Galerkin Solution of Stochastic Beam Bending on Winkler Foundations

In this paper, the Askey-Wiener scheme and the Galerkin method are used to obtain approximate solutions to stochastic beam bending on Winkler foundation. The study addresses Euler-Bernoulli beams with uncertainty in the bending stiffness modulus and in the stiffness of the foundation. Uncertainties are represented by parameterized stochastic processes. The random behavior of beam response is modeled using the Askey-Wiener scheme. One contribution of the paper is a sketch of proof of existence and uniqueness of the solution to problems involving fourth order operators applied to random fields. From the approximate Galerkin solution, expected value and variance of beam displacement responses are derived, and compared with corresponding estimates obtained via Monte Carlo simulation. Results show very fast convergence and excellent accuracies in comparison to Monte Carlo simulation. The Askey-Wiener Galerkin scheme presented herein is shown to be a theoretically solid and numerically efficient method for the solution of stochastic problems in engineering.

BEM formulation for von Karman plates

This work deals with nonlinear geometric plates in the context of von Karman`s theory. The formulation is written such that only the boundary in-plane displacement and deflection integral equations for boundary collocations are required. At internal points, only out-of-plane rotation, curvature and in-plane internal force representations are used. Thus, only integral representations of these values are derived. The nonlinear system of equations is derived by approximating all densities in the domain integrals as single values, which therefore reduces the computational effort needed to evaluate the domain value influences. Hyper-singular equations are avoided by approximating the domain values using only internal nodes. The solution is obtained using a Newton scheme for which a consistent tangent operator was derived. (C) 2009 Elsevier Ltd. All rights reserved.

Consolidation of elastic-plastic saturated porous media by the boundary element method

This paper presents a domain boundary element formulation for inelastic saturated porous media with rate-independent behavior for the solid skeleton. The formulation is then applied to elastic-plastic behavior for the solid. Biot`s consolidation theory, extended to include irreversible phenomena is considered and the direct boundary element technique is used for the numerical solution after time discretization by the implicit Euler backward algorithm. The associated nonlinear algebraic problem is solved by the Newton-Raphson procedure whereby the loading/unloading conditions are fully taken into account and the consistent tangent operator defined. Only domain nodes (nodes defined inside the domain) are used to represent all domain values and the corresponding integrals are computed by using an accurate sub-elementation scheme. The developments are illustrated through the Drucker-Prager elastic-plastic model for the solid skeleton and various examples are analyzed with the proposed algorithms. (c) 2008 Elsevier B.V. All rights reserved.

A STUDY OF PENALTY FORMULATIONS USED IN THE NUMERICAL APPROXIMATION OF A RADIALLY SYMMETRIC ELASTICITY PROBLEM

We consider a class of two-dimensional problems in classical linear elasticity for which material overlapping occurs in the absence of singularities. Of course, material overlapping is not physically realistic, and one possible way to prevent it uses a constrained minimization theory. In this theory, a minimization problem consists of minimizing the total potential energy of a linear elastic body subject to the constraint that the deformation field must be locally invertible. Here, we use an interior and an exterior penalty formulation of the minimization problem together with both a standard finite element method and classical nonlinear programming techniques to compute the minimizers. We compare both formulations by solving a plane problem numerically in the context of the constrained minimization theory. The problem has a closed-form solution, which is used to validate the numerical results. This solution is regular everywhere, including the boundary. In particular, we show numerical results which indicate that, for a fixed finite element mesh, the sequences of numerical solutions obtained with both the interior and the exterior penalty formulations converge to the same limit function as the penalization is enforced. This limit function yields an approximate deformation field to the plane problem that is locally invertible at all points in the domain. As the mesh is refined, this field converges to the exact solution of the plane problem.

Solution of a heterogeneous modeling of a horizontal-flow anaerobic immobilized biomass (HAIB) reactor by the sequencing method

A modeling study was completed to develop a methodology that combines the sequencing and finite difference methods for the simulation of a heterogeneous model of a tubular reactor applied in the treatment of wastewater. The system included a liquid phase (convection diffusion transport) and a solid phase (diffusion reaction) that was obtained by completing a mass balance in the reactor and in the particle, respectively. The model was solved using a pilot-scale horizontal-flow anaerobic immobilized biomass (HAIB) reactor to treat domestic sewage, with the concentration results compared with the experimental data. A comparison of the behavior of the liquid phase concentration profile and the experimental results indicated that both the numerical methods offer a good description of the behavior of the concentration along the reactor. The advantage of the sequencing method over the finite difference method is that it is easier to apply and requires less computational time to model the dynamic simulation of outlet response of HAIB.

