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Analytical Ones (analytical + ones)

Distribution by Scientific Domains
Engineering75%

Selected Abstracts

Dynamic non-planar crack rupture by a finite volume method

GEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2007
M. Benjemaa
SUMMARY Modelling dynamic rupture for complex geometrical fault structures is performed through a finite volume method. After transformations for building up the partial differential system following explicit conservative law, we design an unstructured bi-dimensional time-domain numerical formulation of the crack problem. As a result, arbitrary non-planar faults can be explicitly represented without extra computational cost. On these complex surfaces, boundary conditions are set on stress fluxes and not on stress values. Prescribed rupture velocity gives accurate solutions with respect to analytical ones depending on the mesh refinement, while solutions for spontaneous propagation are analysed through numerical means. An example of non-planar spontaneous fault growth in heterogeneous media demonstrates the good behaviour of the proposed algorithm as well as specific difficulties of such numerical modelling. [source]

Scaled boundary finite-element analysis of a non-homogeneous axisymmetric domain subjected to general loading

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2003
James P. Doherty
Abstract The scaled boundary finite-element method is derived for elastostatic problems involving an axisymmetric domain subjected to a general load, using a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co-ordinate system. The method is particularly well suited to modelling unbounded problems, and the formulation allows a power-law variation of Young's modulus with depth. The efficiency and accuracy of the method is demonstrated through a study showing the convergence of the computed solutions to analytical solutions for the vertical, horizontal, moment and torsion loading of a rigid circular footing on the surface of a homogeneous elastic half-space. Computed solutions for the vertical and moment loading of a smooth rigid circular footing on a non-homogeneous half-space are compared to analytical ones, demonstrating the method's ability to accurately model a variation of Young's modulus with depth. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Free vibrations of shear-flexible and compressible arches by FEM

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2001
Przemyslaw Litewka
Abstract The purpose of this paper is to analyse free vibrations of arches with influence of shear and axial forces taken into account. Arches with various depth of cross-section and various types of supports are considered. In the calculations, the curved finite element elaborated by the authors is adopted. It is the plane two-node, six-degree-of-freedom arch element with constant curvature. Its application to the static analysis yields the exact results, coinciding with the analytical ones. This feature results from the use of the exact shape functions in derivation of the element stiffness matrix. In the free vibration analysis the consistent mass matrix is used. It is obtained on the base of the same functions. Their coefficients contain the influences of shear flexibility and compressibility of the arch. The numerical results are compared with the results obtained for the simple diagonal mass matrix representing the lumped mass model. The natural frequencies are also compared with the ones for the continuous arches for which the analytically determined frequencies are known. The advantage of the paper is a thorough analysis of selected examples, where the influences of shear forces, axial forces as well as the rotary and tangential inertia on the natural frequencies are examined. Copyright © 2001 John Wiley & Sons, Ltd. [source]

A streamfunction,velocity approach for 2D transient incompressible viscous flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2010
Jiten C. Kalita
Abstract We recently proposed (J. Comput. Phys. 2005; 207(1):52,68) a new paradigm for solving the steady-state two-dimensional (2D) Navier,Stokes (N,S) equations using a streamfunction,velocity (,,v) formulation. This formulation was shown to avoid the difficulties associated with the traditional formulations (primitive variables and streamfunction-vorticity formulations). The new formulation was found to be second-order accurate and was found to yield accurate solutions of a number of fluid flow problems. In this paper, we extend the ideas and propose a second-order implicit, unconditionally stable ,,v formulation for the unsteady incompressible N,S equations. The method is used to solve several 2D time-dependent fluid flow problems, including the flow decayed by viscosity problem with analytical solution, the lid-driven square cavity problem, the backward-facing step problem and the flow past a square prism problem. For the problems with known exact solutions, our coarse grid transient solutions are extremely close to the analytical ones even for high Reynolds numbers (Re). For the driven cavity problem, our time-marching steady-state solutions up to Re=7500 provide excellent matches with established numerical results, and for Re=10000, our study concludes that the asymptotic stable solution is periodic as has been found by other authors in recent studies. For the backward step problem, our numerical results are in excellent agreement with established numerical and experimental results. Finally, for the flow past a square prism, we have very successfully simulated the von Kármán vortex street for Re=200. Copyright © 2009 John Wiley & Sons, Ltd. [source]