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Initial-boundary-value Problem (initial-boundary-value + problem)

Distribution by Scientific Domains

Engineering	50%

Selected Abstracts

Analysis of adiabatic shear bands in heat-conducting elastothermoviscoplastic materials by the meshless local Bubnov,Galerkin method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2009
R. C. Batra
Abstract Transient finite coupled thermomechanical simple shearing deformations of a block made of an elastothermoviscoplastic material that exhibits strain and strain-rate hardening, and thermal softening are studied by using the meshless local Bubnov,Galerkin method. A local nonlinear weak formulation and a semidiscrete formulation of the problem are derived. The prescribed velocity at the top and the bottom surfaces of the block is enforced by using a set of Lagrange multipliers. A homogeneous solution of the problem is perturbed by superimposing on it a temperature bump at the center of the block, and the resulting nonlinear initial-boundary-value problem is solved numerically. We have developed an integration scheme to numerically integrate the set of coupled nonlinear ordinary differential equations. The inhomogeneous deformations of the block are found to concentrate in a narrow region of intense plastic deformation usually called a shear band. For a material exhibiting enhanced thermal softening, it is shown that as the shear stress within the region of localization collapses, an unloading elastic shear wave emanates outward from the edges of the shear band. In the absence of an analytical solution, the computed results have been compared with those obtained by the finite element and the modified smoothed particle hydrodynamics methods. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Non-linear finite element analysis of large amplitude sloshing flow in two-dimensional tank

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2004
J. R. Cho
Abstract This paper is concerned with the accurate and stable finite element analysis of large amplitude liquid sloshing in two-dimensional tank under the forced excitation. The sloshing flow is formulated as an initial-boundary-value problem based upon the fully non-linear potential flow theory. The flow velocity field is interpolated from the velocity potential with second-order elements according to least square method, and the free surface conditions are tracked by making use of the direct time differentiation and the predictor,corrector method. Meanwhile, the liquid mesh is adapted such that the incompressibility condition is strictly satisfied. The accuracy and stability of the numerical method introduced are verified from the comparison with the existing reference solutions. As well, the numerical results are compared with those obtained by the linear theory with respect to the liquid fill height and the excitation amplitude. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Point-wise decay estimate for the global classical solutions to quasilinear hyperbolic systems

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2009
Yi Zhou
Abstract In this paper, we first consider the Cauchy problem for quasilinear strictly hyperbolic systems with weak linear degeneracy. The existence of global classical solutions for small and decay initial data was established in (Commun. Partial Differential Equations 1994; 19:1263,1317; Nonlinear Anal. 1997; 28:1299,1322; Chin. Ann. Math. 2004; 25B:37,56). We give a new, very simple proof of this result and also give a sharp point-wise decay estimate of the solution. Then, we consider the mixed initial-boundary-value problem for quasilinear hyperbolic systems with nonlinear boundary conditions in the first quadrant. Under the assumption that the positive eigenvalues are weakly linearly degenerate, the global existence of classical solution with small and decay initial and boundary data was established in (Discrete Continuous Dynamical Systems 2005; 12(1):59,78; Zhou and Yang, in press). We also give a simple proof of this result as well as a sharp point-wise decay estimate of the solution. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Convergence of coercive approximations for a model of gradient type in poroplasticity

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 12 2009
Sebastian Owczarek
Abstract We study the existence theory to the quasi-static initial-boundary-value problem of poroplasticity. In this article the classical quasi-static Biot model is considered for soil consolidation coupled with a nonlinear system of differential equations. This work, for the poroplasticity model of monotone-gradient type, presents a convergence result of the coercive approximation to the solution of the original noncoercive problem. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Dynamic boundary stabilization of a Reissner,Mindlin plate with Timoshenko beam

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 11 2004
Marié Grobbelaar-Van Dalsen
Abstract This paper is concerned with well-posedness results for a mathematical model for the transversal vibrations of a two-dimensional hybrid elastic structure consisting of a rectangular Reissner,Mindlin plate with a Timoshenko beam attached to its free edge. The model incorporates linear dynamic feedback controls along the interface between the plate and the beam. Classical semigroup methods are employed to show the unique solvability of the coupled initial-boundary-value problem. We also show that the energy associated with the system exhibits the property of strong stability. Copyright © 2004 John Wiley & Sons, Ltd. [source]

An Elasto-Plastic Formulation of a Soil-Foundation Interface

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003
Wolfgang Ehlers Prof. Dr.-Ing.
In this paper, a special interface formulation for the continuum mechanical description of the contact zone between soil and geotechnical foundation is presented. The proposed model is based on the Theory of Porous Media (TPM), a consistent approach to describe geomaterials in a macroscopic frame [1]. Assuming quasi-static conditions, strains in the porous soil body are due to an elasto-plastic work-hardening model, whereas the constitutive properties of the interface are based on the continuous elasto-plastic behaviour of the soil body and on the failure kinematics of the contact zone. Using the FE method, a 3-d initial-boundary-value problem of a soil-foundation interaction is discussed with a close look on the occurring localization phenomenon. [source]