Showing papers in "Archives of Computational Methods in Engineering in 2009"

The Hysteresis Bouc-Wen Model, a Survey

Abstract: Structural systems often show nonlinear behavior under severe excitations generated by natural hazards. In that condition, the restoring force becomes highly nonlinear showing significant hysteresis. The hereditary nature of this nonlinear restoring force indicates that the force cannot be described as a function of the instantaneous displacement and velocity. Accordingly, many hysteretic restoring force models were developed to include the time dependent nature using a set of differential equations. This survey contains a review of the past, recent developments and implementations of the Bouc-Wen model which is used extensively in modeling the hysteresis phenomenon in the dynamically excited nonlinear structures.

Multiscale Methods for Composites: A Review

Abstract: Various multiscale methods are reviewed in the context of modelling mechanical and thermomechanical responses of composites. They are developed both at the material level and at the structural analysis level, considering sequential or integrated kinds of approaches. More specifically, such schemes like periodic homogenization or mean field approaches are compared and discussed, especially in the context of non linear behaviour. Some recent developments are considered, both in terms of numerical methods (like FE2) and for more analytical approaches based on Transformation Field Analysis, considering both the homogenization and relocalisation steps in the multiscale methodology. Several examples are shown.

Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations

Abstract: Uncertainty quantification appears today as a crucial point in numerous branches of science and engineering. In the last two decades, a growing interest has been devoted to a new family of methods, called spectral stochastic methods, for the propagation of uncertainties through physical models governed by stochastic partial differential equations. These approaches rely on a fruitful marriage of probability theory and approximation theory in functional analysis. This paper provides a review of some recent developments in computational stochastic methods, with a particular emphasis on spectral stochastic approaches. After a review of different choices for the functional representation of random variables, we provide an overview of various numerical methods for the computation of these functional representations: projection, collocation, Galerkin approaches…. A detailed presentation of Galerkin-type spectral stochastic approaches and related computational issues is provided. Recent developments on model reduction techniques in the context of spectral stochastic methods are also discussed. The aim of these techniques is to circumvent several drawbacks of spectral stochastic approaches (computing time, memory requirements, intrusive character) and to allow their use for large scale applications. We particularly focus on model reduction techniques based on spectral decomposition techniques and their generalizations.

Recirculating Flows Involving Short Fiber Suspensions: Numerical Difficulties and Efficient Advanced Micro-Macro Solvers

Abstract: Numerical modelling of non-Newtonian flows usually involves the coupling between equations of motion characterized by an elliptic character, and the fluid constitutive equation, which defines an advection problem linked to the fluid history. There are different numerical techniques to treat the hyperbolic advection equations. In non-recirculating flows, Eulerian discretizations can give a convergent solution within a short computing time. However, the existence of steady recirculating flow areas induces additional difficulties. Actually, in these flows neither boundary conditions nor initial conditions are known. In this paper we compares different advanced strategies (some of them recently proposed and extended here for addressing complex flows) when they are applied to the solution of the kinetic theory description of a short fiber suspension fluid flows.

Development of the Multi-scale Analysis Model to Simulate Strain Localization Occurring During Material Processing

Abstract: A detailed description of possibilities given by the developed Cellular Automata—Finite Element (CAFE) multi scale model for prediction of the initiation and propagation of micro shear bands and shear bands in metallic materials subjected to plastic deformation is presented in the work. Particular emphasis in defining the criterion for initiation of micro shear and shear bands, as well as in defining the transition rules for the cellular automata, is put on accounting for the physical aspects of these phenomena occurring in two different scales in the material. The proposed approach led to the creation of the real multi scale model of strain localization phenomena. This model predicts material behavior in various thermo-mechanical processes. Selected examples of applications of the developed model to simulations of metal forming processes, which involve strain localization, are presented in the work. An approach based on the Smoothed Particle Hydrodynamic, which allows to overcome difficulties with remeshing in the traditional CAFE method, is a subject of this work as well. In the developed model remeshing becomes possible and difficulties limiting application of the CAFE method to simple deformation processes are solved. Obtained results of numerical simulations are compared with the experimental results of cold rolling process to show good predicative capabilities of the developed model.

Statistical Models of Rough Surfaces for Finite Element 3D-Contact Analysis

Abstract: The present study is divided in two parts. In the first one the complete elasto-plastic microcontact model of anisotropic rough surfaces is given. Rough surfaces are modelled as a random process in which the height of the surface is considered to be a two-dimensional random variable. It is assumed that the surface is statistically homogeneous. The description of anisotropic random surfaces is concentrated on strongly rough surfaces; for such surfaces the summits are represented by highly eccentric elliptic paraboloids. The model is based on the volume conservation of asperities with the plasticity index modified to suit more general geometric contact shapes during plastic deformation process. This model is utilized to determine the total contact area, contact load and contact stiffness which are a combination of the elastic, elasto-plastic and plastic components. The elastic and elasto-plastic stiffness coefficients decrease with increasing variance of the surface height about the mean plane. The standard deviation of slopes and standard deviation of curvatures have no observable effects on the normal contact stiffness. The part two deals with the solution of the fully three-dimensional contact/friction problem taking into account contact stiffnesses in the normal and tangential directions. An incremental non-associated hardening friction law model analogous to the classical theory of plasticity is used. Two numerical examples are selected to show applicability of the method proposed.

