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Unified Formulation (unified + formulation)
Selected AbstractsUnified formulation of radiation conditions for the wave equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2002Steen Krenk Abstract A family of radiation boundary conditions for the wave equation is derived by truncating a rational function approximation of the corresponding plane wave representation, and it is demonstrated how these boundary conditions can be formulated in terms of fictitious surface densities, governed by second-order wave equations on the radiating surface. Several well-established radiation boundary conditions appear as special cases, corresponding to different choices of the coefficients in the rational approximation. The relation between these choices is established, and an explicit formulation in terms of selected directions with ideal transmission is presented. A mechanical interpretation of the fictitious surface densities enables identification of suitable conditions at corners and boundaries of the radiating surface. Numerical examples illustrate excellent results with one or two fictitious layers with suitable corner and boundary conditions. Copyright © 2001 John Wiley & Sons, Ltd. [source] A multiscale modeling of damage and time-dependent behavior of cohesive rocksINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2009A. Abou-Chakra Guéry Abstract The present paper deals with a micromechanical approach to modeling the time-dependent mechanical behavior of a class of cohesive geomaterials. The considered material is Callovo-Oxfordian argillite, which is mainly composed of three constituents: an elastoviscoplastic clay matrix, elastic quartz minerals, and elastic damaged calcite grains. The macroscopic constitutive law is obtained by adapting the incremental method proposed by Hill (J. Mech. Phys. Solids 1965; 13:89,101). Its unified formulation allows a description of not only the time-dependent behavior of the argillite but also its elastoplastic damage response. The developed model is first validated by comparison with finite element solutions and then it is applied to the prediction of argillites' macroscopic responses in connection with their mineralogical compositions. The validity of the model is checked through comparisons between the model's predictions and experimental data. Copyright © 2008 John Wiley & Sons, Ltd. [source] A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part I theoryINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2010G. R. Liu Abstract This paper introduces a G space theory and a weakened weak form (W2) using the generalized gradient smoothing technique for a unified formulation of a wide class of compatible and incompatible methods. The W2 formulation works for both finite element method settings and mesh-free settings, and W2 models can have special properties including softened behavior, upper bounds and ultra accuracy. Part I of this paper focuses on the theory and fundamentals for W2 formulations. A normed G space is first defined to include both continuous and discontinuous functions allowing the use of much more types of methods/techniques to create shape functions for numerical models. Important properties and a set of useful inequalities for G spaces are then proven in the theory and analyzed in detail. These properties ensure that a numerical method developed based on the W2 formulation will be spatially stable and convergent to the exact solutions, as long as the physical problem is well posed. The theory is applicable to any problems to which the standard weak formulation is applicable, and can offer numerical solutions with special properties including ,close-to-exact' stiffness, upper bounds and ultra accuracy. Copyright © 2009 John Wiley & Sons, Ltd. [source] A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part II applications to solid mechanics problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2010G. R. Liu Abstract In part I of this paper, we have established the G space theory and fundamentals for W2 formulation. Part II focuses on the applications of the G space theory to formulate W2 models for solid mechanics problems. We first define a bilinear form, prove some of the important properties, and prove that the W2 formulation will be spatially stable, and convergent to exact solutions. We then present examples of some of the possible W2 models including the SFEM, NS-FEM, ES-FEM, NS-PIM, ES-PIM, and CS-PIM. We show the major properties of these models: (1) they are variationally consistent in a conventional sense, if the solution is sought in a proper H space (compatible cases); (2) They pass the standard patch test when the solution is sought in a proper G space with discontinuous functions (incompatible cases); (3) the stiffness of the discretized model is reduced compared with the finite element method (FEM) model and possibly to the exact model, allowing us to obtain upper bound solutions with respect to both the FEM and the exact solutions and (4) the W2 models are less sensitive to the quality of the mesh, and triangular meshes can be used without any accuracy problems. These properties and theories have been confirmed numerically via examples solved using a number of W2 models including compatible and incompatible cases. We shall see that the G space theory and the W2 forms can formulate a variety of stable and convergent numerical methods with the FEM as one special case. Copyright © 2009 John Wiley & Sons, Ltd. [source] A unified approach for the formulation of interaction problems by the boundary element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2006Yalcín Mengi Abstract A unified formulation is presented, based on boundary element method, in a form suitable for performing the interaction analyses by substructure method for solid,solid and soil,structure problems. The proposed formulation permits the evaluation of all the elements of impedance and input motion matrices simultaneously at a single step in terms of system matrices of the boundary element method without solving any special problem, such as, unit displacement or load problem, as required in conventional methods. It eliminates further the complicated procedure and the need for using scattering analysis in the evaluation of input motion functions. To explain the formulation, it is first given for an inclusion interacting with an infinite surrounding medium under the influence of a seismic input, where both the inclusion and surrounding medium are treated as viscoelastic. It is shown that the formulation for a rigid inclusion may be obtained from that for flexible inclusion as a special case through a