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Element Framework (element + framework)
Kinds of Element Framework Selected AbstractsFailure of masonry arches under impulse base motionEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 14 2007Laura De Lorenzis Abstract Recent seismic events have caused damage or collapse of invaluable historical buildings, further proving the vulnerability of unreinforced masonry (URM) structures to earthquakes. This study aims to understand failure of masonry arches,typical components of URM historic structures,subjected to horizontal ground acceleration impulses. An analytical model is developed to describe the dynamic behaviour of the arch and is used to predict the combinations of impulse magnitudes and durations which lead to its collapse. The model considers impact of the rigid blocks through several cycles of motion, illustrating that failure can occur at lower ground accelerations than previously believed. The resulting failure domains are of potential use for design and assessment purposes. Predictions of the analytical model are compared with results of numerical modelling by the distinct element method, and the good agreement between results validates the analytical model and at the same time confirms the potential of the distinct element framework as a method of evaluating complex URM structures under dynamic loading. Copyright © 2007 John Wiley & Sons, Ltd. [source] An extended finite element framework for slow-rate frictional faulting with bulk plasticity and variable frictionINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2009Fushen Liu Abstract We present an extended finite element (FE) approach for the simulation of slow-rate frictional faulting in geologic media incorporating bulk plasticity and variable friction. The method allows the fault to pass through the interior of FEs without remeshing. The extended FE algorithm for frictional faulting, advocated in two recent articles, emanates from a variational equation formulated in terms of the relative displacement on the fault. In the present paper we consider the combined effects of bulk plasticity and variable friction in a two-dimensional plane strain setting. Bulk plasticity is localized to the fault tip and could potentially be used as a predictor for the initiation and propagation of new faults. We utilize a variable velocity- and state-dependent friction, known as the Dieterich,Ruina or ,slowness' law, formulated in a slip-weakening format. The slip-weakening/variable friction model is then time-integrated according to the generalized trapezoidal rule. We present numerical examples demonstrating the convergence properties of a global Newton-based iterative scheme, as well as illustrate some interesting properties of the variable friction model. Copyright © 2009 John Wiley & Sons, Ltd. [source] Dynamics of unsaturated soils using various finite element formulationsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2009Nadarajah Ravichandran Abstract Unsaturated soils are three-phase porous media consisting of a solid skeleton, pore liquid, and pore gas. The coupled mathematical equations representing the dynamics of unsaturated soils can be derived based on the theory of mixtures. Solution of these fully coupled governing equations for unsaturated soils requires tremendous computational resources because three individual phases and interactions between them have to be taken into account. The fully coupled equations governing the dynamics of unsaturated soils are first presented and then two finite element formulations of the governing equations are presented and implemented within a finite element framework. The finite element implementation of all the terms in the governing equations results in the complete formulation and is solved for the first time in this paper. A computationally efficient reduced formulation is obtained by neglecting the relative accelerations and velocities of liquid and gas in the governing equations to investigate the effects of fluid flow in the overall behavior. These two formulations are used to simulate the behavior of an unsaturated silty soil embankment subjected to base shaking and compared with the results from another commonly used partially reduced formulation that neglects the relative accelerations, but takes into account the relative velocities. The stress,strain response of the solid skeleton is modeled as both elastic and elastoplastic in all three analyses. In the elastic analyses no permanent deformations are predicted and the displacements of the partially reduced formulation are in between those of the reduced and complete formulations. The frequency of vibration of the complete formulation in the elastic analysis is closer to the predominant frequency of the base motion and smaller than the frequencies of vibration of the other two analyses. Proper consideration of damping due to fluid flows in the complete formulation is the likely reason for this difference. Permanent deformations are predicted by all three formulations for the elastoplastic analyses. The complete formulation, however, predicts reductions in pore fluid pressures following strong shaking resulting in somewhat smaller displacements than the reduced formulation. The results from complete and reduced formulations are otherwise comparable for elastoplastic analyses. For the elastoplastic analysis, the partially reduced formulation leads to stiffer response than the other two formulations. The likely reason for this stiffer response in the elastoplastic analysis is the interpolation scheme (linear displacement and linear pore fluid pressures) used in the finite element implementation of the partially reduced formulation. Copyright © 2008 John Wiley & Sons, Ltd. [source] Towards the algorithmic treatment of 3D strong discontinuitiesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2007J. Mergheim Abstract A geometrically non-linear finite element framework for the modelling of propagating discontinuities in three-dimensional continua is presented. By doubling the degrees of freedom in the discontinuous elements, the algorithm allows for arbitrary discontinuities which are not restricted to inter-element boundaries. The deformation