Enhanced aeroelastic energy harvesting by exploiting combined nonlinearities: theory and experiment

Converting aeroelastic vibrations into electricity for low power generation has received growing attention over the past few years. In addition to potential applications for aerospace structures, the goal is to develop alternative and scalable configurations for wind energy harvesting to use in wireless electronic systems. This paper presents modeling and experiments of aeroelastic energy harvesting using piezoelectric transduction with a focus on exploiting combined nonlinearities. An airfoil with plunge and pitch degrees of freedom (DOF) is investigated. Piezoelectric coupling is introduced to the plunge DOF while nonlinearities are introduced through the pitch DOF. A state-space model is presented and employed for the simulations of the piezoaeroelastic generator. A two-state approximation to Theodorsen aerodynamics is used in order to determine the unsteady aerodynamic loads. Three case studies are presented. First the interaction between piezoelectric power generation and linear aeroelastic behavior of a typical section is investigated for a set of resistive loads. Model predictions are compared to experimental data obtained from the wind tunnel tests at the flutter boundary. In the second case study, free play nonlinearity is added to the pitch DOF and it is shown that nonlinear limit-cycle oscillations can be obtained not only above but also below the linear flutter speed. The experimental results are successfully predicted by the model simulations. Finally, the combination of cubic hardening stiffness and free play nonlinearities is considered in the pitch DOF. The nonlinear piezoaeroelastic response is investigated for different values of the nonlinear-to-linear stiffness ratio. The free play nonlinearity reduces the cut-in speed while the hardening stiffness helps in obtaining persistent oscillations of acceptable amplitude over a wider range of airflow speeds. Such nonlinearities can be introduced to aeroelastic energy harvesters (exploiting piezoelectric or other transduction mechanisms) for performance enhancement.

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

Influence of the Solvent Evaporation Rate on the Crystalline Phases of Solution-Cast Poly(Vinylidene Fluoride) Films

The influence of the solvent-evaporation rate on the formation of of. and P crystalline phases in solution-cast poly(vinylidene fluoride) (PVDF) films was systematically investigated. Films were crystallized from PVDF/N,N-dimethylformamide solutions with concentrations of 2.5, 5.0, 10, and 20 wt % at different temperatures. During crystallization, the solvent evaporation rate was monitored in situ by means of a semianalytic balance. With this system, it was possible to determine the evaporation rate for different concentrations and temperatures of the solution under specific ambient conditions (pressure, temperature, and humidity). Fourier-Transform InfraRed spectroscopy with Attenuated Total Reflectance revealed the P-phase content in the PVDF films and its dependence on previous evaporation rates. Based on the relation between the evaporation rate and the PVDF phase composition, a consistent explanation for the different amounts of P phase observed at the upper and lower sample surfaces is achieved. Furthermore, the role of the sample thickness has also been studied. The experimental results show that not only the temperature but also the evaporation rate have to be controlled to obtain the desired crystalline phases in solution-cast PVDF films. (C) 2009 Wiley Periodicals, Inc. J Appl Polym Sci 116: 785-791, 2010

DESIGN OF CONCRETE PLATFORMS OFFSHORE USING THE THREE-LAYER SHELL THEORY

The concrete offshore platforms, which are subjected a several loading combinations and, thus, requires an analysis more generic possible, can be designed using the concepts adopted to shell elements, but the resistance must be verify in particular cross-sections to shear forces. This work about design of shell elements will be make using the three-layer shell theory. The elements are subject to combined loading of membrane and plate, totalizing eight components of internal forces, which are three membrane forces, three moments (two out-of-plane bending moments and one in-plane, or torsion, moment) and two shear forces. The design method adopted, utilizing the iterative process proposed by Lourenco & Figueiras (1993) obtained from equations of equilibrium developed by Gupta (1896) , will be compared to results of experimentally tested shell elements found in the literature using the program DIANA.

An EFG method for the nonlinear analysis of plates undergoing arbitrarily large deformations

The applicability of a meshfree approximation method, namely the EFG method, on fully geometrically exact analysis of plates is investigated. Based on a unified nonlinear theory of plates, which allows for arbitrarily large rotations and displacements, a Galerkin approximation via MLS functions is settled. A hybrid method of analysis is proposed, where the solution is obtained by the independent approximation of the generalized internal displacement fields and the generalized boundary tractions. A consistent linearization procedure is performed, resulting in a semi-definite generalized tangent stiffness matrix which, for hyperelastic materials and conservative loadings, is always symmetric (even for configurations far from the generalized equilibrium trajectory). Besides the total Lagrangian formulation, an updated version is also presented, which enables the treatment of rotations beyond the parameterization limit. An extension of the arc-length method that includes the generalized domain displacement fields, the generalized boundary tractions and the load parameter in the constraint equation of the hyper-ellipsis is proposed to solve the resulting nonlinear problem. Extending the hybrid-displacement formulation, a multi-region decomposition is proposed to handle complex geometries. A criterium for the classification of the equilibrium`s stability, based on the Bordered-Hessian matrix analysis, is suggested. Several numerical examples are presented, illustrating the effectiveness of the method. Differently from the standard finite element methods (FEM), the resulting solutions are (arbitrary) smooth generalized displacement and stress fields. (c) 2007 Elsevier Ltd. All rights reserved.

