This paper proposes a numerical analysis method termed Flow Element Method (FLEM) that can analyze large deformations of a continuum. The theoretical formulation of the method is described, and a typical example considering the geometric stiffness is shown which illustrates the capabilities of this method. Finally, FLEM-DEM coupled code is developed and applied to a centrifugal model test on a stacked-drift-type tunnel as one of the geomechanical applications.
Cette etude propose une methode d'analyse numerique, qui s'appelle la Methode des Élàments Flots (FLEM), qui est capable d'analyser un continu des grosses deformations. La formulation theorique de la methode est decrivee, et un exemple typique eu egard à la raideur geometrique est presente ce qui indique les possibilites de cette methode. Enfin, Ie code d'ensemble FLEM-DEM est developpe et applique à un test des modèles centrifuges sur un ‘stacked-drift-type’ tunnel comme une des applications geomβcaniques.
Dieses Schriftstueck schlagt eine numerische Analysemethode, genannt Flieβ-Elemente-Methode (FLEM) vor, die groβe Deformierungen eines Kontinuums analisieren kann. Die theoretische Formulierung wird beschrieben, ein typisches Beispiel wird gezeigt das die geometrische Steitheit betrachtet, und dieses Beispiel illustriert die Fàhigkeiten dieser Methode. Letztlich wird ein FLEMDEM gekoppelter Code entwickelt und als eine der geomechanischen Anwendungen an ein zentrifugales Testmodell eines ‘stacked-drifttype’ Tunnels angebracht.
This paper deals with a numerical method FLEM (Kiyama H. et.al. 1991) that can analyze large deformational problems of a continuum. The similar method FLAC has been proposed by Cundall, P.A. (1988), but the formulations are quite different in these two methods. A number of common techniques in Distinct Element Method (DEM) (Cundall, P.A. 1971) and Finite Element Method (FEM) have contributed to the development of FLEM. The method would be able to simulate a variety of geotechnical problems successfully. In this paper, FLEM will be formulated in two-dimensions. A continuous domain chosen for the analysis is partitioned by a finite difference grid as shown by solid lines in Figure 1, each nodal point of which has a mass and other physical quantities of the surrounding rectangular sub-section (shown by broken lines). Those subsections bound to each other throughout the domain and give an image of an element assembly in DEM, while those sub-sections never appear as elements in the following analysis. Displacements of the points can be calculated by DEM scheme, i.e. an explicit time-iterative solution scheme of the equation of motion. However, the contact forces acting on the point through the imaginary sub-section's boundaries cannot be obtained with the current DEM scheme, because all the imaginary elements always keep continuities through the boundaries to the adjacent ones as a continuum. In order to determine the force on a node, another rectangular grid of FEM is introduced and put precisely on the former grid as shown by solid lines in Figure 1. The nodal force is calculated by FEM scheme from summation of forces imposed by deformation of the zone (ordinary, 4 elements) surrounding the point. Once the nodal force vector is calculated, DEM computing procedure can be used to get new incremental displacement of the node. Thus the FLEM can formulate dynamic behaviours of a continuum undergoing large geometrical changes. In infinitesimal strain, the stiffness matrix depends on the interpolation function and the constitutive functions of material. In large deformations, the geometric non-linearity has to be considered for the stiffness; so FEM is usually based on either Total Lagragian (TL) or Updated Lagragian (UL) descriptions. FLEM can easily update co-ordinates of nodal points in every step and can refer the updated element shapes for calculations of stress and strain.
