Showing papers on "Finite element limit analysis published in 2013"
01 Jan 2013
TL;DR: The Finite Element Method of Structural Analysis using MATLAB® and Abaqus is described in this article, where the Finite Difference Calculus (FDC) is used.
Abstract: Advanced Finite Elements for Structural AnalysisStructural Analysis with the Finite Element Method. Linear StaticsFinite Element Analysis of Structures through Unified FormulationFinite Element Analysis and Design of Metal StructuresStructural Analysis with the Finite Element Method. Linear StaticsFinite Elements for Structural AnalysisStructural Analysis with the Finite Element MethodStructural Analysis Systems: Finite, boundary element & expert systems in structural analysisFinite Element Analysis for Composite StructuresStructural Analysis SystemsNonlinear Finite Element Analysis in Structural MechanicsKnowledge Based Consultation for Finite Element Structural AnalysisStructural Analysis with Finite ElementsStructural Analysis with the Finite Element MethodFinite Element Analysis of Thin-Walled StructuresThe Finite Element Method: Solid mechanicsFinite Element Structural AnalysisFinite Strip Method in Structural AnalysisFinite Elements in Structural AnalysisFinite Element ProceduresNonlinear Finite Element Analysis of Solids and StructuresStability of Structures by Finite Element MethodsThe Finite Element Method of Structural AnalysisIntroduction to Finite Element Analysis Using MATLAB® and AbaqusThe Finite Element Method in Structural MechanicsStructural Analysis by Finite Difference CalculusSymbolic Analysis of the Finite Element Method in Structural AnalysisComputational Structural Analysis and Finite Element MethodsStructural Analysis with the Finite Element Method. Linear StaticsTwo Level Finite Element Method for Structural AnalysisStructural Analysis with Finite ElementsFinite Element Programs in Structural Engineering and Continuum MechanicsAn Introduction to Matrix Structural Analysis and Finite Element MethodsFinite Elements in Structural AnalysisFinite Element Multidisciplinary AnalysisThe Finite Strip MethodFinite Element Analysis of Solids and StructuresThe Use of Finite Elements in Structural Analysis and Modelling of Engineering JointsStructural Analysis of Composite Wind Turbine BladesFinite Element Structural Analysis
225 citations
[...]
TL;DR: This chapter begins with the classical definition of a finite element as the triplet of a polygon, a polynomial space, and a set of functionals, and shows how to derive shape functions for the most common Lagrange elements.
Abstract: In this chapter we study the concept of a finite element in some more detail. We begin with the classical definition of a finite element as the triplet of a polygon, a polynomial space, and a set of functionals. We then show how to derive shape functions for the most common Lagrange elements. The isoparametric mapping is introduced as a tool to allow for elements with curved boundaries, and to simplify the computation of the element stiffness matrix and load vector. We finish by presenting some more exotic elements.
157 citations
Posted Content•
TL;DR: In this paper, a weak Galerkin (WG) finite element method is introduced and analyzed for the biharmonic equation in its primary form, and the resulting WG finite element formulation is symmetric, positive definite, and parameter-free.
Abstract: A new weak Galerkin (WG) finite element method is introduced and analyzed in this paper for the biharmonic equation in its primary form. This method is highly robust and flexible in the element construction by using discontinuous piecewise polynomials on general finite element partitions consisting of polygons or polyhedra of arbitrary shape. The resulting WG finite element formulation is symmetric, positive definite, and parameter-free. Optimal order error estimates in a discrete $H^2$ norm is established for the corresponding WG finite element solutions. Error estimates in the usual $L^2$ norm are also derived, yielding a sub-optimal order of convergence for the lowest order element and an optimal order of convergence for all high order of elements. Numerical results are presented to confirm the theory of convergence under suitable regularity assumptions.
142 citations
TL;DR: A novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics that achieves high accuracy compared with the extended finite element method (XFEM), and other reference solutions.
Abstract: This paper presents a novel numerical procedure based on the combination of an edge-based smoothed finite element (ES-FEM) with a phantom-node method for 2D linear elastic fracture mechanics. In the standard phantom-node method, the cracks are formulated by adding phantom nodes, and the cracked element is replaced by two new superimposed elements. This approach is quite simple to implement into existing explicit finite element programs. The shape functions associated with discontinuous elements are similar to those of the standard finite elements, which leads to certain simplification with implementing in the existing codes. The phantom-node method allows modeling discontinuities at an arbitrary location in the mesh. The ES-FEM model owns a close-to-exact stiffness that is much softer than lower-order finite element methods (FEM). Taking advantage of both the ES-FEM and the phantom-node method, we introduce an edge-based strain smoothing technique for the phantom-node method. Numerical results show that the proposed method achieves high accuracy compared with the extended finite element method (XFEM) and other reference solutions.
