Numerical Treatment (numerical + treatment)

Distribution by Scientific Domains

Selected Abstracts

Numerical Treatment of Seismic Accelerograms and of Inelastic Seismic Structural Responses Using Harmonic Wavelets

Pol D. Spanos
The effectiveness of the harmonic wavelets for capturing the temporal evolution of the frequency content of strong ground motions is demonstrated. In this regard, a detailed study of important earthquake accelerograms is undertaken and smooth joint time-frequency spectra are provided for two near-field and two far-field records; inherent in this analysis is the concept of the mean instantaneous frequency. Furthermore, as a paradigm of usefulness for aseismic structural purposes, a similar analysis is conducted for the response of a 20-story steel frame benchmark building considering one of the four accelerograms scaled by appropriate factors as the excitation to simulate undamaged and severely damaged conditions for the structure. The resulting joint time-frequency representation of the response time histories captures the influence of nonlinearity on the variation of the effective natural frequencies of a structural system during the evolution of a seismic event. In this context, the potential of the harmonic wavelet transform as a detection tool for global structural damage is explored in conjunction with the concept of monitoring the mean instantaneous frequency of records of critical structural responses. [source]

A simplified analysis of interface failure under compressive normal stress and monotonic or cyclic shear loading

Zenon Mrz
Abstract Interface damage and delamination is usually accompanied by frictional slip at contacting interfaces under compressive normal stress. The present work is concerned with an analysis of progressive interface failure using the cohesive crack model with the critical stress softening and frictional traction present at the contact. Both monotonic and cyclic loadings are considered for anti-plane shear of an elastic plate bonded to a rigid substrate by means of cohesive interface. An analytical solution can be obtained by neglecting the effect of minor shear stress component. The analysis of progressive delamination process revealed three solution types, namely: short, medium and long plate solutions. The long plate solution was obtained under an assumption of quasistatic progressive growth of the delamination zone. In view of snap back response, the quasistatic deformation process cannot be executed by either traction or displacement control. The states of frictional slip accompanied by shake down or incremental failure are distinguished in the case of cyclic loading, related to load amplitude and structural dimensions. The analysis provides a reference solution for numerical treatment of more complex cases. Copyright 2005 John Wiley & Sons, Ltd. [source]

An appropriate quadrature rule for the analysis of plane crack problems in the boundary-element method

E. E. Theotokoglou
Abstract An hypersingular integral equation of a three-dimensional elastic solid with an embedded planar crack subjected to a uniform stress field at infinity is derived. The solution of the boundary-integral equation is succeeded taking into consideration an appropriate Gauss quadrature rule for finite part integrals which is suitable for the numerical treatment of any plane crack with a smooth-contour shape and permit the fast convergence for the results. The problem of a circular and of an elliptical crack in an infinite body subjected to a uniform stress field at infinity is confronted; and the stress intensity factors are calculated. Copyright 2001 John Wiley & Sons, Ltd. [source]

On the numerical treatment of initial strains in biological soft tissues

E. Pea
Abstract In this paper, different methodologies to enforce initial stresses or strains in finite strain problems are compared. Since our main interest relies on the simulation of living tissues, an orthotropic hyperelastic constitutive model has been used to describe their passive material behaviour. Different methods are presented and discussed. Firstly, the initial strain distribution is obtained after deformation from a previously assumed to be known stress-free state using an appropriate finite element approach. This approach usually involves important mesh distortions. The second method consists on imposing the initial strain field from the definition of an initial incompatible ,deformation gradient' field obtained from experimental data. This incompatible tensor field can be imposed in two ways, depending on the origin of the experimental tests. In some cases as ligaments, the experiment is carried out from the stress-free configuration, while in blood vessels the starting point is usually the load-free configuration with residual stresses. So the strain energy function would remain the same for the whole simulation or redefined from the new origin of the experiment. Some validation and realistic examples are presented to show the performance of the strategies and to quantify the errors appearing in each of them. Copyright 2006 John Wiley & Sons, Ltd. [source]

