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Various Boundary Conditions (various + boundary_condition)
Selected AbstractsSolution of the unsaturated soil moisture equation using repeated transformsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2001S. G. Fityus Abstract An alternative method of solution for the linearized ,theta-based' form of the Richards equation of unsaturated flow is developed in two spatial dimensions. The Laplace and Fourier transformations are employed to reduce the Richards equation to an ordinary differential equation in terms of a transformed moisture content and the transform variables, s and ,. Separate analytic solutions to the transformed equation are developed for initial states which are either in equilibrium or dis-equilibrium. The solutions are assembled into a finite layer formulation satisfying continuity of soil suction, thereby facilitating the analysis of horizontally stratified soil profiles. Solution techniques are outlined for various boundary conditions including prescribed constant moisture content, prescribed constant flux and flux as a function of moisture change. Example solutions are compared with linearized finite element solutions. The agreement is found to be good. An adaptation of the method for treating the quasilinearized Richards equation with variable diffusivity is also described. Comparisons of quasilinear solutions with some earlier semi-analytical, finite element and finite difference results are also favourable. Copyright © 2001 John Wiley & Sons, Ltd. [source] Energy,momentum consistent finite element discretization of dynamic finite viscoelasticityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2010M. Groß Abstract This paper is concerned with energy,momentum consistent time discretizations of dynamic finite viscoelasticity. Energy consistency means that the total energy is conserved or dissipated by the fully discretized system in agreement with the laws of thermodynamics. The discretization is energy,momentum consistent if also momentum maps are conserved when group motions are superimposed to deformations. The performed approximation is based on a three-field formulation, in which the deformation field, the velocity field and a strain-like viscous internal variable field are treated as independent quantities. The new non-linear viscous evolution equation satisfies a non-negative viscous dissipation not only in the continuous case, but also in the fully discretized system. The initial boundary value problem is discretized by using finite elements in space and time. Thereby, the temporal approximation is performed prior to the spatial approximation in order to preserve the stress objectivity for finite rotation increments (incremental objectivity). Although the present approach makes possible to design schemes of arbitrary order, the focus is on finite elements relying on linear Lagrange polynomials for the sake of clearness. The discrete energy,momentum consistency is based on the collocation property and an enhanced second Piola,Kirchhoff stress tensor. The obtained coupled non-linear algebraic equations are consistently linearized. The corresponding iterative solution procedure is associated with newly proposed convergence criteria, which take the discrete energy consistency into account. The iterative solution procedure is therefore not complicated by different scalings in the independent variables, since the motion of the element is taken into account for solving the viscous evolution equation. Representative numerical simulations with various boundary conditions show the superior stability of the new time-integration algorithm in comparison with the ordinary midpoint rule. Both the quasi-rigid deformations during a free flight, and large deformations arising in a dynamic tensile test are considered. Copyright © 2009 John Wiley & Sons, Ltd. [source] Free vibration analysis of arches using curved beam elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2003Jong-Shyong Wu Abstract The natural frequencies and mode shapes for the radial (in-plane) bending vibrations of the uniform circular arches were investigated by means of the finite arch (curved beam) elements. Instead of the complicated explicit shape functions of the arch element given by the existing literature, the simple implicit shape functions associated with the tangential, radial (or normal) and rotational displacements of the arch element were derived and presented in matrix form. Based on the relationship between the nodal forces and the nodal displacements of a two-node six-degree-of-freedom arch element, the elemental stiffness matrix was derived, and based on the equation of kinetic energy and the implicit shape functions of an arch element the elemental consistent mass matrix with rotary inertia effect considered was obtained. Assembly of the foregoing elemental property matrices yields the overall stiffness and mass matrices of the complete curved beam. The standard techniques were used to determine the natural frequencies and mode shapes for the curved beam with various boundary conditions and subtended angles. In addition to the typical circular arches with constant curvatures, a hybrid beam constructed by using an arch segment connected with a straight beam segment at each of its two ends was also studied. For simplicity, a lumped mass model for the arch element was also presented. All numerical results were compared with the existing literature or those obtained from the