Showing papers on "Extended 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
TL;DR: In this article, a dual-horizon peridynamics (DH-PD) formulation for fracture in granular and rock-like materials is presented, which does not require any representation of the crack surface and criteria to treat complex fracture patterns such as crack branching and coalescence.
156 citations
TL;DR: The approach is shown to be an efficient means of simulating the three-dimensional non-linear behaviour of masonry under monotonic in-plane, out of plane and cyclic loads and the novel use of XFEM in simulating crack propagation within masonry units without initial definition of crack location is detailed.
143 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: By Brouwer fixed point theorem and fractional Gagliardo-Nirenberg inequality, it is proved the fully discrete system is uniquely solvable.
Abstract: In this paper, a class of nonlinear Riesz space-fractional Schrodinger equations are considered. Based on the standard Galerkin finite element method in space and Crank-Nicolson difference method in time, the semi-discrete and fully discrete systems are constructed. By Brouwer fixed point theorem and fractional Gagliardo-Nirenberg inequality, we prove the fully discrete system is uniquely solvable. Moreover, we focus on a rigorous analysis and consideration of the conservation and convergence properties for the semi-discrete and fully discrete systems. Finally, a linearized iterative finite element algorithm is introduced and some numerical examples are given to confirm the theoretical results.
102 citations
TL;DR: In this paper, a reduction technique is proposed in a tightly coupled model in which the equilibrium and flow continuity equations are solved simultaneously by the Newton-Raphson method, which can significantly accelerate the simulation without worsening the convergence or losing the computational accuracy.
91 citations
TL;DR: In this article, a mesoscale simulation methodology was proposed to predict the progressive damage and resultant failure of carbon fiber reinforced plastic laminates (CFRPs) by modeling the deformation and deformation of fiber matrix.
Abstract: This study seeks to establish a high-fidelity mesoscale simulation methodology that can predict the progressive damage and resultant failure of carbon fiber reinforced plastic laminates (CFRPs). In the proposed scheme, the plastic behavior (i.e., pre-peak nonlinear hardening in the local stress-strain response) is characterized through the pressure-dependent elasto-plastic constitutive law. The evolution of matrix cracking and delamination, which result in post-peak softening in the local stress-strain response, is modeled through cohesive zone models (CZM). The CZM for delamination is introduced through an interface element, but the CZM for matrix cracking is introduced through an extended finite element method (XFEM). Additionally, longitudinal failure, which is dominated by fiber breakage and typically depends on the specimen size, is modeled by the Weibull criterion. The validity of the proposed methodology was tested against an off-axis compression (OAC) test of unidirectional (UD) laminates and an open-hole tensile (OHT) test of quasi-isotropic (QI) laminates. Finally, sensitivity studies were performed to investigate the effect of plasticity and thermal residual stress against the prediction accuracy in the OHT simulation.
91 citations
TL;DR: In this paper, a local mesh refinement approach for fracture analysis of 3D linear elastic solids is developed, considering both 3-D straight and curved planar cracks, and a structural coupling scheme employing variable-node transition hexahedron elements is presented.
90 citations
TL;DR: In this article, the authors presented the numerical simulation and validation of a fatigue propagation test of a semi-elliptical crack located at the side of the rectangular section of a beam subjected to four-point bending.
87 citations
TL;DR: In this article, the authors considered the problem of energy-minimal multiple crack propagation in a linear elastic solid under quasi-static conditions and proposed an energy minimization approach to solve the problem.
79 citations
TL;DR: In this article, a comparative study between Hashin damage criterion and the eXtended Finite Element Method (XFEM) applied to the failure of fiber reinforced polymers (FRP) is presented.
Abstract: This paper presents a comparative study between Hashin damage criterion and the eXtended Finite Element Method (XFEM) applied to the failure of fiber reinforced polymers (FRP). A brief literature review on failure criteria to predict the failure of FRP is firstly presented. Then, finite element models of square plates with different layer configurations, containing a circular hole with distinct radii and subjected to monotonic uniaxial tension are described within the framework of ABAQUS package. The models are validated by comparison between the numerical results and those of a benchmark model. Finally, the influence of (i) stacking sequence, (ii) hole radii and (iii) failure criteria (Hashin and XFEM) on the load vs. elongation paths, stresses distributions and collapse configurations of the plates is shown and discussed and some conclusions are drawn.
TL;DR: A numerical improvement to the crack growth direction criterion is proposed that gives significant gains in accuracy and convergence rates of the fracture paths, especially on coarse meshes.
TL;DR: In this article, the spectral representation of the statistically homogeneous mesoscale random fields for the apparent properties of particle-reinforced composites based on computer-simulated images of their microstructure was derived using spectral representation in conjunction with translation field theory.
