Showing papers on "Finite element limit analysis published in 2003"
Book•
17 Nov 2003TL;DR: In this paper, the authors present a theoretical analysis of the Spectral Element Method and Spectral Analysis of Signals (SAM) in terms of the following: 1.1 Fourier Series. 2.2 Discrete Fourier Transform and FFT. 3.3 Aliasing. 4.4 Reduction from the Finite Models.
Abstract: Preface. Part One Introduction to the Spectral Element Method and Spectral Analysis of Signals. 1 Introduction. 1.1 Theoretical Background. 1.2 Historical Background. 2 Spectral Analysis of Signals. 2.1 Fourier Series. 2.2 Discrete Fourier Transform and the FFT. 2.3 Aliasing. 2.4 Leakage. 2.5 Picket-Fence Effect. 2.6 Zero Padding. 2.7 Gibbs Phenomenon. 2.8 General Procedure of DFT Processing. 2.9 DFTs of Typical Functions. Part Two Theory of Spectral Element Method. 3 Methods of Spectral Element Formulation. 3.1 Force-Displacement Relation Method. 3.2 Variational Method. 3.3 State-Vector Equation Method. 3.4 Reduction from the Finite Models. 4 Spectral Element Analysis Method. 4.1 Formulation of Spectral Element Equation. 4.2 Assembly and the Imposition of Boundary Conditions. 4.3 Eigenvalue Problem and Eigensolutions. 4.4 Dynamic Responses with Null Initial Conditions. 4.5 Dynamic Responses with Arbitrary Initial Conditions. 4.6 Dynamic Responses of Nonlinear Systems. Part Three Applications of Spectral Element Method. 5 Dynamics of Beams and Plates. 5.1 Beams. 5.2 Levy-Type Plates. 6 Flow-Induced Vibrations of Pipelines. 6.1 Theory of Pipe Dynamics. 6.2 Pipelines Conveying Internal Steady Fluid. 6.3 Pipelines Conveying Internal Unsteady Fluid. Appendix 6.A: Finite Element Matrices: Steady Fluid. Appendix 6.B: Finite Element Matrices: Unsteady Fluid. 7 Dynamics of Axially Moving Structures. 7.1 Axially Moving String. 7.2 Axially Moving Bernoulli-Euler Beam. 7.3 Axially Moving Timoshenko Beam. 7.4 Axially Moving Thin Plates. Appendix 7.A: Finite Element Matrices for Axially Moving String. Appendix 7.B: Finite Element Matrices for Axially Moving Bernoulli-Euler Beam. Appendix 7.C: Finite Element Matrices for Axially Moving Timoshenko Beam. Appendix 7.D: Finite Element Matrices for Axially Moving Plate. 8 Dynamics of Rotor Systems. 8.1 Governing Equations. 8.2 Spectral Element Modeling. 8.3 Finite Element Model. 8.4 Numerical Examples. Appendix 8.A: Finite Element Matrices for the Transverse Bending Vibration. 9 Dynamics of Multi-Layered Structures. 9.1 Elastic-Elastic Two-Layer Beams. 9.2 Elastic-Viscoelastic-elastic-Three-Layer (PCLD) Beams. Appendix 9.A: Finite Element Matrices for the Elastic-Elastic Two-Layer Beam. Appendix 9.B: Finite Element Matrices for the Elastic-VEM-Elastic Three-Layer Beam. 10 Dynamics of Smart Structures. 10.1 Elastic-Piezoelectric Two-Layer Beams. 10.2 Elastic-Viscoelastic-Piezoelctric Three-Layer (ACLD) Beams. 11 Dynamics of Composite Laminated Structures. 11.1 Theory of Composite Mechanics. 11.2 Equations of Motion for Composite Laminated Beams. 11.3 Dynamics of Axial-Bending-Shear Coupled Composite Beams. 11.4 Dynamics of Bending-Torsion-Shear Coupled Composite Beams. Appendix 11.A: Finite Element Matrices for Axial-Bending-Shear Coupled Composite Beams. Appendix 11.B: Finite Element Matrices for Bending-Torsion-Shear Coupled Composite Beams. 12 Dynamics of Periodic Lattice Structures. 12.1 Continuum Modeling Method. 12.2 Spectral Transfer Matrix Method. 13 Biomechanics: Blood Flow Analysis. 13.1 Governing Equations. 13.2 Spectral Element Modeling: I. Finite Element. 13.3 Spectral Element Modeling: II. Semi-Infinite Element. 13.4 Assembly of Spectral Elements. 13.5 Finite Element Model. 13.6 Numerical Examples. Appendix 13.A: Finite Element Model for the 1-D Blood Flow. 14 Identification of Structural Boundaries and Joints. 14.1 Identification of Non-Ideal Boundary Conditions. 14.2 Identification of Joints. 15 Identification of Structural Damage. 15.1 Spectral Element Modeling of a Damaged Structure. 15.2 Theory of Damage Identification. 15.3 Domain-Reduction Method. 16 Other Applications. 16.1 SEM-FEM Hybrid Method. 16.2 Identification of Impact Forces. 16.3 Other Applications. References. Index.
