Timoshenko versus Euler beam theory: Pitfalls of a deterministic approach

The selection criteria for Euler-Bernoulli or Timoshenko beam theories are generally given by means of some deterministic rule involving beam dimensions. The Euler-Bernoulli beam theory is used to model the behavior of flexure-dominated (or ""long"") beams. The Timoshenko theory applies for shear-dominated (or ""short"") beams. In the mid-length range, both theories should be equivalent, and some agreement between them would be expected. Indeed, it is shown in the paper that, for some mid-length beams, the deterministic displacement responses for the two theories agrees very well. However, the article points out that the behavior of the two beam models is radically different in terms of uncertainty propagation. In the paper, some beam parameters are modeled as parameterized stochastic processes. The two formulations are implemented and solved via a Monte Carlo-Galerkin scheme. It is shown that, for uncertain elasticity modulus, propagation of uncertainty to the displacement response is much larger for Timoshenko beams than for Euler-Bernoulli beams. On the other hand, propagation of the uncertainty for random beam height is much larger for Euler beam displacements. Hence, any reliability or risk analysis becomes completely dependent on the beam theory employed. The authors believe this is not widely acknowledged by the structural safety or stochastic mechanics communities. (C) 2010 Elsevier Ltd. All rights reserved.

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.

Buckling and post-buckling of extensible rods revisited: A multiple-scale solution

An exact non-linear formulation of the equilibrium of elastic prismatic rods subjected to compression and planar bending is presented, electing as primary displacement variable the cross-section rotations and taking into account the axis extensibility. Such a formulation proves to be sufficiently general to encompass any boundary condition. The evaluation of critical loads for the five classical Euler buckling cases is pursued, allowing for the assessment of the axis extensibility effect. From the quantitative viewpoint, it is seen that such an influence is negligible for very slender bars, but it dramatically increases as the slenderness ratio decreases. From the qualitative viewpoint, its effect is that there are not infinite critical loads, as foreseen by the classical inextensible theory. The method of multiple (spatial) scales is used to survey the post-buckling regime for the five classical Euler buckling cases, with remarkable success, since very small deviations were observed with respect to results obtained via numerical integration of the exact equation of equilibrium, even when loads much higher than the critical ones were considered. Although known beforehand that such classical Euler buckling cases are imperfection insensitive, the effect of load offsets were also looked at, thus showing that the formulation is sufficiently general to accommodate this sort of analysis. (c) 2008 Elsevier Ltd. All rights reserved.

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.

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.

Phase Equilibrium and Optimization Tools: Application for Enhanced Structured Lipids for Foods

Solid-liquid phase equilibrium modeling of triacylglycerol mixtures is essential for lipids design. Considering the alpha polymorphism and liquid phase as ideal, the Margules 2-suffix excess Gibbs energy model with predictive binary parameter correlations describes the non ideal beta and beta` solid polymorphs. Solving by direct optimization of the Gibbs free energy enables one to predict from a bulk mixture composition the phases composition at a given temperature and thus the SFC curve, the melting profile and the Differential Scanning Calorimetry (DSC) curve that are related to end-user lipid properties. Phase diagram, SFC and DSC curve experimental data are qualitatively and quantitatively well predicted for the binary mixture 1,3-dipalmitoyl-2-oleoyl-sn-glycerol (POP) and 1,2,3-tripalmitoyl-sn-glycerol (PPP), the ternary mixture 1,3-dimyristoyl-2-palmitoyl-sn-glycerol (MPM), 1,2-distearoyl-3-oleoyl-sn-glycerol (SSO) and 1,2,3-trioleoyl-sn-glycerol (OOO), for palm oil and cocoa butter. Then, addition to palm oil of Medium-Long-Medium type structured lipids is evaluated, using caprylic acid as medium chain and long chain fatty acids (EPA-eicosapentaenoic acid, DHA-docosahexaenoic acid, gamma-linolenic-octadecatrienoic acid and AA-arachidonic acid), as sn-2 substitutes. EPA, DHA and AA increase the melting range on both the fusion and crystallization side. gamma-linolenic shifts the melting range upwards. This predictive tool is useful for the pre-screening of lipids matching desired properties set a priori.

Liquid-Liquid Equilibrium of Aqueous Two-Phase Systems Containing Some Synthetic Polyelectrolytes and Polyethylene Glycol

Experimental results are presented for the liquid-liquid equilibrium of aqueous two-phase systems containing a synthetic polyelectrolyte (polysodium acrylate, polysodium methacrylate, and polysodium ethylene sulfonate) and polyethylene glycol at (298.2 and 323.2) K. A total of 40 phase diagrams were obtained, comprising data both of the binodal curve (obtained through cloud-point measurements) and of equilibrium compositions. The influences of temperature, the nature of the polyelectrolyte monomer unit, and the chain length of both types of polymers are analyzed and discussed.

