# Numerical Solution (numerical + solution)

Distribution by Scientific Domains

## Selected Abstracts

### Numerical solution for consolidation and desiccation of soft soils

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2002
Daniel T. C. Yao
Abstract The consolidation and desiccation behaviour of soft soils can be described by two time-dependent non-linear partial differential equations using the finite strain theory. Analytical solutions do not exist for these governing equations. In this paper, we develop efficient numerical methods and software for finding the numerical solutions. We introduce a semi-implicit time integration scheme, and show numerically that our method converges. In addition, the numerical solution matches well with the experimental result. A boundary refinement method is also developed to improve the convergence and stability for the case of Neumann type boundary conditions. Interface governing equations are derived to maintain the continuity of consolidation and desiccation processes. This is useful because the soil column can undergo desiccation on top and consolidation on the bottom simultaneously. The numerical algorithms has been implemented into a computer program and the results have been verified with centrifuge test results conducted in our laboratory. Copyright © 2001 John Wiley & Sons, Ltd. [source]

### Numerical solution of the oxygen diffusion in absorbing tissue with a moving boundary

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 9 2006
Abdellatif BoureghdaArticle first published online: 9 FEB 200
Abstract A problem of oxygen diffusion in absorbing medium is complex. A mathematical model of this problem is presented, which has previously been investigated by Crank and Gupta (J. Inst. Math. Appl. 1972; 10: 19,33) is studied using a different method of solution. Approximate analytical and numerical solutions of its partial differential equations are obtained, which describe the diffusion of oxygen in absorbing tissue. A moving boundary is an essential feature of this problem but the conditions which determine its movements are different. The results are compared with those of Crank and Gupta. In most cases the agreement is fair. Copyright © 2006 John Wiley & Sons, Ltd. [source]

### Analysis of coupled seepage and stress fields in rock mass around the Xiaowan arch dam

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2004
Chai Junrui
Abstract The Xiaowan arch dam, with a maximum height of 292 m, is located across the Lancangjiang River in Yunnan Province of China, and once completed will be the highest arch dam in China. Because of the high water head and the arch action, it is necessary to analyse the interaction between seepage and stress fields in rock mass around the Xiaowan arch dam. Numerical solution of coupled seepage and stress fields in rock mass around the Xiaowan arch dam is analysed by means of the multi-level fracture network model and the finite element method. It can be shown from the computation results that storage of the reservoir makes the seepage field change much, and makes the effective vertical stress in rock foundation near the dam and the tensile stress in the abutment rock mass increase, and that the coupled action between seepage and stress fields should be taken into account. Copyright © 2004 John Wiley & Sons, Ltd. [source]

### Direct solution of ill-posed boundary value problems by radial basis function collocation method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2005
A. H.-D.
Abstract Numerical solution of ill-posed boundary value problems normally requires iterative procedures. In a typical solution, the ill-posed problem is first converted to a well-posed one by assuming the missing boundary values. The new problem is solved by a conventional numerical technique and the solution is checked against the unused data. The problem is solved iteratively using optimization schemes until convergence is achieved. The present paper offers a different procedure. Using the radial basis function collocation method, we demonstrate that the solution of certain ill-posed problems can be accomplished without iteration. This method not only is efficient and accurate, but also circumvents the stability problem that can exist in the iterative method. Copyright © 2005 John Wiley & Sons, Ltd. [source]

### Numerical solution of eddy current problems in ferromagnetic bodies travelling in a transverse magnetic field

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2003
W. Peterson
Abstract Eddy currents are investigated in a ferromagnetic bar travelling in a transverse magnetic field. Such an open boundary field problem is analysed by a hybrid approach based on Galerkin finite element formulation coupled with a separation of variables. A steady state is considered, introducing time-periodic boundary conditions. The resultant system of non-linear equations is solved by an iterative procedure based on Brouwer's fixed-point theorem. Numerical results are presented for a bar of circular cross-section made of cast steel or cast iron. Selected examples of the field distribution and characteristics of eddy-current power losses are enclosed in graphic form. Copyright © 2003 John Wiley & Sons, Ltd. [source]