Numerical modelling of free-surface flows in ship hydrodynamics

U. P. Bulgarelli
Abstract Current trends in the investigation of ship hydrodynamics are reviewed with emphasis on the problem of wave-body interaction. This includes the classical seakeeping problem and as a special case, the problem of prediction for the drag encountered by a ship advancing in calm water. Specific issues related to the numerical treatment of the air,water interface are examined, with emphasis on the modelling of wave breaking. The discussion on the large-scale modelling of the flow around ships is focused on the prediction of wave loads, ship motions and resistance in calm water. Copyright 2003 John Wiley & Sons, Ltd. [source]

A finite volume solver for 1D shallow-water equations applied to an actual river

N. Gouta
Abstract This paper describes the numerical solution of the 1D shallow-water equations by a finite volume scheme based on the Roe solver. In the first part, the 1D shallow-water equations are presented. These equations model the free-surface flows in a river. This set of equations is widely used for applications: dam-break waves, reservoir emptying, flooding, etc. The main feature of these equations is the presence of a non-conservative term in the momentum equation in the case of an actual river. In order to apply schemes well adapted to conservative equations, this term is split in two terms: a conservative one which is kept on the left-hand side of the equation of momentum and the non-conservative part is introduced as a source term on the right-hand side. In the second section, we describe the scheme based on a Roe Solver for the homogeneous problem. Next, the numerical treatment of the source term which is the essential point of the numerical modelisation is described. The source term is split in two components: one is upwinded and the other is treated according to a centred discretization. By using this method for the discretization of the source term, one gets the right behaviour for steady flow. Finally, in the last part, the problem of validation is tackled. Most of the numerical tests have been defined for a working group about dam-break wave simulation. A real dam-break wave simulation will be shown. Copyright 2002 John Wiley & Sons, Ltd. [source]

Error analysis and Hertz vector approach for an electromagnetic interaction between a line current and a conducting plate

M.T. Attaf
Abstract In the present paper we first introduce the Hertz vector potential and examine how the specific case of electromagnetic field diffusion problems can be formulated in terms of this potential. Its connection to other commonly used potentials is presented and a basic approach in the form of a suitable set of equations is introduced. The suggested method is then successfully applied to solve the case of an electromagnetic interaction between a straight conductor carrying sinusoidal current and a finite thickness fixed plate. Due to the oscillatory aspect of the integral solution obtained, an appropriate numerical treatment is investigated and various curves are shown to illustrate the convergence behaviour. Copyright 2003 John Wiley & Sons, Ltd. [source]

Development of an improved method for investigating the frictional properties of lubricants under transient EHD conditions

B.-O. hrstrm
Abstract In the design and evaluation of mechanical system performance it is important to know the frictional qualities of the lubricant. Without correct numerical treatment of the lubricant during simulations of large systems, e.g., drive trains in trucks and buses, the results will, to a large extent, be inaccurate. However, obtaining detailed information places demands on the test equipment as the events are both transient and highly loaded. Under quasi-static conditions, forces are measured with force transducers, but in elasto-hydrodynamically lubricated conjunctions, where pressures are so high that the surrounding surfaces deform elastically, this cannot be done without permanently damaging the equipment. The conceptual design of the test equipment must therefore incorporate the measuring process in transient conditions (loading-unloading times of 200,500 ,s) being performed in real time, and allow extreme pressures of up to 3 GPa without component destruction. One way to obtain accurate friction data successfully is to apply a concentrated force pulse to a non-instrumented surface and to measure the response from that pulse elsewhere. The development of a measurement technique, the Lulea ball and bar apparatus, which utilises wave propagation theory, is presented in this paper. An oblique impact on a robust end plate on a rod was used to generate both non-dispersive compression waves and dispersive flexural waves. The normal force created by the axial wave was measured using strain gauges, while the transverse force was derived from the fast Fourier transforms of two lateral acceleration histories, using dynamic beam theory. The relation between the normal and tangential force histories showed the frictional properties at the impact as a function of time. A variety of lubricants was also studied at Hertzian pressures of up to 2.5 GPa, and the development of the method and results are presented. Experiments indicate that different lubricants exhibit different frictional properties and that the resolution in the test equipment is sufficient to indicate this. [source]

