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Solution Domain (solution + domain)
Selected AbstractsA moving-mesh finite-volume method to solve free-surface seepage problem in arbitrary geometriesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2007M. Darbandi Abstract The main objective of this work is to develop a novel moving-mesh finite-volume method capable of solving the seepage problem in domains with arbitrary geometries. One major difficulty in analysing the seepage problem is the position of phreatic boundary which is unknown at the beginning of solution. In the current algorithm, we first choose an arbitrary solution domain with a hypothetical phreatic boundary and distribute the finite volumes therein. Then, we derive the conservative statement on a curvilinear co-ordinate system for each cell and implement the known boundary conditions all over the solution domain. Defining a consistency factor, the inconsistency between the hypothesis boundary and the known boundary conditions is measured at the phreatic boundary. Subsequently, the preceding mesh is suitably deformed so that its upper boundary matches the new location of the phreatic surface. This tactic results in a moving-mesh procedure which is continued until the nonlinear boundary conditions are fully satisfied at the phreatic boundary. To validate the developed algorithm, a number of seepage models, which have been previously targeted by the other investigators, are solved. Comparisons between the current results and those of other numerical methods as well as the experimental data show that the current moving-grid finite-volume method is highly robust and it provides sufficient accuracy and reliability. Copyright © 2007 John Wiley & Sons, Ltd. [source] Source signature and elastic waves in a half-space under a sustainable line-concentrated impulsive normal forceINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2002Moche Ziv Abstract First, the response of an ideal elastic half-space to a line-concentrated impulsive normal load applied to its surface is obtained by a computational method based on the theory of characteristics in conjunction with kinematical relations derived across surfaces of strong discontinuities. Then, the geometry is determined of the obtained waves and the source signature,the latter is the imprint of the spatiotemporal configuration of the excitation source in the resultant response. Behind the dilatational precursor wave, there exists a pencil of three plane waves extending from the vertex at the impingement point of the precursor wave on the stress-free surface of the half-space to three points located on the other two boundaries of the solution domain. These four wave-arresting points (end points) of the three plane waves constitute the source signature. One wave is an inhibitor front in the behaviour of the normal stress components and the particle velocity, while in the behaviour of the shear stress component, it is a surface-axis wave. The second is a surface wave in the behaviour of the horizontal components of the dependent variables, while the third is an inhibitor wave in the behaviour of the shear stress component. An inhibitor wave is so named, since beyond it, the material motion is dying or becomes uniform. A surface-axis wave is so named, since upon its arrival, like a surface wave, the dependent variable in question features an extreme value, but unlike a surface wave, it exists in the entire depth of the solution domain. It is evident from this work that Saint-Venant's principle for wave propagation problems cannot be formulated; therefore, the above results are a consequence of the particular model proposed here for the line-concentrated normal load. Copyright © 2002 John Wiley & Sons, Ltd. [source] An interpolation-based local differential quadrature method to solve partial differential equations using irregularly distributed nodesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2008Hang Ma Abstract To circumvent the constraint in application of the conventional differential quadrature (DQ) method that the solution domain has to be a regular region, an interpolation-based local differential quadrature (LDQ) method is proposed in this paper. Instead of using regular nodes placed on mesh lines in the DQ method (DQM), irregularly distributed nodes are employed in the LDQ method. That is, any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of irregularly distributed nodes in the local physical domain. The feature of the new approach lies in the fact that the weighting coefficients are determined by the quadrature rule over the irregularly distributed local supporting nodes with the aid of nodal interpolation techniques developed in the paper. Because of this distinctive feature, the LDQ method can be consistently applied to linear and nonlinear problems and is really a mesh-free method without the limitation in the solution domain of the conventional DQM. The effectiveness and efficiency of the method are validated by two simple numerical examples by solving boundary-value problems of a linear and a nonlinear partial differential equation. Copyright © 2007 John Wiley & Sons, Ltd. [source] A lumped mass numerical model for cellular materials deformed by impactINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2001Z. H. Tu Abstract When impacted by a relatively rigid body, cellular materials undergo severe deformation and extensive material failure. However, such behaviour may not be well described using traditional numerical approaches such as the finite element method. This paper presents a lumped mass numerical model which can accommodate high degrees of deformation and material failure. The essence of this model is to discretize a block of material into contiguous element volumes, each represented by a mass point. Interactions between a node and its neighbours are accounted for by defining ,connections' that represent their interfaces which transmit stresses. Strains at a node are calculated from the co-ordinates of the surrounding nodes; these also determine the stresses on the interfaces. The governing equations for the entire solution domain are then converted into a system of equations of motion with nodal positions as unknowns. Failure criteria and possible combinations of ,connection' breakage are incorporated to model the occurrence of damage. A practical contact algorithm is also developed to describe the contact interactions between cellular materials and rigid bodies. Simulations for normal and oblique impacts of rigid rectangular, cylindrical and wedge-tipped impactors on crushable foam blocks are presented to substantiate the validity of the model. The generally good correlation between the numerical and experimental results demonstrates that the proposed numerical approach is able to model the impact response of the crushable foam. However, some limitations in modelling crack propagation in oblique impacts by a rigid impactor on foam blocks are observed. Copyright © 2001 John Wiley & Sons, Ltd. [source] Periodic solution for strongly nonlinear vibration systems by He's variational iteration methodMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 18 2009SHA. Hashemi Kachapi Abstract In this paper, we use variational iteration method for strongly nonlinear oscillators. This method is a combination of the traditional variational iteration and variational method. Some examples are given to illustrate the effectiveness and convenience of the method. The obtained results are valid for the whole solution domain with high accuracy. The method can be easily extended to other nonlinear oscillations and hence widely applicable in engineering and science. Copyright © 2009 John Wiley & Sons, Ltd. [source] | ||||||||||