430 citations
TL;DR: In this article, the authors present an extended finite element method (X-FEM) for modeling strong (displacement) and weak (strain) discontinuities within a standard finite element framework.
401 citations
TL;DR: In this paper, a finite element method for linear elastic fracture mechanics using enriched quadratic interpolations is presented, which is enriched with the asymptotic near tip displacement solutions and the Heaviside function so that the finite element approximation is capable of resolving the singular stress field at the crack tip as well as the jump in the displacement field across the crack face.
Abstract: A finite element method for linear elastic fracture mechanics using enriched quadratic interpolations is presented. The quadratic finite elements are enriched with the asymptotic near tip displacement solutions and the Heaviside function so that the finite element approximation is capable of resolving the singular stress field at the crack tip as well as the jump in the displacement field across the crack face without any significant mesh refinement. The geometry of the crack is represented by a level set function which is interpolated on the same quadratic finite element discretization. Due to the higher-order approximation for the crack description we are able to represent a crack with curvature. The method is verified on several examples and comparisons are made to similar formulations using linear interpolants.
233 citations
TL;DR: The partition of unity property of nodal shape functions has been exploited to introduce a higher-order displacement discontinuity in a standard finite element model, able to reproduce the typical cusp-like shape of the process zone at the tip of a cohesive crack.
Abstract: A methodology for the simulation of quasi-static cohesive crack propagation in quasi-brittle materials is presented. In the framework of the recently proposed extended finite element method, the partition of unity property of nodal shape functions has been exploited to introduce a higher-order displacement discontinuity in a standard finite element model. In this way, a cubic displacement discontinuity, able to reproduce the typical cusp-like shape of the process zone at the tip of a cohesive crack, is allowed to propagate without any need to modify the background finite element mesh. The effectiveness of the proposed method has been assessed by simulating mode-I and mixed-mode experimental tests. Copyright © 2003 John Wiley & Sons, Ltd.
210 citations
TL;DR: In this article, the authors present several techniques for modeling cracking within the finite element (FE) framework which use meshes independent of the crack configuration and thus avoid remeshing, combining the traditional FE method with the partition of unity method for modelling individual cracks.
196 citations
TL;DR: In this paper, a finite element method for axisymmetric two-phase flow problems is presented, which uses an enriched finite element formulation, in which the interface can move arbitrarily through the mesh without remeshing.
Abstract: A finite element method for axisymmetric two-phase flow problems is presented. The method uses an enriched finite element formulation, in which the interface can move arbitrarily through the mesh without remeshing. The enrichment is implemented by the extended finite element method (X-FEM) which models the discontinuity in the velocity gradient at the interface by a local partition of unity. It provides an accurate representation of the velocity field at interfaces on an Eulerian grid that is not conformal to the weak discontinuity. The interface is represented by a level set which is also used in the construction of the element enrichment. Surface tension effects are considered and the interface curvature is computed from the level set field. The method is demonstrated by several examples. Copyright © 2003 John Wiley & Sons, Ltd.
