable to C-1 finite element methods, classical nonconforming finiteelement methods and discontinuous Galerkin methods.
Abstract: We consider finite element methods for elliptic distributed optimal control problems with pointwise state constraints on two and three dimensional convex polyhedral domains formulated as fourth order variational inequalities. We develop a new convergence analysis that is applicable to C-1 finite element methods, classical nonconforming finite element methods and discontinuous Galerkin methods.
TL;DR: In this paper, a smoothed finite element method (SFEM), in which the gradient smoothing technique (GST) from mesh-free methods is incorporated into the standard Galerkin variational equation, is proposed to handle the acoustic wave scattering by the obstacles immersed in water.
Abstract: In this work, a smoothed finite element method (SFEM), in which the gradient smoothing technique (GST) from meshfree methods is incorporated into the standard Galerkin variational equation, is proposed to handle the acoustic wave scattering by the obstacles immersed in water. In the SFEM model, only the values of shape functions, not the derivatives at the quadrature points, are required and no coordinate transformation is needed to perform the numerical integration. Due to the softening effects provided by the GST, the original “overly-stiff” FEM model has been properly softened and a more appropriate stiffness of the continuous system can be obtained, then the numerical dispersion error for the acoustic problems is decreased conspicuously and the quality of the numerical solutions can be improved significantly. To tackle the exterior Helmholtz equation in unbounded domains, we use the well-known Dirichlet-to-Neumann (DtN) map to guarantee that there are no spurious reflecting waves from the far field. Numerical tests show that the present SFEM cum DtN map (SFEM-DtN) works well for exterior Helmholtz equation and can provide better solutions than standard FEM.
13 Mar 2017
TL;DR: In this paper, a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh is proposed, which provides a stabilization term which provides control of the jumps in the derivatives of the finite element functions across faces in the vicinity of the boundary.
Abstract: We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element functions across faces in the vicinity of the boundary. We then develop the basic theoretical results including error estimates and estimates of the condition number of the mass and stiffness matrices. We apply the method to the standard displacement problem, the frequency response problem, and the eigenvalue problem. We present several numerical examples including studies of thin bending dominated structures relevant for engineering applications. Finally, we develop a cut finite element method for fibre reinforced materials where the fibres are modeled as a superposition of a truss and a Euler-Bernoulli beam. The beam model leads to a fourth order problem which we discretize using the restriction of the bulk finite element space to the fibre together with a continuous/discontinuous finite element formulation. Here the bulk material stabilizes the problem and it is not necessary to add additional stabilization terms.
TL;DR: In this article, the Reissner-Mindlinear and nonlinear analyses of shear deformable thin and thick arbitrary straight-sided quadrilateral plates are reported using smoothed finite element technique.
Abstract: Linear and nonlinear analyses of shear deformable thin and thick arbitrary straight-sided quadrilateral plates are reported here using smoothed finite element technique. The Reissner-Mindlin plates are discretized with quadrilateral background cells. Then membrane and bending stiffness matrices of background quadrilateral cells are evaluated using edge-based smoothed finite element method(ES-FEM). The shear stiffness matrix is calculated based on "smoothed shear strain approach" and the performance is compared with "edge-consistent four-node quadrilateral finite element". The convergence, accuracy and sensitivity to mesh distortion of the present quadrilateral element is examined. Thereafter, the nonlinear bending and vibration analyses of trapezoidal and arbitrary straight-sided quadrilateral composite plates are presented for which only limited analytical results are available in the literature.
TL;DR: Although both methods are able to give a good prediction, it is observed that, under very large deformation of the medium, GMM lacks robustness due to its meshfree natrue, which makes the definition of the meshless shape functions more difficult and expensive than in MPM.
Abstract: The simulation of large deformation problems, involving complex history-dependent constitutive laws, is of paramount importance in several engineering fields. Particular attention has to be paid to the choice of a suitable numerical technique such that reliable results can be obtained. In this paper, a Material Point Method (MPM) and a Galerkin Meshfree Method (GMM) are presented and verified against classical benchmarks in solid mechanics. The aim is to demonstrate the good behavior of the methods in the simulation of cohesive-frictional materials, both in static and dynamic regimes and in problems dealing with large deformations. The vast majority of MPM techniques in the literatrue are based on some sort of explicit time integration. The techniques proposed in the current work, on the contrary, are based on implicit approaches, which can also be easily adapted to the simulation of static cases. The two methods are presented so as to highlight the similarities to rather than the differences from “standard” Updated Lagrangian (UL) approaches commonly employed by the Finite Elements (FE) community. Although both methods are able to give a good prediction, it is observed that, under very large deformation of the medium, GMM lacks robustness due to its meshfree natrue, which makes the definition of the meshless shape functions more difficult and expensive than in MPM. On the other hand, the mesh-based MPM is demonstrated to be more robust and reliable for extremely large deformation cases.
TL;DR: In this paper, a coupled method for modeling fluid flow in fractured porous media is proposed, which is based on the coupling of the boundary element and finite element methods and is capable of generating both transient flow and steady-state flow responses which are solved in the Laplace domain.
TL;DR: In this article, a tri-layer composed of a positive and a negative temperature-responsive hydrogels layers attached to an elastomeric layer is designed to achieve bi-directional bending while maintaining high strength and stiffness.
TL;DR: In this paper, the authors presented an effective approach to compute the lower bounds of vibration modes or eigenvalues of elasto-dynamic problems, by making use of the important softening effects of node-based S-FEM (NS-FEMS).