### Flow of a third grade fluid due to an accelerated disk

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2010
S. Asghar
Abstract The magnetohydrodynamic (MHD) flow induced by non-coaxial rotation of porous disk and a third grade fluid at infinity is investigated. The disk is moving with uniform acceleration and rotating with a uniform angular velocity. Numerical solution of the governing nonlinear initial and boundary value problem is obtained. The effects of physical parameters on the velocity profiles are examined in detail. The present study shows that the constant acceleration part has a greater influence than the time part of the assumed variable velocity of the disk. Copyright © 2009 John Wiley & Sons, Ltd. [source]

### Oscillatory flow of a fourth-order fluid

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2009
T. Hayat
Abstract This study deals with the incompressible flow of a fourth-order fluid over a porous plate oscillating in its own plane. Numerical solution of the nonlinear problem governing the flow is given. The influence of various parameters of interest on the velocity distribution is shown and discussed with the help of several graphs. Copyright © 2008 John Wiley & Sons, Ltd. [source]

### Numerical solution of steady free-surface flows by the adjoint optimal shape design method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2003
E. H. van Brummelen
Abstract Numerical solution of flows that are partially bounded by a freely moving boundary is of great importance in practical applications such as ship hydrodynamics. Free-boundary problems can be reformulated into optimal shape design problems, which can in principle be solved efficiently by the adjoint method. In this work we investigate the suitability of the adjoint shape optimization method for solving steady free-surface flows. The asymptotic convergence behaviour of the method is determined for free-surface flows in 2D and 3D. It is shown that the convergence behaviour depends sensitively on the occurrence of critical modes. The convergence behaviour is moreover shown to be mesh-width independent, provided that proper preconditioning is applied. Numerical results are presented for 2D flow over an obstacle in a channel. The observed convergence behaviour is indeed mesh-width independent and conform the derived asymptotic estimates. Copyright © 2003 John Wiley & Sons, Ltd. [source]

### Mathematical simulation of calcimine deliming in the production of gelatin

AICHE JOURNAL, Issue 7 2010
Karel Kolomazník
Abstract Calcimine is a valuable by-product originating during the processing of cured hide into leather. It is used as raw material in the production of gelatin and biodegradable sheets. For further usage, it is necessary to remove calcium hydroxide from calcimine by chemical deliming, which is, from the environmental protection point of view, the most important stage of the entire deliming process. In this article, a mathematical description of chemical deliming is proposed, based on the unreacted nucleus approach. Numerical solution of the model is found, concentration fields of the reacting chemicals described, and the evolution of the acido-basic boundary inside calcimine shown. The model is used to justify a simplified way to determine the effective diffusion coefficient of the deliming agent. The model can also be used as a basis for optimization of the deliming process. © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source]

### Theoretical Modeling of the Phase Separation Dynamics in Blends of Reactive Monomers

MACROMOLECULAR THEORY AND SIMULATIONS, Issue 5 2005
Gregory R. Yandek
Abstract Summary: Experimental observations of the dynamics of phase behavior for blends of reactive constituents, i.e. diglycidyl ether of bisphenol A (DGEBA), curing agent methylene dianiline (MDA), and a reactive liquid rubber (R45EPI), have been theoretically modeled by coupling system thermodynamics governed by a summation of the free energies of mixing and network elasticity with reaction kinetics and diffusion equations. Snap-shots of the temporal evolution of ternary phase diagrams have been established based on the self-condensation reactions of DGEBA-MDA and R45EPI as well as a cross-reaction between the two constituents forming a copolymer. Numerical solution of the proposed mean-field model provides good qualitative agreement with experimental results, namely, the observance of phase separation followed by a phase dissolution and subsequent secondary segregation in a 50/25.4/50 DGEBA/MDA/R45EPI mixture, as well as a single gradual phase separation in a 70/25.4/30 mixture. The phase separation dynamics are explained by a competition between the growth in molecular weights of the reactive species rendering the systems towards instability, and the formation of copolymer acting to compatibilize the mixtures. Theoretical phase diagram for a DGEBA/MDA/R45EPI system. [source]

### Numerical solution of large-scale Lyapunov equations, Riccati equations, and linear-quadratic optimal control problems

