An effective and efficient approach for nonlinear seismic analysis of bridges

A simplified and practical approach for nonlinear seismic analysis of highway bridges is proposed. Efficiency and effectiveness of the proposed model is discussed in detail. The effects of soil-structure interaction, analysis methods, and bridge skews on bridge responses are also carefully examined. The results obtained from the simplified model are compared to those of refined models. The paper concludes with a number of real bridge examples and recommendations.     

Deformation of sandwich panels cylindrically bent by point forces. 2. Development of procedure

Our proposed method [1] is extended for the cylindrical bending of an asymmetrical composite panel upon piecewise constant loading and point forces, with and without allowance for transversal stiffness (perfect compliance) in shear or tension/compression along the normal. A set of fundamental functions was obtained for all the cases examined. The properties of functions were studied taking account of the discontinuous nature of the surface loading. The set of functions was normalized for initial values of the variable coordinate. Integral relationships required for analysis were derived and an identical expression of the unit function was represented in terms of the fundamental function set. The boundary problem of a panel supported along the surface of its lower face layer with free ends is reduced to the Cauchy problem. The solution is greatly simplified for a panel symmetrical relative to its mean plane. Asymptotic formulas were obtained for the case of infinite panel length. Relationships are give for the stresses and layer deflections, which permit consideration of all the features of the stress state in addition to simplified calculations for actual panel design.Communication 1, see [1].Institute of Polymer Mechanics, Latvian Academy of Sciences, Riga LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 1, pp. 34–65, January–February, 1997.     

Coupled Models and Parallel Simulations for Three-Dimensional Full-Stokes Ice Sheet Modeling

A three-dimensional full-Stokes computational model is considered for determining the dynamics,temperature,and thickness of ice sheets.The goveming thermomechanical equations consist of the three-dimensional full-Stokes system with nonlinear rheology for the momentum,an advective-diffusion energy equation for temperature evolution,and a mass conservation equation for ice-thickness changes.Here,we discuss the variable resolution meshes,the finite element discretizations,and the parallel algorithms employed by the model components.The solvers are integrated through a well-designed coupler for the exchange of parametric data between components.The discretization utilizes high-quality,variable-resolution centroidal Voronoi Delaunay triangulation meshing and existing parallel solvers.We demonstrate the gridding technology,discretization schemes,and the efficiency and scalability of the parallel solvers through computational experiments using both simplified geometries arising from benchmark test problems and a realistic Greenland ice sheet geometry.     

On a tissue interaction model for skin pattern formation

Summary There is now sound biological evidence that dermal-epidermal communication is essential in the formation of skin organs. Recent experimental results suggest that cell adhesion molecules (CAMs) play an important role during skin pattern formation. We describe here a tissue interaction model for pattern morphogenesis in vertebrate skin which includes such CAMs. A mechanochemical mechanism is used to describe epithelial sheet motion, and a reaction-diffusion-chemotaxis mechanism is used to model the dermal cell movements. Neither of the mechanisms can independently generate spatial patterns in their respective layers. Tissue interaction is introduced using morphogens produced separately in the dermis and epithelium. These morphogens diffuse across the basal lamina, which separates the epidermis and dermis, and induce cell movements and deformation. Analysis of a simplified one-dimensional version shows that under certain conditions spatial patterns can be formed. A nonlinear analysis predicts the solution behavior which is in close agreement with the numerical results.     

Exact solutions of the simplified Keller–Segel model

Lie symmetries of a simplified Keller–Segel system are found and applied for construction of exact solutions. The algorithms for constructing all possible traveling wave and self-similar solutions of the system in question are presented. Several families of such solutions in an explicit form are found, their properties examined and possible applicability for chemotaxis modeling is discussed.     

Simplified modelling of joints and beam-like structures for BIW optimization in a concept phase of the vehicle design process

The paper proposes an engineering approach for the replacement of beam-like structures and joints in a vehicle model. The final goal is to provide the designer with an effective methodology for creating a concept model of such automotive components, so that an NVH optimization of the body in white (BIW) can be performed at the earliest phases of the vehicle design process. The proposed replacement methodology is based on the reduced beam and joint modelling approach, which involves a geometric analysis of beam-member cross-sections and a static analysis of joints. The first analysis aims at identifying the beam center nodes and computing the equivalent beam properties. The second analysis produces a simplified model of a joint that connects three or more beam-members through a static reduction of the detailed joint FE model.In order to validate the proposed approach, an industrial case-study is presented, where beams and joints of the upper region of a vehicle's BIW are replaced by simplified models. Two static load-cases are defined to compare the original and the simplified model by evaluating the stiffness of the full vehicle under torsion and bending in accordance with the standards used by automotive original equipment manufacturer (OEM) companies. A dynamic comparison between the two models, based on global frequencies and modal shapes of the full vehicle, is presented as well.     

