Cost-effective modeling strategies for the analysis of spliced steel connections

The paper presents several cost-effective modeling strategies that can be used by structural engineers in practice to determine the stresses in the spliced members. The computational efficiency and the modeling effort required for the several modeling options are also discussed. The deformation mechanisms and load transfer for several types of connections are illustrated. Optimization techniques are also presented to economize the computer time for connections with large number of bolts. Results are presented to compare the accuracy of several modeling strategies commonly used in practice. It is shown that for eccentric connections, the flexural bending largely affect the maximum tensile and compressive stresses within the joint. The difference may reach up to 54%. Finally, Experimental comparisons are made with the numerical procedures for typical connection model.     

A boundary element method to price time-dependent double barrier options

In this paper we propose a new method for pricing double-barrier options with moving barriers under the Black-Scholes and the CEV models. First of all, by applying a variational technique typical of the boundary element method, we derive an integral representation of the double-barrier option price in which two of the integrand functions are not given explicitly but must be obtained solving a system of Volterra integral equations of the first kind. Second, we develop an ad hoc numerical method to regularize and solve the system of integral equations obtained. Several numerical experiments are carried out showing that the overall algorithm is extraordinarily fast and accurate, even if the barriers are not differentiable functions. Moreover the numerical method presented in this paper performs significantly better than the finite difference approach.     

A Stokes model with cavitation for the numerical simulation of hydrodynamic lubrication

We present a cavitation model based on the Stokes equation and formulate adaptive finite element methods for its numerical solution. A posteriori error estimates and adaptive algorithms are derived, and numerical examples illustrating the theory are supplied, in particular with comparison to the simplified Reynolds model of lubrication. Copyright © 2010 John Wiley & Sons, Ltd.     

Note on the Design Differentiability of the Static Response of Elastic Structures

This paper provides a new proof of design sensitivity of the static response of some typical structures. These structures (beams, plates, and plane elastic solids) have been described previously. A proof of design sensitivity of the inverse state operator was provided there, and design sensitivity of static response was derived. The proof presented here is simpler and self-contained.     

A mapping strategy for the identification of structural systems

In this paper an alternative approach for identification problems is discussed. Unlike existing methods, this new approach combines in a general way finite differences and function approximation and is herein used for the identification of a particular system in structural dynamics, that is the damped Duffing oscillator subject to a swept-sine excitation. The solution obtained by means of the proposed method has been compared with the one obtained by a neural network. The present method gives better results at a low computational cost, with the advantage of solutions in explicit form. Besides, it is possible to prove that the solutions are stable and that from this new approach one can deduce, as a particular case, the approximation previously proposed by other authors.     

Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion

Surfaces can have a significant influence on the overall response of a continuum body but are often neglected or accounted for in an ad hoc manner. This work is concerned with a nonlinear continuum thermomechanics formulation which accounts for surface structures and includes the effects of diffusion and viscoelasticity. The formulation is presented within a thermodynamically consistent framework and elucidates the nature of the coupling between the various fields, and the surface and the bulk. Conservation principles are used to determine the form of the constitutive relations and the evolution equations. Restrictions on the jump in the temperature and the chemical potential between the surface and the bulk are not a priori assumptions, rather they arise from the reduced dissipation inequality on the surface and are shown to be satisfiable without imposing the standard assumptions of thermal and chemical slavery. The nature of the constitutive relations is made clear via an example wherein the form of the Helmholtz energy is explicitly given.     

Are upwind techniques in multi-phase flow models necessary?

Two alternatives of primary variables are compared for two-phase flow in heterogeneous media by solving fully established benchmarks. The first combination utilizes pressure of the wetting fluid and saturation of the non-wetting fluid as primary variables, while the second employs capillary pressure of the wetting fluid and pressure of the non-wetting fluid. While the standard Galerkin finite element method (SGFEM) is known to fail in the physical reproduction of two-phase flow in heterogeneous media (unless employing a fully upwind correction), the second scheme with capillary pressure as a primary variable without applying an upwind technique produces correct physical fluid behaviour in heterogeneous media, as observed from experiments.     

Turing pattern formation for reaction–convection–diffusion systems in fixed domains submitted to toroidal velocity fields

We have studied the effect of advection on reaction–diffusion equations by using toroidal velocity fields. Turing patterns formation in diffusion–advection–reaction problems was studied specifically, considering the Schnackenberg and glycolysis reaction kinetics models. Four cases were analyzed and solved numerically using finite elements. For glycolysis models, the advective effect modified the form of Turing patterns obtained with diffusion–reaction; whereas for Schnackenberg problems, the original patterns distorted themselves slightly, making them rotate in direction of the velocity field. We have also determined that the advective effect surpassed the diffusive one for high values of velocity and instability driven by diffusion was eliminated. On the other hand the advective effect is not considerable for very low values in the velocity field, and there was no modification in the original Turing pattern.     

A simple finite volume method for the shallow water equations

We present a new finite volume method for the numerical solution of shallow water equations for either flat or non-flat topography. The method is simple, accurate and avoids the solution of Riemann problems during the time integration process. The proposed approach consists of a predictor stage and a corrector stage. The predictor stage uses the method of characteristics to reconstruct the numerical fluxes, whereas the corrector stage recovers the conservation equations. The proposed finite volume method is well balanced, conservative, non-oscillatory and suitable for shallow water equations for which Riemann problems are difficult to solve. The proposed finite volume method is verified against several benchmark tests and shows good agreement with analytical solutions.     

Finite element analysis of thermally coupled nonlinear Darcy flows

We consider a coupled system describing nonlinear Darcy flows with temperature dependent viscosity and with viscous heating. We first establish existence, uniqueness, and regularity of the weak solution of the system of equations. Next, we decouple the coupled system by a fixed point algorithm and propose its finite element approximation. Finally, we present convergence analysis with an error estimate between continuous solution and its iterative finite element approximation.© 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010