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 9 2008
Peter Benner
Abstract We study large-scale, continuous-time linear time-invariant control systems with a sparse or structured state matrix and a relatively small number of inputs and outputs. The main contributions of this paper are numerical algorithms for the solution of large algebraic Lyapunov and Riccati equations and linear-quadratic optimal control problems, which arise from such systems. First, we review an alternating direction implicit iteration-based method to compute approximate low-rank Cholesky factors of the solution matrix of large-scale Lyapunov equations, and we propose a refined version of this algorithm. Second, a combination of this method with a variant of Newton's method (in this context also called Kleinman iteration) results in an algorithm for the solution of large-scale Riccati equations. Third, we describe an implicit version of this algorithm for the solution of linear-quadratic optimal control problems, which computes the feedback directly without solving the underlying algebraic Riccati equation explicitly. Our algorithms are efficient with respect to both memory and computation. In particular, they can be applied to problems of very large scale, where square, dense matrices of the system order cannot be stored in the computer memory. We study the performance of our algorithms in numerical experiments. Copyright © 2008 John Wiley & Sons, Ltd. [source]

### Numerical solution of the free-surface viscous flow on a horizontal rotating elliptical cylinder

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2008
Roland Hunt
Abstract The numerical solution of the free-surface fluid flow on a rotating elliptical cylinder is presented. Up to the present, research has concentrated on the circular cylinder for which steady solutions are the main interest. However, for noncircular cylinders, such as the ellipse, steady solutions are no longer possible, but there will be periodic solutions in which the solution is repeated after one full revolution of the cylinder. It is this new aspect that makes the investigation of noncircular cylinders novel. Here we consider both the time-dependent and periodic solutions for zero Reynolds number fluid flow. The numerical solution is expedited by first mapping the fluid film domain onto a rectangle such that the position of the free-surface is determined as part of the solution. For the time-dependent case a simple time-marching method of lines approach is adopted. For the periodic solution the discretised nonlinear equations have to be solved simultaneously over a time period. The resulting large system of equations is solved using Newton's method in which the form of the Jacobian enables a straightforward decomposition to be implemented, which makes matrix inversion manageable. In the periodic case all derivatives have been approximated pseudospectrally with the time derivative approximated by a differentiation matrix which has been specially derived so that the weight of fluid is algebraically conserved. Of interest is the solution for which the weight of fluid is at its maximum possible value, and this has been obtained by increasing the weight until a consistency break-down occurs. Time-dependent solutions do not produce the periodic solution after a long time-scale but have protuberances which are constantly appearing and disappearing. Periodic solutions exhibit spectral accuracy solutions and maximum supportable weight solutions have been obtained for ranges of eccentricity and angular velocity. The maximum weights are less than and approximately proportional to those obtained for the circular case. The shapes of maximum weight solutions is distinctly different from sub-maximum weight solutions. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 [source]

### Numerical solution to a linearized KdV equation on unbounded domain

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2008
Chunxiong Zheng
Abstract Exact absorbing boundary conditions for a linearized KdV equation are derived in this paper. Applying these boundary conditions at artificial boundary points yields an initial-boundary value problem defined only on a finite interval. A dual-Petrov-Galerkin scheme is proposed for numerical approximation. Fast evaluation method is developed to deal with convolutions involved in the exact absorbing boundary conditions. In the end, some numerical tests are presented to demonstrate the effectiveness and efficiency of the proposed method.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 [source]

### Numerical solution of the one-dimensional wave equation with an integral condition

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2007
Abstract The hyperbolic partial differential equation with an integral condition arises in many physical phenomena. In this research a numerical technique is developed for the one-dimensional hyperbolic equation that combine classical and integral boundary conditions. The proposed method is based on shifted Legendre tau technique. Illustrative examples are included to demonstrate the validity and applicability of the presented technique. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 282,292, 2007 [source]

### On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation,

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2005
Mehdi Dehghan
Abstract Numerical solution of hyperbolic partial differential equation with an integral condition continues to be a major research area with widespread applications in modern physics and technology. Many physical phenomena are modeled by nonclassical hyperbolic boundary value problems with nonlocal boundary conditions. In place of the classical specification of boundary data, we impose a nonlocal boundary condition. Partial differential equations with nonlocal boundary specifications have received much attention in last 20 years. However, most of the articles were directed to the second-order parabolic equation, particularly to heat conduction equation. We will deal here with new type of nonlocal boundary value problem that is the solution of hyperbolic partial differential equations with nonlocal boundary specifications. These nonlocal conditions arise mainly when the data on the boundary can not be measured directly. Several finite difference methods have been proposed for the numerical solution of this one-dimensional nonclassic boundary value problem. These computational techniques are compared using the largest error terms in the resulting modified equivalent partial differential equation. Numerical results supporting theoretical expectations are given. Restrictions on using higher order computational techniques for the studied problem are discussed. Suitable references on various physical applications and the theoretical aspects of solutions are introduced at the end of this article. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 [source]

