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CONTENTS
Volume 1, Number 1, March 2008
 

Abstract
The present paper presents multiscale modelling via coupling of the discrete and finite element methods. Theoretical formulation of the discrete element method using spherical or cylindrical particles has been briefly reviewed. Basic equations of the finite element method using the explicit time integration have been given. The micr-macro transition for the discrete element method has been discussed. Theoretical formulations for macroscopic stress and strain tensors have been given. Determination of macroscopic constitutive properties using dimensionless micro-macro relationships has been proposed. The formulation of the multiscale DEM/FEM model employing the DEM and FEM in different subdomains of the same body has been presented. The coupling allows the use of partially overlapping DEM and FEM subdomains. The overlap zone in the two coupling algorithms is introduced in order to provide a smooth transition from one discretization method to the other. Coupling between the DEM and FEM subdomains is provided by additional kinematic constraints imposed by means of either the Lagrange multipliers or penalty function method. The coupled DEM/FEM formulation has been implemented in the authors? own numerical program. Good performance of the numerical algorithms has been demonstrated in a number of examples.

Key Words
multiscale modelling; discrete element method; finite element method; coupling

Address
Jerzy Rojek; Institute of Fundamental Technological Research, Swietokrzyska 21, 00-049 Warsaw, Poland
Eugenio Onate; International Center for Numerical Methods in Engineering (CIMNE), Universidad Politecnica de Cataluna, Campus Norte UPC, 08034 Barcelona, Spain

Abstract
This paper investigates the modelling of coupled soil-structure interaction problems by domain decomposition techniques. It is assumed that the soil-structure system is physically partitioned into soil and structure subdomains, which are independently modelled. Coupling of the separately modelled partitioned subdomains is undertaken with various algorithms based on the sequential iterative Dirichlet- Neumann sub-structuring method, which ensures compatibility and equilibrium at the interface boundaries of the subdomains. A number of mathematical and computational characteristics of the coupling algorithms, including the convergence conditions and choice of algorithmic parameters leading to enhanced convergence of the iterative method, are discussed. Based on the presented coupling algorithms a simulation environment, utilizing discipline-oriented solvers for nonlinear structural and geotechnical analysis, is developed which is used here to demonstrate the performance characteristics and benefits of various algorithms. Finally, the developed tool is used in a case study involving nonlinear soil-structure interaction analysis between a plane frame and soil subjected to ground excavation. This study highlights the relative performance of the various considered coupling algorithms in modelling real soil-structure interaction problems, in which nonlinearity arises in both the structure and the soil, and leads to important conclusions regarding their adequacy for such problems as well as the prospects for further enhancements.

Key Words
soil-structure interaction; nonlinear analysis; domain decomposition; iterative coupling; adaptive relaxation

Address
H. Zolghadr Jahromi, B.A. Izzuddin and L. Zdravkovic; Department of Civil and Environmental Engineering, Imperial College, London SW7 2AZ, UK

Abstract
The theory of microlocal analysis of hyperbolic partial differential equations shows that the energy density associated to their high-frequency solutions satisfies transport equations, or radiative transfer equations for randomly heterogeneous materials with correlation lengths comparable to the (small) wavelength. The main limitation to the existing developments is the consideration of boundary or interface conditions for the energy and power flow densities. This paper deals with the high-frequency transport regime in coupled heterogeneous structures. An analytical model for the derivation of high-frequency power flow reflection/transmission coefficients at a beam or a plate junction is proposed. These results may be used in subsequent computations to solve numerically the transport equations for coupled systems, including interface conditions. Applications of this research concern the prediction of the transient response of slender structures impacted by acoustic or mechanical shocks.

Key Words
vibration; high-frequency; transport; interface; coupling

Address
Structural Dynamics and Coupled Systems Department, ONERA, 29, Avenue de la Division Leclerc, 92322 Chatillon Cedex, France

Abstract
A derivation is given of two-scale models that are able to describe deformation and flow in a fluid-saturated and progressively fracturing porous medium. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for a fluid-saturated porous medium, which are assumed to hold on the macroscopic scale. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures are independent from the underlying discretization. The finite element equations are derived for this two-scale approach and integrated over time. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of the coupling terms. A consistent linearization is given for use within a Newton-Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach.

Key Words
multiscale analysis; fracture; porous media; multiphase media; cohesive cracks.

Address
Rene de Borst; Department of Mechanical Engineering, Eindhoven University of Technology, The Netherlands
Julien Rethore; LMT, E.N.S. de Cachan, France
Marie-Angele Abellan; LTDS-ENISE - UMR CNRS 5513, Saint-Etienne, France

Abstract
This paper presents an optimization-based method for computing a minimal bounding ellipsoid that contains the set of static responses of an uncertain braced frame. Based on a non-stochastic modeling of uncertainty, we assume that the parameters both of brace stiffnesses and external forces are uncertain but bounded. A brace member represents the sum of the stiffness of the actual brace and the contributions of some non-structural elements, and hence we assume that the axial stiffness of each brace is uncertain. By using the S-lemma, we formulate a semidefinite programming (SDP) problem which provides an outer approximation of the minimal bounding ellipsoid. The minimum bounding ellipsoids are computed for a braced frame under several uncertain circumstances.