transformation. Then, the formulation is extended to other types of interaction problems: a multi-inclusion problem and an interaction problem involving a foundation embedded in a viscoelastic half-space. It is found that the proposed formulation remains essentially the same for all kinds of interaction problems and it can be used not only in regular interaction analysis, but also in the analysis involving diffraction of waves in a medium containing holes. Copyright © 2005 John Wiley & Sons, Ltd. [source] A unified formulation for continuum mechanics applied to fluid,structure interaction in flexible tubesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2005C. J. Greenshields Abstract This paper outlines the development of a new procedure for analysing continuum mechanics problems with a particular focus on fluid,structure interaction in flexible tubes. A review of current methods of fluid,structure coupling highlights common limitations of high computational cost and solution instability. It is proposed that these limitations can be overcome by an alternative approach in which both fluid and solid components are solved within a single discretized continuum domain. A single system of momentum and continuity equations is therefore derived that governs both fluids and solids and which are solved with a single mesh using finite volume discretization schemes. The method is validated first by simulating dynamic oscillation of a clamped elastic beam. It is then applied to study the case of interest,wave propagation in highly flexible tubes,in which a predicted wave speed of 8.58 m/s falls within 2% of an approximate analytical solution. The method shows further good agreement with analytical solutions for tubes of increasing rigidity, covering a range of wave speeds from those found in arteries to that in the undisturbed fluid. Copyright © 2005 John Wiley & Sons, Ltd. [source] An improved weighting method with multibounds formulation and convex programming for multicriteria structural optimizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 9 2001W. H. Zhang Abstract This paper presents an improved weighting method for multicriteria structural optimization. By introducing artificial design variables, here called as multibounds formulation (MBF), we demonstrate mathematically that the weighting combination of criteria can be transformed into a simplified problem with a linear objective function. This is a unified formulation for one criterion and multicriteria problems. Due to the uncoupling of involved criteria after the transformation, the extension and the adaptation of monotonic approximation-based convex programming methods such as the convex linearization (CONLIN) or the method of moving asymptotes (MMA) are made possible to solve multicriteria problems as efficiently as for one criterion problems. In this work, a multicriteria optimization tool is developed by integrating the multibounds formulation with the CONLIN optimizer and the ABAQUS finite element analysis system. Some numerical examples are taken into account to show the efficiency of this approach. Copyright © 2001 John Wiley & Sons, Ltd. [source] HF,CC model for atoms and molecules,INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 4-5 2002E. Clementi Abstract The Hartree,Fock,Clementi,Corongiu method (HF,CC) is revisited, aiming at an unified formulation for post-HF energy computations in atomic and molecular systems. For atomic systems new parameterizations of the HF,CC functional are proposed for the computation of atoms. The previous HF,CC molecular functional (Clementi, E.; Corongiu, G. Theochem 2001, 543, 39), revisited and recalibrated with a new optimization of the parameters, is tested with a sample of 131 molecules, including radicals, H-bond, and van der Waals systems. The atomization energy is decomposed into "HF classic" energy (the sum of the HF nuclear electron, HF kinetic, and HF Coulomb energies), "HF exchange" energy, and correlation energy; the latter is computed with a scaling functional with atomic, covalent, ionic, and van der Waals contributions. For the sample of 131 molecules, the computed HF,CC atomization energies have an average standard deviation of 1.89 kcal/mol. The atomic and molecular components of the correlation energy are decomposed into nuclear electron, kinetic, Coulomb, and exchange contributions; these decompositions characterize the HF,CC model and are used to explain the origin of the chemical bond. Computations on van der Waals systems show the validity of the HF,CC method also for long-range weak interactions. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002 [source] A convection scheme for data assimilation: Description and initial testsTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 606 2005Philippe Lopez Abstract A new simplified parametrization of subgrid-scale convective processes has been developed and tested in the framework of the ECMWF Integrated Forecasting System for the purpose of variational data assimilation, singular vector calculations and adjoint sensitivity experiments. Its formulation is based on the full nonlinear convection scheme used in ECMWF forecasts, but a set of simplifications has been applied to substantially improve its linear behaviour. These include the specification of a single closure assumption based on convective available potential energy, the uncoupling of the equations for the convective mass flux and updraught characteristics and a unified formulation of the entrainment and detrainment rates. Simplified representations of downdraughts and momentum transport are also included in the new scheme. Despite these simplifications, the forecasting ability of the new convective parametrization is shown to remain satisfactory even in seasonal integrations. A detailed study of its Jacobians and the validity of the linear hypothesis is presented. The new scheme is also tested in combination with the new simplified parametrization of large-scale clouds and precipitation recently developed at ECMWF. In contrast with the simplified convective parametrization currently used in ECMWF's operational 4D-Var, its tangent-linear and adjoint versions account for perturbations of all convective quantities including convective mass flux, updraught characteristics and precipitation fluxes. Therefore the new scheme is expected to be beneficial when combined with radiative calculations that are directly affected by condensation and precipitation. Examples are presented of applications of the new moist physics in 1D-Var retrievals using microwave brightness temperature measurements and in adjoint sensitivity experiments. Copyright © 2005 Royal Meteorological Society. [source] | ||||||||||