130 citations
TL;DR: A version of the Particle Finite Element Method applicable to geomechanics applications is presented and the capabilities of the scheme is demonstrated on a range of quasi-static and dynamic problems involving very large deformations.
108 citations
TL;DR: A methodology is established which will enable design modifications of a soft tissue probe that steers through complex mechanical interactions with the surrounding material as well as direct comparison of finite element and experimental force–displacement plots and energy distributions.
Abstract: Detailed finite element modelling of needle insertions into soft tissue phantoms encounters difficulties of large deformations, high friction, contact loading and material failure. This paper demonstrates the use of cohesive elements in high-resolution finite element models to overcome some of the issues associated with these factors. Experiments are presented enabling extraction of the strain energy release rate during crack formation. Using data from these experiments, cohesive elements are calibrated and then implemented in models for validation of the needle insertion process. Successful modelling enables direct comparison of finite element and experimental force–displacement plots and energy distributions. Regions of crack creation, relaxation, cutting and full penetration are identified. By closing the loop between experiments and detailed finite element modelling, a methodology is established which will enable design modifications of a soft tissue probe that steers through complex mechanical intera...
90 citations
Book•
10 Jun 2013
TL;DR: In this article, a simple truss with Abaqus beam element and a simple beam with rigid jointed frames are used to solve problems in the presence of Hinged End Global and Local Coordinate Systems.
Abstract: Introduction Prologue Finite Element Analysis and the User Aim of the Book Book Organization Bar Element Introduction One-Dimensional Truss Element Global Stiffness Matrix Assembly Boundary Conditions Solution of the System of Equations Support Reactions Members' Forces Computer Code: truss.m Problems Analysis of a Simple Truss with Abaqus Beam Element Introduction Stiffness Matrix Uniformly Distributed Loading Internal Hinge Computer Code: beam.m Problems Analysis of a Simple Beam with Abaqus Rigid Jointed Frames Introduction Stiffness Matrix of a Beam-Column Element Stiffness Matrix of a Beam-Column Element in the Presence of Hinged End Global and Local Coordinate Systems Global Stiffness Matrix Assembly and Solution for Unknown Displacements Computer Code: frame.m Analysis of a Simple Frame with Abaqus Stress and Strain Analysis Introduction Stress Tensor Deformation and Strain Stress-Strain Constitutive Relations Solved Problems Weighted Residual Methods Introduction General Formulation Galerkin Method Weak Form Integrating by Part over Two and Three Dimensions (Green Theorem) Rayleigh Ritz Method Finite Element Approximation Introduction General and Nodal Approximations Finite Element Approximation Basic Principles for the Construction of Trial Functions Two-Dimensional Finite Element Approximation Shape Functions of Some Classical Elements for C0 Problems Numerical Integration Introduction Gauss Quadrature Integration over a Reference Element Integration over a Triangular Element Solved Problems Plane Problems Introduction Finite Element Formulation for Plane Problems Spatial Discretization Constant Strain Triangle Linear Strain Triangle The Bilinear Quadrilateral The 8-Node Quadrilateral Solved Problem with MATLAB Axisymmetric Problems Definition Strain-Displacement Relationship Stress-Strain Relations Finite Element Formulation Programming Analysis with Abaqus Using the 8-Node Quadrilateral Thin and Thick Plates Introduction Thin Plates Thick Plate Theory or Mindlin Plate Theory Linear Elastic Finite Element Analysis of Plates Boundary Conditions Computer Program for Thick Plates Using the 8-Node Quadrilateral Analysis with Abaqus Appendix A: List of MATLAB Modules and Functions Appendix B: Statically Equivalent Nodal Forces Appendix C: Index Notation and Transformation Laws for Tensors References and Bibliography Index
77 citations
TL;DR: In this article, the authors investigated the benefits and accuracy of a finite element simulation of a blast loaded thin aluminum plate by validating the results with small-scale blast loading experiments, and concluded that the use of an explicit integration scheme instead of an implicit scheme dramatically reduces the computational effort without significant loss of accuracy.
76 citations
TL;DR: The main advantages of the proposed computational approach are that it can greatly save computer memory and CPU time, and it has good accuracy at the same time while it allows to easily building nonlinear behavior for high order mechanical theories to deal with problems which cannot be handled by classical multiscale or homogenization theories.