### Numerical solution of thermal convection problems using the multidomain boundary element method

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2002
W. F. Florez
Abstract The multidomain dual reciprocity method (MD-DRM) has been effectively applied to the solution of two-dimensional thermal convection problems where the momentum and energy equations govern the motion of a viscous fluid. In the proposed boundary integral method the domain integrals are transformed into equivalent boundary integrals by the dual reciprocity approach applied in a subdomain basis. On each subregion or domain element the integral representation formulas for the velocity and temperature are applied and discretised using linear continuous boundary elements, and the equations from adjacent subregions are matched by additional continuity conditions. Some examples showing the accuracy, the efficiency and flexibility of the proposed method are presented. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 469,489, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10016 [source]

### Numerical solution of the three-dimensional parabolic equation with an integral condition ,

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2002
Mehdi Dehghan
Abstract Developement of numerical methods for obtaining approximate solutions to the three dimensional diffusion equation with an integral condition will be carried out. The numerical techniques discussed are based on the fully explicit (1,7) finite difference technique and the fully implicit (7,1) finite difference method and the (7,7) Crank-Nicolson type finite difference formula. The new developed methods are tested on a problem. Truncation error analysis and numerical examples are used to illustrate the accuracy of the new algorithms. The results of numerical testing show that the numerical methods based on the finite difference techniques discussed in the present article produce good results. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 193,202, 2002; DOI 10.1002/num.1040 [source]

### Numerical solution of a minimax ergodic optimal control problem

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007
Aragone Laura S.
In this work we consider an L, minimax ergodic optimal control problem with cumulative cost. We approximate the cost function as a limit of evolutions problems. We present the associated Hamilton-Jacobi-Bellman equation and we prove that it has a unique solution in the viscosity sense. As this HJB equation is consistent with a numerical procedure, we use this discretization to obtain a procedure for the primitive problem. For the numerical solution of the ergodic version we need a perturbation of the instantaneous cost function. We give an appropriate selection of the discretization and penalization parameters to obtain discrete solutions that converge to the optimal cost. We present numerical results. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

### An economic model of the limits to foraging range in central place foragers with numerical solutions for bumblebees

ECOLOGICAL ENTOMOLOGY, Issue 3 2000
James E. Cresswell
Summary 1. A model is described that evaluates the maximum economic foraging range in central place foragers by using optimality criteria to discriminate between foraging sites at different distances from the forager's central place. 2. The basic model can be varied to suit foragers that optimise either their rate of net energy uptake or their foraging efficiency. 3. The model requires specification of the time and energy budgets of travel and foraging, and of the rewards obtainable at potential foraging sites. 4. The specific case of bumblebees, whose foraging ranges are poorly known, is considered. 5. Numerical solutions of the model for parameter values that represent bumblebees and their forage predict economic foraging ranges exceeding several kilometres. The model demonstrates that economics alone can explain extensive flight ranges in bees. [source]

### Implicit integration of a chemo-plastic constitutive model for partially saturated soils

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2008
H. W. Zhang
Abstract A chemo-plastic constitutive model for partially saturated soils is proposed in this paper based on the existing models developed in Hueckel (Int. J. Numer. Anal. Meth. Geomech. 1997; 21:43,72) and Gallipoli et al. (Geotechnique 2003; 53:123,135). The chemical softening effects due to the increase in contaminant mass concentration are considered based on Hueckel's chemo-plastic model. Gallipoli's model is used to simulate the effects of suction and degree of saturation on mechanical behavior of partially saturated porous materials. In order to implement the proposed model in a finite element code, a fully implicit backward-Euler integration algorithm is put forward. Numerical solutions for the tests at local level and the application of the algorithm to the real boundary value problem demonstrate the accuracy and convergence properties of the proposed integration scheme. Copyright © 2008 John Wiley & Sons, Ltd. [source]