Heat transfer at high energy devices with prescribed cooling flow

Jens Breuer
Abstract We study the heat transfer from a high-energy electric device into a surrounding cooling flow. We analyse several simplifications of the model to allow an easier numerical treatment. First, the flow variables velocity and pressure are assumed to be independent from the temperature which allows a reduction to Prandtl's boundary layer model and leads to a coupled nonlinear transmission problem for the temperature distribution. Second, a further simplification using a Kirchhoff transform leads to a coupled Laplace equation with nonlinear boundary conditions. We analyse existence and uniqueness of both the continuous and discrete systems. Finally, we provide some numerical results for a simple two-dimensional model problem. Copyright 2006 John Wiley & Sons, Ltd. [source]

Application of a computer model to evaluate the ability of plastics to act as functional barriers

Jong-Koo Han
Abstract A simulation model computer program, which accounts for not only the diffusion process inside the polymer but also partitioning of the contaminant between the polymer and the contacting phase, was developed based on a numerical treatment, the finite element method, to quantify migration through multilayer structures. The accuracy of the model in predicting migration was demonstrated successfully by comparing simulated results to experimental data. For this study, three-layer co-extruded high density polyethylene (HDPE) film samples, having a symmetrical structure with a contaminated core layer and virgin outer layers as the functional barriers, were fabricated with varying thickness of the outer layers and with a known amount of selected contaminant simulant, 3,5-di-t-butyl-4-hydroxytoluene (BHT), in the core layer. Migration of the contaminant simulant from the core layer to the liquid food simulants was determined experimentally as a function of the thickness of the outer layer at different temperatures. The computer program, developed as a total solution package for migration problems, can be applied not only to multilayer structures made with the same type of plastics but also to structures with different plastics, e.g. PP/PE/PP. This work might provide the potential for wider use of recycled plastic, especially polyolefins, which have lower barrier properties, in food packaging, and simplification of the task of convincing the FDA that adequate safety guarantees have been provided. Copyright 2003 John Wiley & Sons, Ltd. [source]

Resonant gravity-wave drag enhancement in linear stratified flow over mountains

M. A. C. Teixeira
Abstract High-drag states produced in stratified flow over a 2D ridge and an axisymmetric mountain are investigated using a linear, hydrostatic, analytical model. A wind profile is assumed where the background velocity is constant up to a height z1 and then decreases linearly, and the internal gravity-wave solutions are calculated exactly. In flow over a 2D ridge, the normalized surface drag is given by a closed-form analytical expression, while in flow over an axisymmetric mountain it is given by an expression involving a simple 1D integral. The drag is found to depend on two dimensionless parameters: a dimensionless height formed with z1, and the Richardson number, Ri, in the shear layer. The drag oscillates as z1 increases, with a period of half the hydrostatic vertical wavelength of the gravity waves. The amplitude of this modulation increases as Ri decreases. This behaviour is due to wave reflection at z1. Drag maxima correspond to constructive interference of the upward- and downward-propagating waves in the region znumerical treatment of nonlinear effects is presented, where zc appears to become more relevant, and flow over a 2D ridge qualitatively changes its character. But these effects, and their connection with linear theory, still need to be better understood. Copyright 2005 Royal Meteorological Society. [source]

Second-order backward stochastic differential equations and fully nonlinear parabolic PDEs

Patrick Cheridito
For a d -dimensional diffusion of the form dXt = ,(Xt)dt + ,(Xt)dWt and continuous functions f and g, we study the existence and uniqueness of adapted processes Y, Z, ,, and A solving the second-order backward stochastic differential equation (2BSDE) If the associated PDE has a sufficiently regular solution, then it follows directly from It's formula that the processes solve the 2BSDE, where ,, is the Dynkin operator of X without the drift term. The main result of the paper shows that if f is Lipschitz in Y as well as decreasing in , and the PDE satisfies a comparison principle as in the theory of viscosity solutions, then the existence of a solution (Y, Z,,, A) to the 2BSDE implies that the associated PDE has a unique continuous viscosity solution v and the process Y is of the form Yt = v(t, Xt), t , [0, T]. In particular, the 2BSDE has at most one solution. This provides a stochastic representation for solutions of fully nonlinear parabolic PDEs. As a consequence, the numerical treatment of such PDEs can now be approached by Monte Carlo methods. 2006 Wiley Periodicals, Inc. [source]