Standard Boundary Conditions Research Articles

Identification of the test setup influence on the modal properties of a short wind turbine blade during fatigue test

Modal testing of different test artefacts requires a multitude of decisions to be taken before the test, active experiment and analyses stages of the entire testing campaign. Modal test is often performed only once, and one of its major application is to validate the numerical model. The test-related decisions may impair the quality of the test results and in turn the following correlation and model updating procedure. The current paper provides a systematic approach for the parametric study of the test setup influence on the blade modal properties. The same wind turbine blade has been configured in four different test setups, including heavy instrumentation of the blade for the fatigue certification tests. The main objective of the research was to provide a comprehensive assessment of the impact of the test setup on the modes. Experimentally supported evidence has been found that mounting blade on the test block modifies the system structural dynamics. Not only existing global blade modes receive a shift in frequencies, but also new coupled modes may emerge. A new finding of the presented research is an experimental based characterisation of the impact of heavy excitation equipment for fatigue test. Adding exciters of a mass nearly equal of the blade mass has little influence on the identified natural frequencies of the first two modes, while lower all frequencies from the third mode onwards. The structural damping ratios are also affected, and generally increased. A vibration engineering standard free-free boundary conditions with the impact hammer excitation serves as a baseline model, to which the other test setup are compared. The estimated modal models of the intact blade will serve as a reference for the modal based damage detection methods application.

Non-standard boundary conditions for the linearized Korteweg-de Vries equation

<p style='text-indent:20px;'>This paper aims to solve numerically the linearized Korteweg-de Vries equation. We begin by deriving suitable boundary conditions then approximate them using finite difference method. The methodology of derivation, used in this paper, yields to Non-Standard Boundary Conditions (NSBC) that perfectly absorb wave reflections at the boundary. In addition, these NSBC are exact and local in time and space for non necessarily supported initial data and source terms. We finish with numerical examples that show the absorbing quality of these boundary conditions. Further comparisons are made using standard boundary conditions like, Dirichlet, Neumann and a variant of absorbing boundary conditions called discrete artificial ones.

Entropy stable boundary conditions for the Euler equations

We consider the initial-boundary value Euler equations with the aim to derive boundary conditions that yield an entropy bound for the physical (Navier-Stokes) entropy. We begin by reviewing the entropy bound obtained for standard no-penetration wall boundary conditions and propose a numerical implementation. The main results are the derivation of full-state boundary conditions (far-field, inlet, outlet) and the accompanying entropy stable implementations. We also show that boundary conditions obtained from linear theory are unable to bound the entropy and that non-linear bounds require additional boundary conditions. We corroborate our theoretical findings with numerical experiments.

Soft photon theorems from CFT Ward identites in the flat limit of AdS/CFT

S-matrix elements in flat space can be obtained from a large AdS-radius limit of certain CFT correlators. We present a method for constructing CFT operators which create incoming and outgoing scattering states in flat space. This is done by taking the flat limit of bulk operator reconstruction techniques. Using this method, we obtain explicit expressions for incoming and outgoing U(1) gauge fields. Weinberg soft photon theorems then follow from Ward identites of conserved CFT currents. In four bulk dimensions, gauge fields on AdS can be quantized with standard and alternative boundary conditions. Changing the quantization scheme corresponds to the S-transformation of SL(2, ℤ) electric-magnetic duality in the bulk. This allows us to derive both, the electric and magnetic soft photon theorems in flat space from CFT physics.

On thermomechanics of multilayered beams

In this paper, the mechanical behavior of multilayered small-scale beams in nonisothermal environment is investigated. Scale phenomena are modeled by means of the mathematically well-posed and experimentally consistent stress-driven integral formulation of elasticity. The present research extends the treatment in Barretta, Čanađija, Luciano, and de Sciarra (2018b) confined to elastically homogeneous nano-scopic structures. It is shown that the non-locality leads to a complex coupling between axial and transverse elastic displacements. Such a size-dependent phenomenon makes the solution of the relevant nonlocal thermoelastostatic problem, governed by a system of two ordinary differential equations with ten standard boundary conditions and non-classical constitutive boundary conditions, significantly more involved with respect to treatments in literature. Thus, a novel solution methodology, based on Laplace transforms, is proposed and illustrated by examining simple structural schemes of current applicative interest in Nanomechanics and Nanotechnology.