### A coupled model for solid deformation and gas leak flow

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2004
Peide Sun
Abstract From the viewpoint of interaction mechanics of solid and gas, a coupled mathematical model is presented for solid coal/rock-mass deformation and gas leak flow in parallel deformable coal seams. Numerical solutions using the strong implicit procedure (SIP) method to the coupled mathematical model for double parallel coal seams are also developed in detail. Numerical simulations for the prediction of safety range using protection layer mining are performed with experimental data from a mine with potential danger of coal/gas outbursts. Analyses show that the numerical simulation results are consistent with the measured data on the spot. The coupled model shows a positive future for applications in a wide range of gas-leak-flow-related problems in mining engineering, gas drainage engineering and mining safety engineering. Copyright © 2004 John Wiley & Sons, Ltd. [source]

### Numerical solutions for flow in porous media

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2003
J.G. Wang
Abstract A numerical approach is proposed to model the flow in porous media using homogenization theory. The proposed concept involves the analyses of micro-true flow at pore-level and macro-seepage flow at macro-level. Macro-seepage and microscopic characteristic flow equations are first derived from the Navier,Stokes equation at low Reynolds number through a two-scale homogenization method. This homogenization method adopts an asymptotic expansion of velocity and pressure through the micro-structures of porous media. A slightly compressible condition is introduced to express the characteristic flow through only characteristic velocity. This characteristic flow is then numerically solved using a penalty FEM scheme. Reduced integration technique is introduced for the volumetric term to avoid mesh locking. Finally, the numerical model is examined using two sets of permeability test data on clay and one set of permeability test data on sand. The numerical predictions agree well with the experimental data if constraint water film is considered for clay and two-dimensional cross-connection effect is included for sand. Copyright © 2003 John Wiley & Sons, Ltd. [source]

### Theoretical investigation of the cavity expansion problem based on a hypoplasticity model

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2001
V. A. Osinov
Abstract The problem of the symmetric quasi-static large-strain expansion of a cavity in an infinite granular body is studied. The body is assumed to be dry or fully drained so that the presence of the pore water can be disregarded. Both spherical and cylindrical cavities are considered. Numerical solutions to the boundary value problem are obtained with the use of the hypoplastic constitutive relation calibrated for a series of granular soils. As the radius of the cavity increases, the stresses and the density on the cavity surface asymptotically approach limit values corresponding to a so-called critical state. For a given soil, the limit values depend on the initial stresses and the initial density. A comparison is made between the solutions for different initial states and different soils. Applications to geotechnical problems such as cone penetration test and pressuremeter test are discussed. Copyright © 2001 John Wiley & Sons, Ltd. [source]

### DQ-based simulation of weakly nonlinear heat conduction processes

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2008
S. Tomasiello
Abstract In this paper, an explicit form for the numerical solution of problems in the space,time domain by using quadrature rules is proposed. The compact form of the shape functions recently proposed by the author is useful to the scope. Numerical solutions for the time-dependent one-dimensional nonlinear heat conduction problem are calculated by means of the iterative differential quadrature method, a method proposed by the author and based on quadrature rules. The accuracy of the solution and stability analysis show good performance of the approach. Copyright © 2007 John Wiley & Sons, Ltd. [source]

### Hydromagnetic flow and heat transfer of a conducting Casson fluid in a rectangular channel

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2006
Hazem Ali Attia
Abstract The transient hydromagnetic flow of an electrically conducting viscous incompressible non-Newtonian Casson fluid bounded by two parallel non-conducting plates is studied with heat transfer considering the Hall effect. An external uniform magnetic field is applied perpendicular to the plates and the fluid motion is subjected to a pressure gradient in the axial direction. The lower plate is stationary and the upper plate is suddenly set into motion and simultaneously suddenly isothermally heated to a temperature other than the lower plate temperature. Numerical solutions are obtained for the governing momentum and energy equations taking the Joule and viscous dissipations into consideration. The effect of the Hall term and the parameter describing the non-Newtonian behaviour on both the velocity and temperature distributions are studied. Copyright © 2005 John Wiley & Sons, Ltd. [source]

### Solution of clamped rectangular plate problems

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2004
Robert L. Taylor
Abstract In this brief note, we present an efficient scheme for determining very accurate solutions to the clamped rectangular plate problem. The method is based upon the classical double cosine series expansion and an exploitation of the Sherman,Morrison,Woodbury formula. If the cosine expansion involves M terms and N terms in the two plate axes directions, then the classical method for this problem involves solving a system of (MN) × (MN) equations. Our proposal reduces the problem down to a system of well-conditioned N × N equations (or M × M when M < N). Numerical solutions for rectangular plates with various side ratios are presented and compared to the solution generated via Hencky's method. Corrections to classical results and additional digits for use in finite-element convergence studies are given. As an application example, these are used to show the rate of convergence for thin plate finite-element solutions computed using the Bogner,Fox,Schmit element. Copyright © 2004 John Wiley & Sons, Ltd. [source]