field is interpolated independently on both sides of the discontinuity. In contrast to the X-FEM, the suggested approach thus relies exclusively on displacement degrees of freedom. On the discontinuity surface, the jump in the deformation is related to the cohesive tractions to account for smooth crack opening. Computational difficulties characteristic of three-dimensional crack propagation are addressed. The performance of the method is elaborated by means of a homogeneous three-dimensional tension problem and by means of the classical peel test. Copyright © 2006 John Wiley & Sons, Ltd. [source] An enriched element-failure method (REFM) for delamination analysis of composite structuresINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2009X. S. Sun Abstract This paper develops an enriched element-failure method for delamination analysis of composite structures. This method combines discontinuous enrichments in the extended finite element method and element-failure concepts in the element-failure method within the finite element framework. An improved discontinuous enrichment function is presented to effectively model the kinked discontinuities; and, based on fracture mechanics, a general near-tip enrichment function is also derived from the asymptotic displacement fields to represent the discontinuity and local stress intensification around the crack-tip. The delamination is treated as a crack problem that is represented by the discontinuous enrichment functions and then the enrichments are transformed to external nodal forces applied to nodes around the crack. The crack and its propagation are modeled by the ,failed elements' that are applied to the external nodal forces. Delamination and crack kinking problems can be solved simultaneously without remeshing the model or re-assembling the stiffness matrix with this method. Examples are used to demonstrate the application of the proposed method to delamination analysis. The validity of the proposed method is verified and the simulation results show that both interlaminar delamination and crack kinking (intralaminar crack) occur in the cross-ply laminated plate, which is observed in the experiment. Copyright © 2009 John Wiley & Sons, Ltd. [source] Finite element modelling of fibre reinforced polymer sandwich panels exposed to heatINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2004P. Krysl Abstract A finite element model that predicts temperature distribution in a composite panel exposed to a heat source, such as fire, is described. The panel is assumed to be composed of skins consisting of polymer matrix reinforced with fibres and a lightweight core (the paper concentrates on the crucial aspect of the problem, i.e. the behaviour of the ,hot' skin of the panel. The core is assumed not to decompose, and the ,cold' skin is treated exactly as the ,hot' skin.) It is assumed that the polymer matrix undergoes chemical decomposition. Such a model results in a set of coupled non-linear transient partial differential equations. A Galerkin finite element framework is formulated to yield a fully implicit time stepping scheme. The crucial input parameters for the model are carefully identified for subsequent experimental determination. Copyright © 2004 John Wiley & Sons, Ltd. [source] On the design of energy,momentum integration schemes for arbitrary continuum formulations.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004Applications to classical, chaotic motion of shells Abstract The construction of energy,momentum methods depends heavily on three kinds of non-linearities: (1) the geometric (non-linearity of the strain,displacement relation), (2) the material (non-linearity of the elastic constitutive law), and (3) the one exhibited in displacement-dependent loading. In previous works, the authors have developed a general method which is valid for any kind of geometric non-linearity. In this paper, we extend the method and combine it with a treatment of material non-linearity as well as that exhibited in force terms. In addition, the dynamical formulation is presented in a general finite element framework where enhanced strains are incorporated as well. The non-linearity of the constitutive law necessitates a new treatment of the enhanced strains in order to retain the energy conservation property. Use is made of the logarithmic strain tensor which allows for a highly non-linear material law, while preserving the advantage of considering non-linear vibrations of classical metallic structures. Various examples and applications to classical and non-classical vibrations and non-linear motion of shells are presented, including (1) chaotic motion of arches, cylinders and caps using a linear constitutive law and (2) large overall motion and non-linear vibration of shells using non-linear constitutive law. Copyright © 2004 John Wiley & Sons, Ltd. [source] Stabilized finite element method for viscoplastic flow: formulation with state variable evolutionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2003Antoinette M. Maniatty Abstract A stabilized, mixed finite element formulation for modelling viscoplastic flow, which can be used to model approximately steady-state metal-forming processes, is presented. The mixed formulation is expressed in terms of the velocity, pressure and state variable fields, where the state variable is used to describe the evolution of the material's resistance to plastic flow. The resulting system of equations has two sources of well-known instabilities, one due to the incompressibility constraint and one due to the convection-type state variable equation. Both of these instabilities are handled by adding mesh-dependent stabilization terms, which are functions of the Euler,Lagrange equations, to the usual Galerkin method. Linearization of the weak form is derived to enable a Newton,Raphson implementation into an object-oriented finite element framework. A progressive solution strategy is used for improving convergence for highly non-linear material behaviour, typical for metals. Numerical experiments using the stabilization method with hierarchic shape functions for the velocity, pressure and state variable fields in viscoplastic flow and metal-forming problems show that the stabilized