128 citations
TL;DR: In this paper, numerical limit analysis is used to assess the stability of slopes subjected to seismic loading, and the lower and upper bound theorems are formulated as linear problems to be solved using linear programming techniques.
Abstract: Numerical limit analysis is used to assess the stability of slopes subjected to seismic loading. The soil is assumed to follow the Mohr–Coulomb failure criterion. The lower and upper bound theorems are formulated as linear problems to be solved using linear programming techniques. Based on finite element discretisation of the slope, the velocity field is optimised to find the lowest upper bound, and the stress field is optimised to obtain the highest lower bound. Limit equilibrium computations and log-spiral upper bound solutions were also performed for comparison purposes. Additionally, finite element analyses were done for selected cases. Results from the limit equilibrium and finite element methods are in excellent agreement with the rigorous lower and upper bounds for all cases studied. The slip surfaces obtained from both the limit equilibrium and log-spiral upper bound methods lie within the plastic zones obtained for the slopes from both finite element and numerical limit analysis. Plots are presen...
123 citations
TL;DR: In this paper, a closed-form estimate of curvature for hinged multilayer structures with initial strains with variable width has been developed, where the finite element method is used for modeling of self-positioning microstructures.
Abstract: Closed-form estimate of curvature for hinged multilayer structures with initial strains is developed. The finite element method is used for modeling of self-positioning microstructures. The geometrically nonlinear problem with large rotations and large displacements is solved using step procedure with node coordinate update. Finite element results for curvature of the hinged micromirror with variable width is compared to closed-form estimates.
121 citations
TL;DR: In this article, the ultimate bearing capacity of a strip footing resting on a sand layer over clay soil is obtained by applying advanced upper and lower bound techniques, which are obtained by using a linear combination of upper-and lower-bound techniques.
Abstract: Rigorous plasticity solutions for the ultimate bearing capacity of a strip footing resting on a sand layer over clay soil are obtained by applying advanced upper and lower bound techniques. The stu...
112 citations
TL;DR: In this paper, a finite element approach for the analysis of the wave propagation in an infinitely long plate is presented, where a nonreflecting boundary condition such that there will be no spurious reflections generated by the finite boundary of the finite element model is introduced.
102 citations
TL;DR: In this article, the elastic T-stress for semi-elliptical surface cracks in finite thickness plates is calculated using three-dimensional finite element analyses and empirical equations for the T-stress at three locations: the deepest, the surface and the middle points of the crack front under tension or bending.
TL;DR: In this article, a new finite element is presented for the simulation of delamination growth in thin-layered composite structures, based on a solid-like shell element: a volume element that can be used for very thin applications due to a higher-order displacement field in the thickness direction.
Abstract: In this contribution a new finite element is presented for the simulation of delamination growth in thin-layered composite structures. The element is based on a solid-like shell element: a volume element that can be used for very thin applications due to a higher-order displacement field in the thickness direction. The delamination crack can occur at arbitrary locations and is incorporated in the element as a jump in the displacement field by using the partition of unity property of finite element shape functions. The kinematics of the element as well as the finite element formulation are described. The performance of the element is demonstrated by means of two examples. Copyright © 2003 John Wiley & Sons, Ltd.
TL;DR: In this paper, the authors investigated the stability of an idealised heading in undrained soil conditions, where the heading is rigidly supported along its length, while the face is free to move.
TL;DR: In this article, a finite element model for flexible pavements is presented, where the analysis is carried out using the finite element computer package ABAQUS/STANDARD.
TL;DR: In this paper, the authors provided detailed plastic limit load solutions for cylinders containing part-through surface cracks under combined axial tension, internal pressure and global bending, using elastic-perfectly-plastic material behavior, together with analytical solutions based on equilibrium stress fields.
TL;DR: In this article, the p-version finite element method is applied to finite strain problems and the behavior of high order finite elements is studied for an isotropic hyperelastic material in the case of near incompressibility.
TL;DR: This paper develops a sub-domain inverse finite element method for characterizing the material properties of inflated hyperelastic membranes, including soft tissues, which can assume homogeneity of the material behavior as well as of the local stress and strain fields.