TL;DR: In this article, the authors present an algorithmic framework for matrix-free evaluation of Galerkin finite element operators based on sum factorization on quadrilateral and hexahedral meshes.
Abstract: We present an algorithmic framework for matrix-free evaluation of discontinuous Galerkin finite element operators based on sum factorization on quadrilateral and hexahedral meshes. We identify a set of kernels for fast quadrature on cells and faces targeting a wide class of weak forms originating from linear and nonlinear partial differential equations. Different algorithms and data structures for the implementation of operator evaluation are compared in an in-depth performance analysis. The sum factorization kernels are optimized by vectorization over several cells and faces and an even-odd decomposition of the one-dimensional compute kernels. In isolation our implementation then reaches up to 60\% of arithmetic peak on Intel Haswell and Broadwell processors and up to 50\% of arithmetic peak on Intel Knights Landing. The full operator evaluation reaches only about half that throughput due to memory bandwidth limitations from loading the input and output vectors, MPI ghost exchange, as well as handling variable coefficients and the geometry. Our performance analysis shows that the results are often within 10\% of the available memory bandwidth for the proposed implementation, with the exception of the Cartesian mesh case where the cost of gather operations and MPI communication are more substantial.
TL;DR: In this article, a multiscale extended finite element method (MsXFEM) is used to determine the effective elastic properties of heterogeneous materials and the elastic properties are calculated by analyzing a representative volume element (RVE) under periodic boundary conditions.
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...
TL;DR: In this paper, the authors presented the application of a fretting fatigue crack propagation predictive technique to a railway axle subjected to bending fatigue loading condition, which is based on combining the eXtended Finite Element Method (XFEM) with two fatigue crack growth criteria, namely Maximum Tangential Stress (MTS) and minimum shear stress range.
TL;DR: To improve the convergence rate in time, the weighted and shifted Grünwald difference method is used and a higher order finite difference scheme of the Caputo fractional derivative is developed to improve the time convergence rate of the methods.
Abstract: In this paper, a class of distributed-order time fractional diffusion equations (DOFDEs) on bounded domains is considered. By L1 method in temporal direction, a semi-discrete variational formulation of DOFDEs is obtained firstly. The stability and convergence of this semi-discrete scheme are discussed, and the corresponding fully discrete finite element scheme is investigated. To improve the convergence rate in time, the weighted and shifted Grunwald difference method is used. By this method, another finite element scheme for DOFDEs is obtained, and the corresponding stability and convergence are considered. And then, as a supplement, a higher order finite difference scheme of the Caputo fractional derivative is developed. By this scheme, an approach is suggested to improve the time convergence rate of our methods. Finally, some numerical examples are given for verification of our theoretical analysis.
TL;DR: The proposed technique has been verified effectively through fundamental examples including Riesz, Left/Right Riemann–Liouville fractional derivative and can be readily extended to more general fractional differential equations with different boundary conditions and low-order terms.
TL;DR: Numerical results for 3D, steady-state and transient problems demonstrate that the CutFEM analyses are sufficiently accurate, and the optimized designs agree well with results from prior studies solved in 2D or by density approaches.
TL;DR: The breakthrough is developing an algorithm to form stiffness matrix on unstructured triangular meshes, which can help to deal with space fractional terms on any convex domain, and develop a finite element method for FPDEs on irregular domain.
TL;DR: A simple, efficient and accurate Bezier extraction based T-spline XIGA (BEBT-XIGA) has been proposed for the crack simulations and several crack problems have been solved.
TL;DR: In this paper, the authors proposed a lumped mass matrix is strictly diagonal and can yield the results in agreement with the consistent mass matrix, but has more excellent dynamic property than the latter.
Abstract: Summary
The partition of unity based methods, such as the extended finite element method and the numerical manifold method, are able to construct global functions that accurately reflect local behaviors through introducing locally defined basis functions beyond polynomials. In the dynamic analysis of cracked bodies using an explicit time integration algorithm, as a result, huge difficulties arise in deriving lumped mass matrices because of the presence of those physically meaningless degrees of freedom associated with those locally defined functions. Observing no spatial derivatives of trial or test functions exist in the virtual work of inertia force, we approximate the virtual work of inertia force in a coarser manner than the virtual work of stresses, where we inversely utilize the ‘from local to global’ skill. The proposed lumped mass matrix is strictly diagonal and can yield the results in agreement with the consistent mass matrix, but has more excellent dynamic property than the latter. Meanwhile, the critical time step of the numerical manifold method equipped with an explicit time integration scheme and the proposed mass lumping scheme does not decrease even if the crack in study approaches the mesh nodes — a very excellent dynamic property. Copyright © 2017 John Wiley & Sons, Ltd.