An adaptive volumetric flux boundary condition for lattice Boltzmann methods

This paper presents a spatially and temporally adaptive boundary condition to specify the volumetric flow rate for lattice Boltzmann methods. The approach differs from standard velocity boundary conditions because it allows the velocity to vary over the boundary region provided that the total flux through the boundary satisfies a prescribed constraint, which is a typical scenario for laboratory experimental studies. This condition allows the boundary pressure to adjust dynamically to yield a specified boundary flow rate as a means to avoid unphysical mismatch between the boundary velocity and the interior flow field that can arise when a standard velocity boundary condition is applied. The method is validated for simulation of one- and two-fluid flow in complex materials, with conditions determined to match typical experiments used to study flow in porous media.

Evaluation of clinically relevant operating conditions for left ventricular assist device investigations.

Standardized boundary conditions for flow rate and pressure difference are currently not available for the development and certification process of ventricular assist devices. Thus, interdisciplinary studies lack comparability and quantitative assessment. Universally valid boundary conditions could be used for the application of numerical and experimental investigations and the approval procedure of ventricular assist devices. In order to define such boundaries, physiological data from INCOR® patients were evaluated. A total of 599 out of possible 627 ventricular assist device patients were analyzed regarding their cardiac demands of flow rate and pressure head. An analysis of long-term data was performed, in order to provide respective, static mean values for benchmark testing. Furthermore, the short-term data of 188 patients delivered field data-based dynamic flow and pressure curves. The results of the study revealed physiologically reasonable boundary conditions, which can be applied in numerical or experimental investigations of ventricular assist devices. For steady flow analysis, single values for flow rate (4.46 L/min) and pressure head (62 mmHg) are suggested. For the support of pulsatile and unsteady flow studies, seven typical patients and one representative dynamic curve for flow rate and pressure head are proposed.The standardized results provided in this article, can be used in favor of interdisciplinary comparability of future numerical computations or in vitro ventricular assist device tests in research, development, and approval.

Higher–order nonlocal gradient elasticity: A consistent variational theory

A consistent variational theory of the higher–order nonlocal gradient elasticity is conceived to appropriately introduce the nonlocality to the higher-order strain gradient theory. The abstract variational approach, based on appropriate functional spaces of test fields, is applied to establish the higher–order nonlocal gradient mechanics of elastic beams in flexure. Two nonlocal and two gradient characteristic lengths are exploited to describe the size–dependent response of continua with nano–structures. Integral convolutions of the higher–order constitutive law are restored to the equivalent differential problem endowed with non–standard boundary conditions of constitutive–type. The higher–order strain gradient theory, higher–order nonlocal elasticity and modified nonlocal strain gradient theory, extensively adopted in the community of Engineering Science, are demonstrated to be particular cases of the introduced higher-order nonlocal gradient theory. The well-posedness of the developed higher-order nonlocal gradient problem is revealed by studying the flexural response of structures with wide-ranging applications in nano-engineering. Exact analytical solution for elastostatic deflections of nano-beams is derived and new benchmark examples of nano-mechanics interest are detected. The higher-order nonlocal gradient elasticity theory can effectively characterize nanoscopic phenomena in advanced nano–composites and nano–structures.

Impulsive generation of jets by flow focusing

Here we characterize the origin and subsequent disintegration into droplets of the type of high-speed jets formed after the sudden implosion of a locally spherical cavity. The full spatio-temporal evolution of these types of impulsively generated jets is described here making use of just the initial values of the interfacial normal velocity at the axis of symmetry and of its corresponding second derivative along the azimuthal direction, obtained straightforwardly from the solution of the Laplace equation subjected to standard boundary conditions. The predicted time evolutions of the jet tip radius and velocity, and of the radii of the ejected droplets, are shown to agree well with experimental observations.

On the three‐dimensional stationary exterior Stokes problem with non standard boundary conditions

AbstractWe study the three‐dimensional stationary exterior Stokes problem with non standard boundary conditions corresponding to a slip‐without‐friction boundary conditions. Because the flow domain is unbounded, we set the problem in weighted spaces in order to control the behavior at infinity of solutions. This functional framework allows to prescribe various behaviors at infinity of the solutions. The established results are related to the existence and the uniqueness of strong and very weak solutions. Our strategy relies on the fact that due to the boundary conditions, the pressure and the velocity can be decoupled and, as a result, we solve two separate systems to find these quantities.

Nonlocal boundary value problems with BV-type data

In this paper we present some existence and uniqueness results for solutions of second order boundary value problems, which are functions of bounded variation along with their derivatives. To this end, we apply fixed point theorems to an equivalent nonlinear perturbed Hammerstein integral equation. Here we consider non- standard boundary conditions like coupled boundary conditions, uncoupled boundary conditions, or integral-type boundary conditions. We also prove an abstract result concerning the spectral radii of some general classes of operators which applies to all boundary value problems mentioned above. The abstract results are throughout illustrated by a large number of examples.

