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Primary Unknowns (primary + unknown)
Selected AbstractsCoupled simulation of wave propagation and water flow in soil induced by high-speed trainsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2008P. Kettil Abstract The purpose of this paper is to simulate the coupled dynamic deformation and water flow that occur in saturated soils when subjected to traffic loads, which is a problem with several practical applications. The wave propagation causes vibrations leading to discomfort for passengers and people in the surroundings and increase wear on both the vehicle and road structure. The water flow may cause internal erosion and material transport in the soil. Further, the increased pore water pressure could reduce the bearing capacity of embankments. The saturated soil is modelled as a water-saturated porous medium. The traffic is modelled as a number of moving wheel contact loads. Dynamic effects are accounted for, which lead to a coupled problem with solid displacements, water velocity and pressure as primary unknowns. A finite element program has been developed to perform simulations. The simulations clearly demonstrate the induced wave propagation and water flow in the soil. The simulation technique is applicable to railway as well as road traffic. Copyright © 2007 John Wiley & Sons, Ltd. [source] An optimally convergent discontinuous Galerkin-based extended finite element method for fracture mechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2010Yongxing Shen Abstract The extended finite element method (XFEM) enables the representation of cracks in arbitrary locations of a mesh. We introduce here a variant of the XFEM rendering an optimally convergent scheme. Its distinguishing features are as follows: (a) the introduction of singular asymptotic crack tip fields with support on only a small region around the crack tip (the enrichment region), (b) only one and two enrichment functions are added for anti-plane shear and planar problems, respectively and (c) the relaxation of the continuity between the enrichment region and the rest of the domain, and the adoption of a discontinuous Galerkin (DG) method therein. The method is provably stable for any positive value of a stabilization parameter, and by weakly enforcing the continuity between the two regions it eliminates ,blending elements' partly responsible for the suboptimal convergence of some early XFEMs. Moreover, the particular choice of enrichment functions results in a surprisingly sparse stiffness matrix that remains reasonably conditioned as the mesh is refined. More importantly, the stress intensity factors can be extracted with a satisfactory accuracy as primary unknowns. Quadrature strategies required for the optimal convergence are also discussed. Finally, the DG method was modified to retain stability based on an inf-sup condition. Copyright © 2009 John Wiley & Sons, Ltd. [source] Lower bound limit analysis with adaptive remeshingINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2005Andrei V. Lyamin Abstract The objective of this work is to present an adaptive remeshing procedure for lower bound limit analysis with application to soil mechanics. Unlike conventional finite element meshes, a lower bound grid incorporates statically admissible stress discontinuities between adjacent elements. These discontinuities permit large stress jumps over an infinitesimal distance and reduce the number of elements needed to predict the collapse load accurately. In general, the role of the discontinuities is crucial as their arrangement and distribution has a dramatic influence on the accuracy of the lower bound solution (Limit Analysis and Soil Plasticity, 1975). To ensure that the discontinuities are positioned in an optimal manner requires an error estimator and mesh adaptation strategy which accounts for the presence of stress singularities in the computed stress field. Recently, Borges et al. (Int. J. Solids Struct. 2001; 38:1707,1720) presented an anisotropic mesh adaptation strategy for a mixed limit analysis formulation which used a directional error estimator. In the present work, this strategy has been tailored to suit a discontinuous lower bound formulation which employs the stresses and body forces as primary unknowns. The adapted mesh has a maximum density of discontinuities in the direction of the maximum rate of change in the stress field. For problems involving strong stress singularities in the boundary conditions (e.g. a strip footing), the automatic generation of discontinuity fans, centred on the singular points, has been implemented. The efficiency of the proposed technique is demonstrated by analysis of two classical soil mechanics problems; namely the bearing capacity of a rigid strip footing and the collapse of a vertical cut. Copyright © 2005 John Wiley & Sons, Ltd. [source] Applications of numerical eigenfunctions in the fractal-like finite element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2004D. K. L. Tsang Abstract The fractal-like finite element method is an accurate and efficient method to determine the stress intensity factors (SIF) around crack tips. The use of a self-similar mesh together with the William's eigenfunctions reduce the number of unknowns significantly. The SIFs are the primary unknowns and no post-processing is required. In all previous studies, we used the analytic eigenfunction expression to perform the global transformation. However, the eigenfunction cannot be found analytically in general crack problems. Two-dimensional axisymmetrical cracks are considered here. The resulting static equilibrium equations in local co-ordinates are non-homogeneous ordinary differential equations, for which the analytic eigenfunction cannot be found completely. We use a finite difference method to determine all the eigenfunctions needed numerically. Our evaluated SIF values show very close agreement with published results. Copyright © 2004 John Wiley & Sons, Ltd. [source] Theory and numerics of geometrically non-linear open system mechanicsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2003E. Kuhl Abstract The present contribution aims at deriving a general theoretical and numerical framework for open system thermodynamics. The balance equations for open systems differ from the classical balance equations by additional terms arising from possible local changes in mass. In contrast to existing formulations, these changes not only originate from additional mass sources or sinks but also from a possible in- or outflux of matter. Constitutive equations for the mass source and the mass flux are discussed for the particular model problem of bone remodelling in hard tissue mechanics. Particular emphasis is dedicated to the spatial discretization of the coupled system of the balance of mass and momentum. To this end we suggest a geometrically non-linear monolithic finite element based solution technique introducing the density and the deformation map as primary unknowns. It is supplemented by the consistent linearization of the governing equations. The resulting algorithm is validated qualitatively for classical examples from structural mechanics as well as for biomechanical applications with particular focus on the functional adaption of bones. It turns out that, owing to the additional incorporation of the mass flux, the proposed model is able to simulate size effects typically encountered in microstructural materials such as open-pored cellular solids, e.g. bones. Copyright © 2003 John Wiley & Sons, Ltd. [source] | ||||||||||