TL;DR: In this paper, the authors considered the problem of energy minimization of the total energy of the mechanical system with respect to the crack extension directions and crack extension lengths under quasi-static conditions.
TL;DR: In this paper, a numerical analysis based on the finite element method is presented to simulate blast-induced hard rock fracture propagation in a sound granite that remains linear elastic right up the breakage.
TL;DR: In this paper, an unstructured mesh Galerkin finite element method was used to discretize in space and the Crank-Nicolson scheme was used for discretizing the Caputo time fractional derivative.
Abstract: Most existing research on applying the finite element method to discretize space fractional operators is studied on regular domains using either uniform structured triangular meshes, or quadrilateral meshes. Since many practical problems involve irregular convex domains, such as the human brain or heart, which are difficult to partition well with a structured mesh, the existing finite element method using the structured mesh is less efficient. Research on the finite element method using a completely unstructured mesh on an irregular domain is of great significance. In this paper, a novel unstructured mesh finite element method is developed for solving the time-space fractional wave equation on a two-dimensional irregular convex domain. The novel unstructured mesh Galerkin finite element method is used to discretize in space and the Crank-Nicolson scheme is used to discretize the Caputo time fractional derivative. The implementation of the unstructured mesh Crank-Nicolson Galerkin method (CNGM) is detailed and the stability and convergence of the numerical scheme are analysed. Numerical examples are presented to verify the theoretical analysis. To highlight the ability of the proposed unstructured mesh Galerkin finite element method, a comparison of the unstructured mesh with the structured mesh in the implementation of the numerical scheme is conducted. The proposed numerical method using an unstructured mesh is shown to be more effective and feasible for practical applications involving irregular convex domains.
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.
TL;DR: In this paper, a flat shell element, MISS-4, is extended to the geometrically nonlinear analysis of variable-angle tow (VAT) composite plates using Koiter's asymptotic approach.
Abstract: The design of lightweight structures is often driven by buckling phenomena. Increasing demands for fuel-efficient aircraft structures makes post-buckled designs attractive from a structural weight perspective. However, the need for reliable and efficient design tools that accurately model the emerging nonlinear post-buckled landscape, potentially one containing multiple branches, remains. With this aim, a previously derived flat shell element, MISS-4, is extended to the geometrically nonlinear analysis of variable-angle tow (VAT) composite plates using Koiter's asymptotic approach. The curvilinear fiber paths in VAT lamina open the design space for tailoring the buckling and post-buckling capability of plates and shells. A finite element implementation of Koiter's asymptotic approach allows the pre-critical and post-critical behavior of slender elastic structures to be evaluated in a computationally efficient manner. Its implementation uses a fourth-order expansion of the strain energy, and requires both the structural modeling and finite element discretization procedures to be, at least, of fourth order. The corotational approach adopted in the MISS-4 element readily fulfills this requirement by starting from a linear finite element discretization. VAT plates with prismatic fiber variations and different loading conditions are analyzed using the MISS-4 element and numerical results of the post-buckling paths are presented. The computed equilibrium paths are compared to benchmark results using the commercial finite element package ABAQUS, and strong asymptotic solutions of the differential equations. The results document the good accuracy and reliability of the proposed modeling approach, and also highlight the importance of multi-modal analysis when multiple buckling modes coincide as is the case in long plates, shells and other optimized thin-walled structures.
TL;DR: An adaptive extended IGA (XIGA) approach based on polynomial splines over hierarchical T-meshes (PHT-splines) for modeling crack propagation is presented, in which discontinuous enrichment functions are added to the IGA approximation and this method does not require remeshing as the cracks grow.
Abstract: Summary
Adaptive local refinement is one of the main issues for isogeometric analysis (IGA). In this paper, an adaptive extended IGA (XIGA) approach based on polynomial splines over hierarchical T-meshes (PHT-splines) for modeling crack propagation is presented. The PHT-splines overcome certain limitations of non-uniform rational B-splines (NURBS)-based formulations; in particular, they make local refinements feasible. To drive the adaptive mesh refinement, we present a recovery-based error estimator for the proposed method. The method is based on the XIGA method, in which discontinuous enrichment functions are added to the IGA approximation and this method does not require remeshing as the cracks grow. In addition, crack propagation is modeled by successive linear extensions, that are determined by the stress intensity factors (SIFs) under linear elastic fracture mechanics. The proposed method has been used to analyze numerical examples, and the SIFs results were compared with reference results. The findings demonstrate the accuracy and efficiency of the proposed method. This article is protected by copyright. All rights reserved.
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.