Abstract: Quantification of the mechanical behavior of hyperelastic membranes in their service configuration, particularly biological tissues, is often challenging because of the complicated geometry, material heterogeneity, and nonlinear behavior under finite strains. Parameter estimation thus requires sophisticated techniques like the inverse finite element method. These techniques can also become difficult to apply, however, if the domain and boundary conditions are complex (e.g. a non-axisymmetric aneurysm). Quantification can alternatively be achieved by applying the inverse finite element method over sub-domains rather than the entire domain. The advantage of this technique, which is consistent with standard experimental practice, is that one can assume homogeneity of the material behavior as well as of the local stress and strain fields. In this paper, we develop a sub-domain inverse finite element method for characterizing the material properties of inflated hyperelastic membranes, including soft tissues. We illustrate the performance of this method for three different classes of materials: neo-Hookean, Mooney Rivlin, and Fung-exponential.
TL;DR: In this article, the authors measured and modelled the plastic collapse response of aluminium egg-box panels subjected to out-of-plane compression and found that the collapse strength and energy absorption are sensitive to the level of in-plane constraint, with collapse dictated either by plastic buckling or by a travelling plastic knuckle mechanism.
TL;DR: In this article, the authors consider the problem of assessing the convergence of mixed-formulated finite elements and propose a new physics-based procedure to evaluate the performance of shell elements.
TL;DR: In this article, the penetration performance of GT model military vehicle door subjected to the ballistic impact of a bullet with semispherical nose shape is investigated using 3-D nonlinear dynamic explicit finite element code LS-DYNA.
TL;DR: The least-squares functional is based on the stress-displacement formulation with the symmetry condition of the stress tensor imposed in the first-order system and is shown to be optimal in the (broken) H1 and H(div) norms uniform in the incompressible limit.
Abstract: This paper develops a least-squares finite element method for linear elasticity in both two and three dimensions. The least-squares functional is based on the stress-displacement formulation with the symmetry condition of the stress tensor imposed in the first-order system. For the respective displacement and stress, using the Crouzeix--Raviart and Raviart--Thomas finite element spaces, our least-squares finite element method is shown to be optimal in the (broken) H1 and H(div) norms uniform in the incompressible limit.
TL;DR: In this paper, the authors show that the numerical instability characterized by checkerboard patterns can be completely controlled when non-conforming four-node finite elements are employed in topology optimization problems.
Abstract: The objective of the present study is to show that the numerical instability characterized by checkerboard patterns can be completely controlled when non-conforming four-node finite elements are employed. Since the convergence of the non-conforming finite element is independent of the Lame parameters, the stiffness of the non-conforming element exhibits correct limiting behaviour, which is desirable in prohibiting the unwanted formation of checkerboards in topology optimization. We employ the homogenization method to show the checkerboard-free property of the non-conforming element in topology optimization problems and verify it with three typical optimization examples.
TL;DR: In this paper, the authors extended electromechanical fracture mechanics and finite element techniques for crack analyses to three-dimensional crack configurations and presented numerical results of the stress-intensity factors and energy release rates for these crack configurations.
TL;DR: In this paper, the authors used finite element stress analysis to optimize both design and material selection in loadbearing components in artificial hip joints based on the static load analysis, by selecting the peak load during the patient activity.
TL;DR: In this article, a dual variational functional is constructed and used to derive Trefftz finite element formulation for the anti-plane electroelastic problem and a special trial function is used to develop a special purpose element with local defects.
Abstract: Applications of the Trefftz finite element method to anti-plane electroelastic problems are presented in this paper. A dual variational functional is constructed and used to derive Trefftz finite element formulation. Special trial functions which satisfy boundary conditions are also used to develop a special purpose element with local defects. The performance of the proposed element model is assessed by an example and comparison is made with results obtained by other approaches. The Trefftz finite element approach is demonstrated to be ideally suited for the analysis of the anti-plane problem.
TL;DR: In this article, two new methods for adaptive refinement of a B-spline finite element solution within an integrated mechanically-based computer aided engineering system are presented, a local variant of np-refinement and a local version of h-refining.