High Performance Inverse Preconditioning

Abstract: The derivation of parallel numerical algorithms for solving sparse linear systems on modern computer systems and software platforms has attracted the attention of many researchers over the years. In this paper we present an overview on the design issues of parallel approximate inverse matrix algorithms, based on an anti-diagonal “wave pattern” approach and a “fish-bone” computational procedure, for computing explicitly various families of exact and approximate inverses for solving sparse linear systems. Parallel preconditioned conjugate gradient-type schemes in conjunction with parallel approximate inverses are presented for the efficient solution of sparse linear systems. Applications of the proposed parallel methods by solving characteristic sparse linear systems on symmetric multiprocessor systems and distributed systems are discussed and the parallel performance of the proposed schemes is given, using MPI, OpenMP and Java multithreading.

Numerical Simulation of Matrix Reinforced Composite Materials Subjected to Compression Loads

Abstract: This paper reviews the most common formulations to obtain the compression strength of long fiber composites due to fiber buckling. This failure mode was first studied by Rosen (Fibre Composite Materials, pp. 37–45, 1965) who defined two different fiber buckling modes, extensional and transverse. Further studies improved the first model proposed by Rosen by defining with more accuracy the mechanics of the problem. Although each formulation use a different approach to solve the problem, all of them agree in the dependence of fiber buckling on three main parameters: matrix shear strength, fiber initial misalignments and volumetric participation of the fibers in the composite.

Parallel Iterative Substructuring in Structural Mechanics

Abstract: Finite Element Tearing and Interconnecting (FETI) methods are a family of nonoverlapping domain decomposition methods which have been proven to be robust and parallel scalable for a variety of elliptic partial differential equations. Here, an introduction to the classical onelevel FETI methods is given, as well as to the more recent dual-primal FETI methods and some of their variants. With the advent of modern parallel computers with thousands of processors, certain inexact components are needed in these methods to maintain scalability. An introduction to a recent class of inexact dual-primal FETI methods is presented. Scalability results for an elasticity problem using 65 536 processor cores of the JUGENE supercomputer at Forschungszentrum Julich show the potential of these methods. A hyperelastic problem from biomechanics is presented as an application of the methods to nonlinear finite element analysis.

Numerical Simulation and Experimental Validation of Coupled Flow, Heat Transfer and Electromagnetic Problems in Electrical Transformers

Abstract: The paper presents a state-of-the-art of the numerical modeling of the coupled problems involving heat, fluid flow and electromagnetic phenomena in electrical transformers. Mathematical descriptions of both Computational Fluid Dynamics (CFD) and electromagnetic (EMAG) models are given. Since these models include other submodels for a definition of boundary conditions as local and temperature-dependent convective and radiative heat fluxes, heat generation terms, temperature-dependent and effective values of material properties for different constructions of coils etc., the component problems published in a subject literature are also reported. Moreover, a coupling procedure of the CFD and EMAG solutions to examine the specific power losses within coils and a core is outlined. On the basis of the mathematical model, a numerical example of a three phase medium-power dry-type electrical transformer is presented. A validation of the numerical calculations is performed using the experimental transformer temperature tests in the short-circuit, open-circuit, and under rated parameters according to the current European Standards for dry-type transformers. During the tests, temperatures were measured at selected points on transformer elements using thermocouples and thermometers, while on the external tank walls an infrared thermography was employed.

Nonlinear Formulations of a Four-Node Quasi-Conforming Shell Element

Abstract: The quasi-conforming technique was introduced in the 1980’s to meet the challenge of inter-elements conforming problems and give a unified treatment of both conforming and nonconforming elements. While the linear formulation is well established, the nonlinear formulation based on the quasi-conforming technique that includes geometric and material nonlinearity is presented in this paper. The formulation is derived in the framework of an updated Lagrangian stress resultant, co-rotational approach. The geometric nonlinear formulation provides solutions to buckling and postbuckling behaviour while the material nonlinear formulation considers the spread of plasticity within the element while maintaining an explicit construction of element matrices. Aside from the elasto-plastic constitutive relation, formulations on laminate composites and reinforced concrete are also presented. The formulations of laminate composite and reinforced concrete material are present based on the layer concept, the material properties can vary throughout the thickness and across the surface of a shell element. The various failure criteria for laminate composite are included in the formulation which makes it possible to analyses the progressive failure of fibre and matrix. For the reinforced concrete material, the nonlinearities as a result of tensile cracking, tension stiffening between cracks, the nonlinear response of concrete in compression, and the yielding of the reinforcement are considered. The steel reinforcement is modeled as a bilinear material with strain hardening.

Regularization Methods for the Solution of Inverse Problems in Solar X-ray and Imaging Spectroscopy

Abstract: Astronomical practice often requires addressing remote sensing problems, whereby the radiation emitted by a source far in the sky and measured through ‘ad hoc’ observational techniques, contains very indirect information on the physical process at the basis of the emission. The main difficulties in this investigations rely on the poor quality of the measurements and on the ill-posedness of the mathematical model describing the relation between the measured data and the target functions. In the present paper we consider a set of problems in solar physics in the framework of the NASA Ramaty High Energy Solar Spectroscopic Imager (RHESSI) mission. The data analysis activity is essentially based on the regularization theory for ill-posed inverse problems and a review of the main regularization methods applied in this analysis is given. Furthermore, we describe the main results of these applications, in the case of both synthetic data and real observations recorded by RHESSI.