Abstract: The smoothed finite element method (S-FEM) has been recently developed as an effective solver for solid mechanics problems. This paper represents an effective approach to compute the lower bounds of vibration modes or eigenvalues of elasto-dynamic problems, by making use of the important softening effects of node-based S-FEM (NS-FEM). We first use NS-FEM, FEM and the analytic approach to compute the eigenvalues of transverse free vibration in strings and membranes. It is found that eigenvalues by NS-FEM are always smaller than those by FEM and the analytic method. However, NS-FEM produces spurious unphysical modes because of overly soft behavior. A technique is then proposed to remove them by analyzing their vibration shapes (eigenvectors). It is observed that spurious modes with excessively large wave numbers, which are unrelated to the physical deflection shapes but related to the discretization density, therefore can be easily removed. The final results of NS-FEM become the lower bound of eigenvalues and the accuracy can be improved via mesh refinement. And NS-FEM solutions (softer) are more reliable, because the large wave number component can be used as an indicator, which is available in FEM (stiffer), on the quality of the numerical solutions. The proposed NS-FEM procedure offers a viable and practical computational means to effectively compute the lower bounds of eigenvalues for solid mechanics problems.
TL;DR: In this paper, a polynomial pressure projection (P3) formulation in the smoothed finite element methods (S-FEMs) is applied to stabilize the pressure solutions for nearly-incompressible and incompressible solids.
Abstract: In this paper, we apply a polynomial pressure projection (P3) formulation in the smoothed finite element methods (S-FEMs) to stabilize the pressure solutions for nearly-incompressible and incompressible solids. The P3 technique, using equal-order approximation, is implemented in the cell-based S-FEM (CS), edge-based S-FEM (ES) and node-based S-FEM (NS) all using simplest triangular element. The proposed P3-S-FEMs (P3-CS, P3-ES, P3-NS) are supposed to address issues of volumetric locking and pressure oscillation using equal-order displacement-pressure approximations. Numerical examples are employed to verify and check performances of the proposed methods, demonstrating that all the P3-S-FEMs are fully volumetric locking free. Except for P3-NS, P3-CS and P3-ES are without pressure oscillation. Another founding of P3-S-FEMs is that P3 technique can further soft the whole system besides S-FEMs. The excellent properties of these S-FEMs for compressible materials are still maintained by P3-S-FEMs, such as the insensitiveness to mesh distortion. The unique upper bound property of NS-FEM is also inherited by P3-NS. In the performance studies, P3-ES stands out on accuracy, convergence and efficiency among three proposed methods.
TL;DR: In this paper, a stable nodal integration method for analyzing coupling problems of electromagnetic field and mechanical field using linear triangular mesh is proposed, whose coefficient matrix is computed using the smoothed shape function derivatives together with the variance terms over the equivalent smoothing domain associated with nodes of the mesh.
TL;DR: In this article, the authors investigated the benefits of a recently developed linear smoothing procedure which provides better approximation to higher-order polynomial fields in the basis, and observed that the stress intensity factors computed through the proposed linear smoothed extended finite element method is more accurate than that obtained through smoothed XFEM.
Abstract: The extended finite element method was introduced in 1999 to treat problems involving discontinuities with no or minimal remeshing through appropriate enrichment functions. This enables elements to be split by a discontinuity, strong or weak, and hence requires the integration of discontinuous functions or functions with discontinuous derivatives over elementary volumes. A variety of approaches have been proposed to facilitate these special types of numerical integration, which have been shown to have a large impact on the accuracy and the convergence of the numerical solution. The smoothed extended finite element method (XFEM), for example, makes numerical integration elegant and simple by transforming volume integrals into surface integrals. However, it was reported in the literature that the strain smoothing is inaccurate when non‐polynomial functions are in the basis. In this paper, we investigate the benefits of a recently developed Linear smoothing procedure which provides better approximation to higher‐order polynomial fields in the basis. Some benchmark problems in the context of linear elastic fracture mechanics are solved and the results are compared with existing approaches. We observe that the stress intensity factors computed through the proposed linear smoothed XFEM is more accurate than that obtained through smoothed XFEM.
TL;DR: In this paper, a stochastic perturbation edge-based smoothed FEM method (SP-ES-FEM) is proposed for the analysis of structural-acoustics problems in the mid-frequency regime.
Abstract: Among the current methods in predicting the response of structural-acoustics problems in mid-frequency regime, some problems such as low accuracy and inability to deal with the uncertainties still need to be solved. To eliminate these issues, a novel stochastic perturbation edge-based smoothed FEM method (SP-ES-FEM) is proposed for the analysis of structural-acoustics problems in this work. The edge-based smoothing technique is applied in the standard FEM approach to soften the over-stiff behavior of structural-acoustics problems aiming to improve the accuracy of deterministic response predictions. Then, this approach, for the first time, intends to introduce the first-order perturbation technique into the edge-based smoothed FEM theory frame especially for the probabilistic analysis of structural-acoustics problems. The response of the coupled systems can be expressed simply as a linear function of all the pre-defined input variables by using the change of variable techniques. Due to the linear relationships of variables and response, the probability density function and cumulative probability density function of the response can be obtained based on the simple mathematical transformation of probability theory. The proposed approach not only improves the numerical accuracy of deterministic output quantities with respect to a given random variable, but also can handle the randomness well in the systems. Two numerical examples for frequency response analysis of random structural-acoustics are presented and verified by Monte Carlo simulation, to demonstrate the effectiveness of the present method.