Abstract: In this paper, we propose to implement, in the framework of a commercial finite element software, a computational multilevel finite element method for the modeling of composite materials and structures. In the present approach, the unknown constitutive relationship at the macroscale is obtained by solving a local finite element problem at the microscale. The main advantages of the proposed computational approach are that it can greatly save computer memory and CPU time, and it has good accuracy at the same time while it allows to easily building nonlinear behavior for high order mechanical theories to deal with problems which cannot be handled by classical multiscale or homogenization theories. The linear and the non-linear cases are introduced and implemented in ABAQUS. A Python script and user-defined FORTRAN subroutines have been developed for this purpose. Finally numerical results show that the method presented in this paper is effective and reliable.
73 citations
TL;DR: In this article, upper bound rigid block methods and finite element limit analysis are applied to investigate the undrained stability of rectangular tunnels, and the upper and lower solutions for tunnel stability are summarised in a series of stability charts for use in tunnel design.
71 citations
TL;DR: In this article, the stability of a plane strain square tunnel in undrained clay is investigated using rigid-block upper bound methods as well as finite element limit analysis, and an approximate closed-form expression is developed for use by practising engineers.
TL;DR: It is shown that a subsequence of the sequence of finite element solutions converges to a weak solution of the problem as the finite element discretization parameter $h$ tends to $0$.
Abstract: We develop the analysis of finite element approximations of implicit power-law-like models for viscous incompressible fluids. The Cauchy stress and the symmetric part of the velocity gradient in the class of models under consideration are related by a, possibly multivalued, maximal monotone $r$-graph with $1
TL;DR: In this article, a frequency-dependent dynamic finite element method is developed to obtain the forced vibration response of damped non-local rods, and the stiffness and mass matrices of the nonlocal rods are also obtained using the conventional finite element methods.
TL;DR: In this paper, a more simple methodology is proposed based on scaling the experimental mode shapes of a structure using the mass matrix of a finite element model, and two approaches are compared; one approach is reduced to the set of measurement points using SEREP and a second approach is expanded to all DOFs in the model using a newly published principle called the local correspondence principle.
TL;DR: In this article, an Euler-Bernoulli stress resultant beam finite element for static collapse analysis of planar reinforced concrete beams and frames is presented in detail, where the pre-failure inelastic effects are described by the (axial force dependent) bending elastoplasticity with bi-linear isotropic hardening.
Posted Content•
TL;DR: An adaptive finite element algorithm with a quite general marking strategy is introduced and the convergence rate and quasi-optimal complexity of the Kohn-Sham model approximations are proved.
Abstract: The Kohn-Sham equation is a powerful, widely used approach for computation of ground state electronic energies and densities in chemistry, materials science, biology, and nanosciences. In this paper, we study the adaptive finite element approximations for the Kohn-Sham model. Based on the residual type a posteriori error estimators proposed in this paper, we introduce an adaptive finite element algorithm with a quite general marking strategy and prove the convergence of the adaptive finite element approximations. Using D{\" o}rfler's marking strategy, we then get the convergence rate and quasi-optimal complexity. We also carry out several typical numerical experiments that not only support our theory,but also show the robustness and efficiency of the adaptive finite element computations in electronic structure calculations.
TL;DR: In this paper, the authors provide a method for applying modal identification (i.e., the separation of general deformations into fundamental modal deformation classes: local, distortional, global, shear, and transverse extension) to the collapse analysis of thin-walled members modeled using material and geometric nonlinear shell finite element analysis.
Abstract: The objective of this paper is to provide a method for applying modal identification (i.e. the separation of general deformations into fundamental modal deformation classes: local, distortional, global, shear, and transverse extension) to the collapse analysis of thin-walled members modeled using material and geometric nonlinear shell finite element analysis. The advantage of such a modal identification is the ability to categorize and reduce the complicated deformations that occur in a shell finite element model—and ultimately to (a) quantitatively associate failures with particular classes, e.g. state a model as a local failure, and (b) track the evolution of the classes, e.g., mixed local and distortional buckling leading to a distortional failure in a given model. Ultimately, this capability will aid Specification development, which must simplify complicated behavior down to strength predictions in isolated buckling-induced limit states. The modal identification method is enabled by creating a series of base vectors, consistent with the fundamental deformation classes, that are used to categorize the general finite element displacements. The base vectors are constructed using the constrained finite strip method for general end boundary conditions, previously developed by the authors. A fairly sizeable minimization problem is required for assigning the contributions to the fundamental deformation classes. The procedure is illustrated with shell finite element examples of cold-formed steel members modeled to collapse with geometric or/and material nonlinearity. The failure modes of the member are tracked (i.e., identified as a function of displacement), and the collapse mechanism is investigated. The provided examples provide both proof of concept for the modal identification and demonstrate the potential of using such information to better understand the behavior of thin-walled members.