finite element method based on the conventional straight beam element and good agreements were achieved. Copyright © 2003 John Wiley & Sons, Ltd. [source] In-plane vibrations of shear deformable curved beamsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2001Moshe Eisenberger Abstract This paper presents the exact dynamic stiffness matrix for a circular beam with a uniform cross-section. The stiffness matrix is frequency dependent, and the natural frequencies are those that cause the matrix to become singular. Using this matrix the exact natural frequencies of circular beams with various boundary conditions are calculated and compared with available results in the literature. Copyright © 2001 John Wiley & Sons, Ltd. [source] CHARMM: The biomolecular simulation programJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 10 2009B. R. Brooks Abstract CHARMM (Chemistry at HARvard Molecular Mechanics) is a highly versatile and widely used molecular simulation program. It has been developed over the last three decades with a primary focus on molecules of biological interest, including proteins, peptides, lipids, nucleic acids, carbohydrates, and small molecule ligands, as they occur in solution, crystals, and membrane environments. For the study of such systems, the program provides a large suite of computational tools that include numerous conformational and path sampling methods, free energy estimators, molecular minimization, dynamics, and analysis techniques, and model-building capabilities. The CHARMM program is applicable to problems involving a much broader class of many-particle systems. Calculations with CHARMM can be performed using a number of different energy functions and models, from mixed quantum mechanical-molecular mechanical force fields, to all-atom classical potential energy functions with explicit solvent and various boundary conditions, to implicit solvent and membrane models. The program has been ported to numerous platforms in both serial and parallel architectures. This article provides an overview of the program as it exists today with an emphasis on developments since the publication of the original CHARMM article in 1983. © 2009 Wiley Periodicals, Inc.J Comput Chem, 2009. [source] Exact boundary observability for 1-D quasilinear wave equationsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2006Tatsien Li (Daqian Li) Abstract By means of a direct and constructive method based on the theory of semi-global C2 solution, the local exact boundary observability and an implicit duality between the exact boundary controllability and the exact boundary observability are shown for 1-D quasilinear wave equations with various boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd. [source] Tectonic Constraints on the Transformation of Paleozoic Framework of Uplift and Depression in the Ordos AreaACTA GEOLOGICA SINICA (ENGLISH EDITION), Issue 6 2006WANG Qingfei Abstract: During the Paleozoic, the Ordos area in the western North China Plate was located at the intersecting position of microplates and controlled by their interaction. The structural framework in the Ordos area, which underwent transformations in the Ordovician, the Carboniferous and the Permian respectively, was dominated by the alternation of uplift and depression. The transformations of structural framework are utilized as the clues to investigate the microplates' interacting type and its response in the Ordos area. According to the regional structural evolution, the Ordos area is simplified into an isopachous, isotropic and elastic shell model, and under proposed various boundary conditions, three series of numerical simulations corresponding to the three structural transformations are carried out to determine the detailed tectonic constraints. Numerical simulations reveal that the structure of the uplift and depression, which is similar to the actual pattern, develops only under one special boundary condition in each of the three series, indicating that the structural framework responds to the unique tectonic background. The simulation results show that in the Early Paleozoic, the L-shaped paleouplift formed nearby the southwestern corner of the Ordos area because the intensity of the compressions in the southern and western boundaries resulting from the ocean-continent collisions was similar. In the Late Paleozoic, it evolved into continent-continent (or arc-continent) interaction in the southern and northern boundaries; in the preliminary stage of the interaction, since the interface between the North China Plate and the plates on the south and north was narrow, the relative acting force was little and the regional western boundary immobile, and the structural framework in the basin was characterized by the N-S trending slender-waist,shaped uplift; as the interface between the plates expanded gradually, the extrusive force in the southern and northern boundaries of the North China Plate increased, resulting in the paleogeographic divisions showing E-W trending, and, the western boundary of the basin was extruded westward due to the intense compression inducing the local NE trending of paleogeographic division in the central area. The simulation results further reflect that the symmetry of the uplift-depression pattern is restricted by that of the boundary conditions, suggesting that the Paleozoic structural transformations of the Ordos area under boundary constraints accord with the universal physical symmetrical principle. [source] | ||||||||||