finite element method is effective and efficient for non-linear steady forming problems. Finally, the results are discussed and conclusions are inferred. Copyright © 2002 John Wiley & Sons, Ltd. [source] A method for representing boundaries in discrete element modelling,part II: KinematicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2001M. Kremmer Abstract The application of the DEM to engineering problems involving the dynamic behaviour of discontinuous media has necessitated the introduction of moving boundary surfaces. In this paper a method is presented for modelling three-dimensional moving boundary surfaces within the discrete element framework. The surfaces of boundary objects are discretized into triangular planar surfaces using the finite wall method. Wall elements are grouped and each group is associated with a single discrete boundary object which may move independently. Movement comprises any combination of translation and rotation of wall element groups, subject to a given acceleration and velocity during a calculation cycle. The scheme is explicit due to rigidity of the wall elements which are stationary fixed in position and orientation over a time step. Any in-plane velocity is handled as a contact point velocity within a calculation cycle. The kinematic conditions at each calculation cycle may be pre-defined or returned from a separate calculation of rigid body motion of the boundary object. The method provides a means for coupling sphere-based particle dynamics with rigid body dynamics and structural analysis of boundary components. Copyright © 2001 John Wiley & Sons, Ltd. [source] A level set characteristic Galerkin finite element method for free surface flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2005Ching-Long Lin Abstract This paper presents a numerical method for free surface flows that couples the incompressible Navier,Stokes equations with the level set method in the finite element framework. The implicit characteristic-Galerkin approximation together with the fractional four-step algorithm is employed to discretize the governing equations. The schemes for solving the level set evolution and reinitialization equations are verified with several benchmark cases, including stationary circle, rotation of a slotted disk and stretching of a circular fluid element. The results are compared with those calculated from the level set finite volume method of Yue et al. (Int. J. Numer. Methods Fluids 2003; 42:853,884), which employed the third-order essentially non-oscillatory (ENO) schemes for advection of the level set function in a generalized curvilinear coordinate system. The comparison indicates that the characteristic Galerkin approximation of the level set equations yields more accurate solutions. The second-order accuracy of the Navier,Stokes solver is confirmed by simulation of decay vortex. The coupled system of the Navier,Stokes and level set equations then is validated by solitary wave and broken dam problems. The simulation results are in excellent agreement with experimental data. Copyright © 2005 John Wiley & Sons, Ltd. [source] A least square extrapolation method for the a posteriori error estimate of the incompressible Navier Stokes problemINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2005M. Garbey Abstract A posteriori error estimators are fundamental tools for providing confidence in the numerical computation of PDEs. To date, the main theories of a posteriori estimators have been developed largely in the finite element framework, for either linear elliptic operators or non-linear PDEs in the absence of disparate length scales. On the other hand, there is a strong interest in using grid refinement combined with Richardson extrapolation to produce CFD solutions with improved accuracy and, therefore, a posteriori error estimates. But in practice, the effective order of a numerical method often depends on space location and is not uniform, rendering the Richardson extrapolation method unreliable. We have recently introduced (Garbey, 13th International Conference on Domain Decomposition, Barcelona, 2002; 379,386; Garbey and Shyy, J. Comput. Phys. 2003; 186:1,23) a new method which estimates the order of convergence of a computation as the solution of a least square minimization problem on the residual. This method, called least square extrapolation, introduces a framework facilitating multi-level extrapolation, improves accuracy and provides a posteriori error estimate. This method can accommodate different grid arrangements. The goal of this paper is to investigate the power and limits of this method via incompressible Navier Stokes flow computations. Copyright © 2005 John Wiley & Sons, Ltd. [source] An elastoplastic model based on the shakedown concept for flexible pavements unbound granular materialsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2005Taha Habiballah Abstract Nowadays, the problem of rutting of flexible pavements linked to permanent deformations occurring in the unbound layers is taken into account only by mechanistic empirical formulas. Finite element modelling of realistic boundary value problems with incremental rheological models will lead to unrealistic calculation time for large cycle numbers. The objective of the authors is to present a simplified model which can be used to model the flexible pavements rutting with the finite elements framework. This method is based on the shakedown theory developed by Zarka which is usually associated to materials like steels. It has been adapted for granular materials by introducing a yield surface taking into account the mean stress influence on the mechanical behaviour and a dependency of the hardening modulus with the stress state. The Drucker,Prager yield surface has been used with a non-associated flow rule. Comparisons with repeated load triaxial tests carried out on a subgrade soil have been done. These comparisons underline the capabilities of the model to take into account the cyclic behaviour of unbound materials for roads. Finally, a discussion, dealing with the use of the simplified method within a finite element modelling of a full-scale experiment, is presented. Copyright © 2005 John Wiley & Sons, Ltd. [source] | ||||||||||