### Numerical modeling of creep and creep damage in thin plates of arbitrary shape from materials with different behavior in tension and compression under plane stress conditions

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2009
A. Zolochevsky
Abstract A constitutive model for describing the creep and creep damage in initially isotropic materials with characteristics dependent on the loading type, such as tension, compression and shear, has been applied to the numerical modeling of creep deformation and creep damage growth in thin plates under plane stress conditions. The variational approach of establishing the basic equations of the plane stress problem under consideration has been introduced. For the solution of two-dimensional creep problems, the fourth-order Runge,Kutta,Merson's method of time integration, combined with the Ritz method and R-functions theory, has been used. Numerical solutions to various problems have been obtained, and the processes of creep deformation and creep damage growth in thin plates of arbitrary shape have been investigated. The influence of tension,compression asymmetry on the stress,strain state and damage evolution, with time, in thin plates of arbitrary shape, has been discussed. Copyright © 2009 John Wiley & Sons, Ltd. [source]

### Numerical simulations of a transient injection flow at low Mach number regime

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008
A. Beccantini
Abstract In this paper, a transient injection flow at low Mach number regime is investigated. Three different methods are used and analyzed. Two of them are based on asymptotic models of the Navier,Stokes equations valid for small Mach numbers, whereas the other is based on the full compressible Navier,Stokes equations, with particular care given to the discretization at low Mach numbers. Numerical solutions are computed both with or without the gravity force. Finally, the performance of the solvers in terms of CPU-time consumption is investigated, and the sensitivity of the solution to some parameters, which affect CPU time is also performed. Copyright © 2008 John Wiley & Sons, Ltd. [source]

### A numerical study of wave structures developed on the free surface of a film flowing on inclined planes and subjected to surface shear

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2006
N. H. Shuaib
Abstract In this work, we determine the different patterns of possible wave structures that can be observed on a thin film flowing on an inclined plane when at the free surface a shear force (surface traction) is applied. Different wave structures are obtained dependening on the selected combination of downstream and upstream boundary conditions and initial conditions. The resulting initial boundary value problems are solved numerically using the direct BEM numerical solution of the complete two-dimensional Stokes system of equations. In our numerical results, the initial discontinuous shock profiles joining uniform fluid depths are smoothed due to the two-dimensional character of the Stokes formulation, including the effect of the gravitational force as well as the interfacial surface tension force. In this way, physically feasible continuous surface profiles are determined, in which the initial uniform depths are joined by smooth moving wave structures. Numerical solutions have been attained to reproduce the different patterns of possible wave structures previously reported in the literature and extended to identify some other new structures and features defining the behaviour of the surface patterns. Copyright © 2006 John Wiley & Sons, Ltd. [source]

### A computational model for impact failure with shear-induced dilatancy

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 14 2003
Z. Chen
Abstract It has been observed in plate impact experiments that some brittle solids may undergo elastic deformation at the shock wave front, and fail catastrophically at a later time when they are shocked near but below the apparent Hugoniot elastic limit. Because this phenomenon appears to have features different from those of usual inelastic waves, it has been interpreted as the failure wave. To design an effective numerical procedure for simulating impact failure responses, a three-dimensional computational damage model is developed in this paper. The propagation of the failure wave behind the elastic shock wave is described by a non-linear diffusion equation. Macroscopic shear-induced dilatancy is assumed and treated as a one-to-one measure of the mean intensity of microcracking. The damage evolution in time is determined based on the assumption that the deviatoric strain energy in the elastically compressed material (undamaged) is converted, through the damaging process, into the volumetric potential energy in the comminuted and dilated material. For the ease in large-scale simulations, the coupled damage diffusion equation and the stress wave equation are solved via a staggered manner in a single computational domain. Numerical solutions by using both the finite element method and the material point method, i.e. with and without a rigid mesh connectivity, are presented and compared with the experimental data available. It is shown that the model simulations capture the essential features of the failure wave phenomenon observed in shock glasses, and that the numerical solutions for localized failure are not mesh-dependent. Copyright © 2003 John Wiley & Sons, Ltd. [source]