Key Words
semidefinite program; data uncertainty; uncertain linear equation; interval analysis; braced frame

Address
Yoshihiro Kanno; Dept. of Mathematical Informatics, University of Tokyo, Tokyo 113-8656, Japan
Izuru Takewaki; Dept. of Urban and Environmental Engineering, Kyoto University, Kyoto 615-8540, Japan

Abstract
Current methodologies used for the inference of thin film stresses through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. These methodologies have recently been extended to non-uniform stress and curvature states for the thin film subject to non-uniform, isotropic misfit strains. In this paper we study the same thin film/substrate system but subject to non-uniform, anisotropic misfit strains. The film stresses and system curvatures are both obtained in terms of the non-uniform, anisotropic misfit strains. For arbitrarily non-uniform, anisotropic misfit strains, it is shown that a direct relation between film stresses and system curvatures cannot be established. However, such a relation exists for uniform or linear anisotropic misfit strains, or for the average film stresses and average system curvatures when the anisotropic misfit strains are arbitrarily non-uniform.

Key Words
anisotropic film misfit strains and stresses; non-uniform film stresses and system curvatures; stress-curvature relations; non-local effects; interfacial shear

Address
Y. Huang; Dept. of Civil and Environmental Engineering and Dept. of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA
D. Ngo; Dept. of Mechanical and Industrial Eng., Univ. of Illinois, Urbana, IL 61801, USA
X. Feng; Dept. of Engineering Mechanics, Tsinghua Univ., Beijing, China
A.J. Rosakis; Graduate Aeronautical Laboratory, California Inst. of Technology, Pasadena, CA 91125, USA

Abstract
Elliptical tubes may buckle in an elastic local buckling failure mode under uniform compression. Previous analyses of the local buckling of these members have assumed that the cross-section is hollow, but it is well-known that the local buckling capacity of thin-walled closed sections may be increased by filling them with a rigid medium such as concrete. In many applications, the medium many not necessarily be rigid, and the infill can be considered to be an elastic material which interacts with the buckling of the elliptical tube that surrounds it. This paper uses an energy-based technique to model the buckling of a thin-walled elliptical tube containing an elastic infill, which elucidates the physics of the buckling phenomenon from an engineering mechanics basis, in deference to a less generic finite element approach to the buckling problem. It makes use of the observation that the local buckling in an elliptical tube is localised with respect to the contour of the ellipse in its cross-section, with the localisation being at the region of lowest curvature. The formulation in the paper is algebraic and it leads to solutions that can be determined by implementing simple numerical solution techniques. A further extension of this formulation to a stiffness approach with multiple degrees of buckling freedom is described, and it is shown that using the simple one degree of freedom representation is sufficiently accurate for determining the elastic local buckling coefficient.

Key Words
elastic buckling; elastic restraint; ellipse; local buckling; localisation; Ritz technique

Address
M.A. Bradford and A. Roufegarinejad; Centre for Infrastructure Eng. and Safety, School of Civil and Environmental Eng., The Univ. of New South Wales, Sydney, NSW 2052, Australia

Abstract
A brief review of the research works on ground vibrations caused by trains moving in underground tunnels is first given. Then, the finite/infinite element approach for simulating the soil-tunnel interaction system with semi-infinite domain is summarized. The tunnel is assumed to be embedded in a homogeneous half-space or stratified soil medium. The train moving underground is modeled as an infinite harmonic line load. Factors considered in the parametric studies include the soil stratum depth, damping ratio and shear modulus of the soil with or without tunnel, and the thickness of the tunnel lining. As far as ground vibration is concerned, the existence of a concrete tunnel may somewhat compensate for the loss due to excavation of the tunnel. For a soil stratum resting on a bedrock, the resonance peak and frequency of the ground vibrations caused by the underground load can be rather accurately predicted by ignoring the existence of the tunnel. Other important findings drawn from the parametric studies are given in the conclusion.

Key Words
ground vibration; infinite element; moving load; soil vibration; soil-tunnel interaction; subway; tunnel

Address
Y. B. Yang; Dept. of Civil Engineering, Nat\'l Taiwan University, No. 1, Section 4, Roosevelt Road,
Taipei 10617, Taiwan
H. H. Hung; Nat\'l Center for Research on Earthquake Engineering, Taipei 10688, Taiwan
L. C. Hsu; Dept. of Civil Engineering, Nat\'l Taiwan University, No. 1, Section 4, Roosevelt Road, Taipei 10617, Taiwan


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