Comparison of the simplified and full MHD models for laminar incompressible flow past a circular cylinder

In the majority of research on incompressible magnetohydrodynamic (MHD) flows, the simplified model with the low magnetic Reynolds number assumption has been adopted because it reduces the number of equations to be solved. However, because the effect of flow on magnetic field is also neglected, the solutions of the simplified model may be different from those of the full model. As an example, the flow of an electrically conducting fluid past a circular cylinder under a magnetic field is investigated numerically using the simplified and full models in this paper. To solve the problems, two second-order compact finite difference algorithms based on the streamfunction-velocity formulation of the simplified model and the quasi-streamfunction-velocity formulation of the full model are developed respectively.Numerical simulations are carried out over a wide range of Hartmann number for steady-state laminar problems with both models. For the full model, magnetic Reynolds number (Re_m) is chosen from 0.01 to 10. The computed results show that solutions of the simplified MHD model are not exactly the same as those of the full MHD model for this flow problem in most cases even if Re_m in the full model is very low. Only in the special case that a strong external magnetic field is exerted perpendicular to the dominant flow direction, can the simplified MHD model be regarded as an approximation of the full MHD model with low Re_m.     

Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows

A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer–Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.     

Finding nonoscillatory solutions to difference schemes for the advection equation

The advection equation is solved using a weighted adaptive scheme that combines a monotone scheme with the central-difference approximation of the first spatial derivative. The determination of antidiffusion fluxes is treated as an optimization problem. The solvability of the optimization problem is analyzed, and the differential properties of the cost functional are examined. It is shown that the determination of antidiffusion fluxes is reduced to a linear programming problem in the case of an explicit scheme and to a nonlinear programming problem or a sequence of linear programming problems in the case of an implicit scheme. A simplified monotonization algorithm is proposed. Numerical results are presented.     

Exactly solvable quantum mechanical models with Stückelberg divergences

We consider an exactly solvable quantum mechanical model with an infinite number of degrees of freedom that is an analogue of the model of N scalar fields (λ/N)(ϕ^{a a})² in the leading order in 1/N. The model involves vacuum and S-matrix divergences and also the Stückelberg divergences, which are absent in other known renormalizable quantum mechanical models with, divergences (such as the particle in a δ-shape potential or the Lee model). To eliminate divergences, we renormalize the vacuum energy and charge and transform the Hamiltonian by a unitary transformation with a singular dependence on the regularization parameter. We construct the Hilbert space with a positive-definite metric, a self-adjoint Hamiltonian operator, and a representation for the operators of physical quantities. Neglecting the terms that lead to the vacuum divergences fails to improve and, on the contrary, worsens the renormalizability properties of the model. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 125, No. 1, pp. 91–106, October, 2000.     

Bayesian estimation and inference for log-ACD models

This paper adapts Bayesian Markov chain Monte Carlo methods for application to some auto-regressive conditional duration models. Subsequently, the properties of these estimators are examined and assessed across a range of possible conditional error distributions and dynamic specifications, including under error mis-specification. A novel model error distribution, employing a truncated skewed Student-t distribution is proposed and the Bayesian estimator assessed for it. The results of an extensive simulation study reveal that favourable estimation properties are achieved under a range of possible error distributions, but that the generalised gamma distribution assumption is most robust and best preserves these properties, including when it is incorrectly specified. The results indicate that the powerful numerical methods underlying the Bayesian estimator allow more efficiency than the (quasi-) maximum likelihood estimator for the cases considered.     

On a simplified model for radiating flows

We consider a simplified model arising in radiation hydrodynamics which is based on the barotropic Navier–Stokes system describing the macroscopic fluid motion and a P1-approximation (see below) of the transport equation modeling the propagation of radiative intensity. We establish global-in-time existence of strong solutions for the associated Cauchy problem when initial data are close to a stable radiative equilibrium and local existence for large data with no vacuum. All our results are stated in the so-called critical Besov spaces.     

Approximate methods for analyzing the growth of large cracks in fatigue damaged aircraft sheet material and lap joints

Several levels of approximation are investigated to account for the effect of small fatigue cracks on the residual strength of aircraft sheet materials and fuselage lap joints containing major cracks. A version of the Dugdale model is proposed which accounts for strain hardening of the sheet in an approximate way and which incorporates a criterion for crack advance leading to crack growth resistance. This model builds upon the model proposed by Nilsson and Hutchinson [1] and accounts for the detailed interaction between the major crack and the small damage cracks. A simpler version of the model uses the damage-reduced local strength of the sheet or joint in assessing the effect of the major crack on residual strength. The simpler approach thus bypasses the necessity of a direct determination of the highly complicated details of the interaction of the small cracks in a lap joint with a major crack.     