Abstract: This article presents two new methods for adaptive refinement of a B-spline finite element solution within an integrated mechanically based computer aided engineering system. The proposed techniques for adaptively refining a B-spline finite element solution are a local variant of np-refinement and a local variant of h-refinement. The key component in the np-refinement is the linear co-ordinate transformation introduced into the refined element. The transformation is constructed in such a way that the transformed nodal configuration of the refined element is identical to the nodal configuration of the neighbour elements. Therefore, the assembly proceeds as with classic finite elements, while the solution approximation conforms exactly along the inter-element boundaries. For the h-refinement, this transformation is introduced into a construction that merges the super element from the finite element world with the hierarchical B-spline representation from the computational geometry. In the scope of developing sculptured surfaces, the proposed approach supports C0 as well as the Hermite B-spline C1 continuous shapes. For sculptured solids, C0 continuity only is considered in this article. The feasibility of the proposed methods in the scope of the geometric design is demonstrated by several examples of creating sculptured surfaces and volumetric solids. Numerical performance of the methods is demonstrated for a test case of the two-dimensional Poisson equation. Copyright © 2003 John Wiley & Sons, Ltd.
TL;DR: The method combines the topology optimization and the existing h-adaptive finite element methods in order to improve the definition of the material boundary and reduce the effective number of design variables.
Abstract: In this paper, we propose a new procedure for the layout optimization of structures making use of h-adaptive methods. The method combines the topology optimization and the existing h-adaptive finite element methods in order to: (i) improve the definition of the material boundary, i.e. the contour between the material and void regions; (ii) reduce the effective number of design variables; and (iii) bound the relative solution error. The refinement strategy is applied to a given element if: (a) the measure of the quality of the element is below a given lower bound; (b) the element is a ‘material element’ or has a side which forms the ‘material boundary’ of the given optimum layout; and (c) the element average error estimate is larger than a multiple of the average error of the mesh. After the h-adaptive refinement, the mesh quality is improved with the application of a conditional Laplacian smoothing process. The formulation of the optimization problem is defined by the minimization of the compliance of the structure subjected to a volume and side constraints. The design variable is then the average density of the material, which is considered to be constant within each finite element. Copyright © 2003 John Wiley & Sons, Ltd.
Book•
01 Jan 2003
TL;DR: The Finite Element Method for Stochastic Structures (FEM) as mentioned in this paper is based on the exact inverse of stiffness matrix (INF) matrix, which is used to measure stiffness.
Abstract: 1. Fundamentals of Finite Element Method 2. Finite Element Method for Stochastic Structures - A Review and Improvement 3. Finite Element Method for Stochastic Structures Based on Exact Inverse of Stiffness Matrix 4. FEM Based on Direct Exact Inverse of Stiffness Matrix 5. Variational Principles-Based FEM for Stochastic Beams 6. Element-Level Flexibility-Based Finite Element Method for Stochastic Structures 7. A Comparison of Stochastic and Interval Finite Elements Biblography Appendices
TL;DR: In this paper, the p-version finite element method was used to carry out limit analysis using a mathematical programming-based static approach, which is used to overcome the locking behavior that may occur in plane strain and 3D problems for such common yield criteria as von Mises'.
TL;DR: In this paper, a finite element model is proposed to simulate the precision and ultraprecision grinding of steel and to describe the temperature fields developed during the process, using the commercial implicit finite element code MARC.
Abstract: A finite element model is proposed to simulate the precision and ultraprecision grinding of steel and to describe the temperature fields developed during the process. The grinding is modelled using the commercial implicit finite element code MARC. In order to obtain the input data required for the model and to examine the heat damage induced to the workpiece, a series of experiments was performed with the same grinding conditions, but using different aluminium oxide grinding wheels of different bonding on the same work material. Comparison between numerical results obtained from the proposed model and experimental predictions, as well as numerical and analytical calculations reported in the literature, revealed a good agreement between theory and practice, indicating therefore that the model may be suitable for industrial applications.