Role of price and enforcement in water allocation: Insights from Game Theory

As many countries are moving toward water sector reforms, practical issues of how water management institutions can better effect allocation, regulation, and enforcement of water rights have emerged. The problem of nonavailability of water to tailenders on an irrigation system in developing countries, due to unlicensed upstream diversions is well documented. The reliability of access or equivalently the uncertainty associated with water availability at their diversion point becomes a parameter that is likely to influence the application by users for water licenses, as well as their willingness to pay for licensed use. The ability of a water agency to reduce this uncertainty through effective water rights enforcement is related to the fiscal ability of the agency to monitor and enforce licensed use. In this paper, this interplay across the users and the agency is explored, considering the hydraulic structure or sequence of water use and parameters that define the users and the agency`s economics. The potential for free rider behavior by the users, as well as their proposals for licensed use are derived conditional on this setting. The analyses presented are developed in the framework of the theory of ""Law and Economics,`` with user interactions modeled as a game theoretic enterprise. The state of Ceara, Brazil, is used loosely as an example setting, with parameter values for the experiments indexed to be approximately those relevant for current decisions. The potential for using the ideas in participatory decision making is discussed. This paper is an initial attempt to develop a conceptual framework for analyzing such situations but with a focus on the reservoir-canal system water rights enforcement.

Numerical solution of the two-phase expansion of a metastable flashing liquid jet using the dispersion-controlled dissipative scheme

This paper presents a study of the stationary phenomenon of superheated or metastable liquid jets, flashing into a two-dimensional axisymmetric domain, while in the two-phase region. In general, the phenomenon starts off when a high-pressure, high-temperature liquid jet emerges from a small nozzle or orifice expanding into a low-pressure chamber, below its saturation pressure taken at the injection temperature. As the process evolves, crossing the saturation curve, one observes that the fluid remains in the liquid phase reaching a superheated condition. Then, the liquid undergoes an abrupt phase change by means of an oblique evaporation wave. Across this phase change the superheated liquid becomes a two-phase high-speed mixture in various directions, expanding to supersonic velocities. In order to reach the downstream pressure, the supersonic fluid continues to expand, crossing a complex bow shock wave. The balance equations that govern the phenomenon are mass conservation, momentum conservation, and energy conservation, plus an equation-of-state for the substance. A false-transient model is implemented using the shock capturing scheme: dispersion-controlled dissipative (DCD), which was used to calculate the flow conditions as the steady-state condition is reached. Numerical results with computational code DCD-2D vI have been analyzed. Copyright (C) 2009 John Wiley & Sons, Ltd.

Galerkin finite element method for incompressible thermofluid flows framed within the bond graph theory

In this paper a bond graph methodology is used to model incompressible fluid flows with viscous and thermal effects. The distinctive characteristic of these flows is the role of pressure, which does not behave as a state variable but as a function that must act in such a way that the resulting velocity field has divergence zero. Velocity and entropy per unit volume are used as independent variables for a single-phase, single-component flow. Time-dependent nodal values and interpolation functions are introduced to represent the flow field, from which nodal vectors of velocity and entropy are defined as state variables. The system for momentum and continuity equations is coincident with the one obtained by using the Galerkin method for the weak formulation of the problem in finite elements. The integral incompressibility constraint is derived based on the integral conservation of mechanical energy. The weak formulation for thermal energy equation is modeled with true bond graph elements in terms of nodal vectors of temperature and entropy rates, resulting a Petrov-Galerkin method. The resulting bond graph shows the coupling between mechanical and thermal energy domains through the viscous dissipation term. All kind of boundary conditions are handled consistently and can be represented as generalized effort or flow sources. A procedure for causality assignment is derived for the resulting graph, satisfying the Second principle of Thermodynamics. (C) 2007 Elsevier B.V. All rights reserved.

Surface tension of flotation solution and its influence on the selectivity of the separation between apatite and gangue minerals

This work presents and discusses the influence of the surface tension (gamma(LV)) of methanol/water mixtures on the flotation response of apatite versus gangue minerals conditioned with flotation reagents (75 g/t cornstarch and 100 g/t Berol 867) at pH 10.6. Berol 867 is a collector composed of sodium alkyl sarcosinate plus nonionic surfactant. The highest Schulz efficiency of separation (recovery of apatite minus recovery of gangue) was achieved at approximate to 51.0 mN/m. The critical surface tension of wettability (gamma(C)) of apatite was found to occur at 34.7 mN/m when determined by means of gamma flotation experiments, , and it was 33.9 mN/m when determined by Zisman`s approach.

Post-failure behaviour of impulsively loaded circular plates

The dynamic plastic response of a simply supported circular plate is analysed. Emphasis is given to the plate behaviour after it has broken free from the supports due to a local material failure. The theoretical rigid plastic analysis predicts various features of the response such as the time to failure, residual kinetic energy and the critical velocity at failure. The residual kinetic energy of the plate could be significant enough to cause secondary impact damage. It is shown that the shape of the plate changes after breaking free from the supports, which is important for forensic investigations. The solution for various cases were proven to be exact in the context of the upper and lower bounds theorems of the theory of plasticity. (C) 2009 Elsevier Ltd. All rights reserved.