TL;DR: In this paper, a finite element analysis of partial strength steel joints is presented, where failure of the joint is confined to the end plate and is predicted by means of micromechanical models based on void growth mechanisms and coalescence, which are practical to apply to finite element analyses without additional modelling effort.
TL;DR: A two-level finite element discretization of the nonlinear stationary quasi-geostrophic equations, which model the wind driven large scale ocean circulation, shows that, for the appropriate scaling between the coarse and fine mesh sizes, the two- level algorithm significantly decreases the computational time of the standard one-level algorithm.
Abstract: In this paper we proposed a two-level finite element discretization of the nonlinear stationary quasi-geostrophic equations, which model the wind driven large scale ocean circulation. Optimal error estimates for the two-level finite element discretization were derived. Numerical experiments for the two-level algorithm with the Argyris finite element were also carried out. The numerical results verified the theoretical error estimates and showed that, for the appropriate scaling between the coarse and fine mesh sizes, the two-level algorithm significantly decreases the computational time of the standard one-level algorithm.
TL;DR: Stress-hybrid quadrilateral finite element with embedded strong discontinuity for failure analysis of plane stress solids was used in this article, where the authors proposed a new finite element for plane stress analysis.
Abstract: Stress-hybrid quadrilateral finite element with embedded strong discontinuity for failure analysis of plane stress solids
TL;DR: In this paper, the upper bound finite-elements limit analysis was used to compute the bearing capacity of a rigid strip footing placed over fully granular, cohesive-frictional, and fully cohesive soils.
Abstract: SUMMARY
By using the upper bound finite-elements limit analysis, with an inclusion of single and two horizontal layers of reinforcements, the ultimate bearing capacity has been computed for a rigid strip footing placed over (i) fully granular, (ii) cohesive-frictional, and (iii) fully cohesive soils. It is assumed that (i) the reinforcements are structurally strong so that no axial tension failure can occur, (ii) the reinforcement sheets have negligible resistance to bending, and (iii) the shear failure can take place between the reinforcement and soil mass. It is expected that the different approximations on which the analysis has been based would generally remain applicable for reinforcements in the form of geogrid sheets. A method has been proposed to incorporate the effect of the reinforcement in the analysis. The efficiency factors, ηc and ηγ, to be multiplied with Nc and Nγ , for finding the bearing capacity of reinforced foundations, have been established. The results have been obtained (i) for different values of ϕ in case of fully granular and cohesive-frictional soils, and (ii) for different rates at which the cohesion increases with depth for a fully cohesive soil. The optimum positions of the reinforcements' layers have also been determined. The effect of the reinforcements' length on the results has also been analyzed. As compared to cohesive soils, the granular soils, especially with higher values of ϕ, cause a much greater increase in the bearing capacity. The results compare reasonably well with the available theoretical and experimental data from literature. Copyright © 2013 John Wiley & Sons, Ltd.
TL;DR: In this paper, a simple one-dimensional two-node layered composite beam element is developed for accurate modeling of structural behavior of steel/fiber reinforced polymer-reinforced concrete beams under a combined mechanical and thermal loading in fire conditions.
TL;DR: In this paper, the actual structure of the radial truck tire, including the contact nonlinearity boundaries, such as tire-rim and tire-road interactions, is considered, and an axisymmet is proposed.
Abstract: Based on taking comprehensively into account the actual structure of the radial truck tire, including the contact non-linearity boundaries, such as tire-rim and tire-road interactions, an axisymmet...
TL;DR: In this article, a new membrane finite element for linear and nonlinear analysis is developed by the use of the strain based approach, and it is based on the assumed functions for the various components of strain which satisfy the compatibility equation.
TL;DR: In this article, a framework combining a classical strain localization analysis with a homogenization-based finite element method was proposed to predict the onset of plastic flow localization, which has high applicability to various types of material with a characteristic microstructure that may have significant heterogeneity as long as its representative volume element can be represented by a finite element discretization.
TL;DR: In this paper, the displacement finite element, lower and upper bound finite element limit analysis and analytical upper bound plasticity methods are employed to investigate the undrained limiting lateral resistance of piles in a pile row.
TL;DR: In this paper, an improved simple collapse mechanism which intermix inhomogeneous deforming region and rigid blocks translation together is proposed based on the multi-rigid-block upper-bound analysis.
TL;DR: The outcomes of research show that the method settles a series of problems of parameter association and model update in the process of finite element modeling which establishes a key technical basis for finite element parametric analysis and optimization design.
TL;DR: In this paper, the influence of internal pressure and shape imperfections of pipe bends on collapse load was investigated under in-plane closing bending moment using finite element limit analysis based on elastic-perfectly plastic material considering geometric nonlinearity.