The influence of thermal radiation on MHD flow of Maxwellian fluids above stretching sheets

Flow induced in a viscoelastic fluid by a linearly stretched sheet is investigated assuming that the fluid is Maxwellian and the sheet is subjected to a transverse magnetic field. The objective is to investigate the effects of parameters such as elasticity number, magnetic number, radiative heat transfer, Prandtl number, and Eckert number on the temperature field above the sheet. To do this, boundary layer theory will be used to simplify energy and momentum equations assuming that fluid physical/rheological properties remain constant. A suitable similarity transformation will be used to transform boundary layer equations from PDEs into ODEs. Homotopy analysis method (HAM) will be invoked to find an analytical solution for the temperature field above the sheet knowing the velocity profiles (see Alizadeh-Pahlavan et al. [Alizadeh-Pahlavan A, Aliakbar V, Vakili-Farahani F, Sadeghy K. MHD flows of UCM fluids above porous stretching sheets using two-auxiliary parameter homotopy analysis method. Commun. Nonlinear Sci Numer Simulat, in press]). The importance of manipulating the transverse velocity component, v, will be discussed on the temperature field above the sheet.     

两参数广义Poisson过程

定义了两参数广义Ｐｏｉｓｓｏｎ过程，得到了它的基本性质、局部鞅性和各种两参数Ｍａｒｋｏｖ性，研究了它的跳线和样本函数，对跳线和样本函数作了形象、明确和深刻的刻划，可以说是一目了然的。     

Flow Optimization on Traffic Networks

This work has been motivated by the work of [1]. Here in traffic models for networks based on PDE's are considered. A simplified algebraic model is derived from PDE‐based model. Optimization problem is to minimize cost functional measuring properties of network flows. We use a new approach to solve the minization problem for the reformulated algebraic model. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Space-Mapping and Optimal Shape Design

Optimal shape design is a common problem in practice. In most cases this means that a complex geometry has to be optimized such that it satisfies a desired quantity. The direct optimization is very difficult and time consuming, if it is possible at all. Therefore, often only simplified models are derived and optimized. In general this does not yield an optimal solution. For this reason the space–mapping method is introduced, which combines the results of the complex model, e.g. a 3D model, and a simplified model, e.g. a 1D or 2D model. The derivation of a simplified model of a filter device and the following optimization is presented. Finally, the advantages of the space–mapping method applied to this example is shown. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability analysis of models of cell production systems

We investigate the qualitative behaviour of the models of cell production systems, in the form of systems of nonlinear delay differential equations. Considered are three general models of a system involving the subpopulations of stem cells, precursor cells and mature cells, with different configurations of regulation feedbacks. The models correspond basically to the blood cell production process; however, other applications are possible. First, the simplified version (describable by ordinary differential equations) is considered. Fairly complete characterization of the trajectories is possible in this case, using the Lyapunov functions and phase plane techniques. Next, for the general models, the stability of equations linearized around the equilibria is investigated. Certain results can be obtained here, using both exact methods and numerical procedures based on an original lemma on the zeros of exponential polynomials. Then global properties (boundedness, attractivity, etc.) are examined for the nonlinear, delay case using a range of methods: Lyapunov functionals, Razumikhin functions and direct estimates on solutions. Certain special cases of our models reduce to previous literature models of blood production. Results of our analysis enable to exclude these configurations of regulation feedbacks which yield model behaviour not compatible with biological and medical observations. Techniques developed in this paper are applicable to a wide range of possible models of cell production systems.     

The numerical analysis of the influence of the blankholder force and the friction coefficient on the value of the drawing force

In this paper the numerical analysis of the drawing process with the blankholder is presented. The influence of the value of the blankholder force on the value of the drawing force and drawpiece height is examined. A different friction coefficient of the sheet metal for die and blankholder is considered. A defect at the lack of the blankholder is presented. The analysis in the system ANSYS/LS-DYNA is passed. The material model with the mixed hardening, isotropic and isothermal is used. Technological parameters of the sheet-metal to drawing, the die, the stamp and the blankholder from the literatures are chosen. Examples results of computer simulations are presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fermion pair creation by a strong Coulomb field in 2+1 dimensions

The creation of charged fermion pairs by a strong external Coulomb field in a space with two dimensions is investigated. Exact solutions to the Dirac equation are found for the Coulomb external field in 2+1 dimensions. The equation for determining the critical charge is obtained and is numerically solved for a simplified model. The critical charge for 2+1 dimensions is much less than the critical charge for the similar model with 3+1 dimensions. The influence of the vacuum polarization on the critical charge is studied in the one-loop approximation to the (2+1)-dimensional quantum electrodynamics. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 116, No. 2, pp. 277–287, August, 1998.