Fast Transforms for Acoustic Imaging-Part I: Theory

The classical approach for acoustic imaging consists of beamforming, and produces the source distribution of interest convolved with the array point spread function. This convolution smears the image of interest, significantly reducing its effective resolution. Deconvolution methods have been proposed to enhance acoustic images and have produced significant improvements. Other proposals involve covariance fitting techniques, which avoid deconvolution altogether. However, in their traditional presentation, these enhanced reconstruction methods have very high computational costs, mostly because they have no means of efficiently transforming back and forth between a hypothetical image and the measured data. In this paper, we propose the Kronecker Array Transform ( KAT), a fast separable transform for array imaging applications. Under the assumption of a separable array, it enables the acceleration of imaging techniques by several orders of magnitude with respect to the fastest previously available methods, and enables the use of state-of-the-art regularized least-squares solvers. Using the KAT, one can reconstruct images with higher resolutions than was previously possible and use more accurate reconstruction techniques, opening new and exciting possibilities for acoustic imaging.

Numerical Study of Hypersonic Leeward Flow over a Blunt Nosed Delta Wing

A kinetic theory based Navier-Stokes solver has been implemented on a parallel supercomputer (Intel iPSC Touchstone Delta) to study the leeward flowfield of a blunt nosed delta wing at 30-deg incidence at hypersonic speeds (similar to the proposed HERMES aerospace plane). Computational results are presented for a series of grids for both inviscid and laminar viscous flows at Reynolds numbers of 225,000 and 2.25 million. In addition, comparisons are made between the present and two independent calculations of the some flows (by L. LeToullec and P. Guillen, and S. Menne) which were presented at the Workshop on Hypersonic Flows for Re-entry Problems, Antibes, France, 1991.

It's all very well, in theory: Theoretical perspectives and their applications in contemporary pedagogical research

Current debates about educational theory are concerned with the relationship between knowledge and power and thereby issues such as who possesses a truth and how have they arrived at it, what questions are important to ask, and how should they best be answered. As such, these debates revolve around questions of preferred, appropriate, and useful theoretical perspectives. This paper overviews the key theoretical perspectives that are currently used in physical education pedagogy research and considers how these inform the questions we ask and shapes the conduct of research. It also addresses what is contested with respect to these perspectives. The paper concludes with some cautions about allegiances to and use of theories in line with concerns for the applicability of educational research to pressing social issues.

Simulations of Bose fields at finite temperature

We introduce a time-dependent projected Gross-Pitaevskii equation to describe a partially condensed homogeneous Bose gas, and find that this equation will evolve randomized initial wave functions to equilibrium. We compare our numerical data to the predictions of a gapless, second order theory of Bose-Einstein condensation [S. A. Morgan, J. Phys. B 33, 3847 (2000)], and find that we can determine a temperature when the theory is valid. As the Gross-Pitaevskii equation is nonperturbative, we expect that it can describe the correct thermal behavior of a Bose gas as long as all relevant modes are highly occupied. Our method could be applied to other boson fields.

Half-Filled Layered Organic Superconductors and the Resonating-Valence-Bond Theory of the Hubbard-Heisenberg Model

We present a resonating-valence-bond theory of superconductivity for the Hubbard-Heisenberg model on an anisotropic triangular lattice. Our calculations are consistent with the observed phase diagram of the half-filled layered organic superconductors, such as the beta, beta('), kappa, and lambda phases of (BEDT-TTF)(2)X [bis(ethylenedithio)tetrathiafulvalene] and (BETS)(2)X [bis(ethylenedithio)tetraselenafulvalene]. We find a first order transition from a Mott insulator to a d(x)(2)-y(2) superconductor with a small superfluid stiffness and a pseudogap with d(x)(2)-y(2) symmetry.

The effects of Australian tall poppy attitudes on American value based leadership theory

A survey study of twenty-two Australian CEOs and their subordinates assessed relationships between Australian leader motives, Australian value based leader behaviour, subordinate tall poppy attitudes and subordinate commitment, effectiveness, motivation and satisfaction (CEMS). On the whole, the results showed general support for value based leadership processes. Subsequent regression analyses of the second main component of Value Based Leadership Theory, value based leader behaviour, revealed that the collectivistic, inspirational, integrity and visionary behaviour sub-scales of the construct were positively related with subordinate CEMS. Although the hypothesis that subordinate tall poppy attitudes would moderate value based leadership processes was not clearly supported, subsequent regression analyses found that subordinate tall poppy attitudes were negatively related with perceptions of value based leader behaviour and CEMS. These findings suggest complex relationships between the three constructs, and the proposed model for the Australian context is accordingly amended. Overall, the research supports the need to consider cultural-specific attitudes in management development.