3D finite element analysis of Al7075-T6 drilling with coated solid tooling

Due to the fact that simulation of drilling was added in commercial finite element analysis (FEA) software only recently, 3D finite element modelling is an invaluable asset during related researches. The present study employs 3D FEA to model the drilling process of Al7075-T6 alloy with solid carbide tooling, investigates important phenomena that occur during drilling and finally compares the simulated results with experimental data. A number of simulations were performed with DEFORM3D™ software at different cutting conditions; cutting speed of 50m/min, 100m/min, 150m/min and feed of 0.15mm/rev, 0.20mm/rev, 0.25mm/rev. The proposed model takes into consideration certain aspects like damage initiation and evolution of the material, contact interface between the drill bit and the workpiece and standard boundary conditions. Eventually, the acquired numerical data for thrust force were compared to the experimental results for the same cutting conditions and parameters. To obtain the experimental data, a series of nine drilling tests were performed. Upon validation of the numerical data, the temperature distribution on the tool tip – workpiece interface, as well as the chip morphology (shape and curling radius) were determined. Results showed a good agreement between the numerical and the experimental data. Specifically, thrust force and chip morphology exhibited an agreement of about 95% and 90% respectively, which confirms the potential of 3D FEA implementation on machining investigations.

Topology optimization of steering knuckle structure

Steering knuckle connects steering system, suspension system and braking system to the chassis. The steering knuckle contributes a significant weight to the total weight of a vehicle. Increasing the efficiency of an automobile without compromising the performances is the major challenge faced by the manufacturers. This paper presents an effective topology optimization of steering knuckle used in a vehicle with the primary objective of minimizing weight. The study on optimization of knuckle is divided into two phases, the first phase involves making of a computer-aided design model of the original steering knuckle and carry out finite element analysis on the knuckle by estimating the loads, which are acting on the component. In the second phase, design optimization of the model of steering knuckle is carried out, and excess material is removed at the region where induced stress is negligible as obtained in finite element analysis assuming standard boundary and loading conditions. The paper describes a research work carried out to optimize structural topology giving the essential details. The methodology may be applied to optimize structural components used in applications where the ratio of desired properties to the cost, generally in terms of weight, is to be optimized. In the case of automobiles, strength to weight ratio has to be maximized. New researchers working in the area will have an understanding of the procedures, and further, the techniques may be applied to design in general.

Fractionalized Edge Spins and Boundary Conditions in Frustrated Ferromagnetic Quantum Spin Chains

We examine frustrated ferromagnetic S = 1 spin chains at zero temperature by using the density-matrix renormalization group method. In open boundary conditions, the S = 1 quantum spin chains are known to produce fractionalized free spins on each edge, which causes difficulty in the numerical calculation of the thermodynamic ground states. To overcome this, we propose modified open boundary conditions to suppress the formation of fractionalized edge spins. The comparison of the physical properties of the ground states, which are obtained from the modified and the standard open boundary conditions, reveals that the modified open boundary conditions are more effective in improving the convergence behavior and reducing the computational costs.

What is the fractional Laplacian? A comparative review with new results

The fractional Laplacian in Rd, which we write as (−Δ)α/2 with α∈(0,2), has multiple equivalent characterizations. Moreover, in bounded domains, boundary conditions must be incorporated in these characterizations in mathematically distinct ways, and there is currently no consensus in the literature as to which definition of the fractional Laplacian in bounded domains is most appropriate for a given application. The Riesz (or integral) definition, for example, admits a nonlocal boundary condition, where the value of a function must be prescribed on the entire exterior of the domain in order to compute its fractional Laplacian. In contrast, the spectral definition requires only the standard local boundary condition. These differences, among others, lead us to ask the question: “What is the fractional Laplacian?” Beginning from first principles, we compare several commonly used definitions of the fractional Laplacian theoretically, through their stochastic interpretations as well as their analytical properties. Then, we present quantitative comparisons using a sample of state-of-the-art methods. We discuss recent advances on nonzero boundary conditions and present new methods to discretize such boundary value problems: radial basis function collocation (for the Riesz fractional Laplacian) and nonharmonic lifting (for the spectral fractional Laplacian).In our numerical studies, we aim to compare different definitions on bounded domains using a collection of benchmark problems. We consider the fractional Poisson equation with both zero and nonzero boundary conditions, where the fractional Laplacian is defined according to the Riesz definition, the spectral definition, the directional definition, and the horizon-based nonlocal definition. We verify the accuracy of the numerical methods used in the approximations for each operator, and we focus on identifying differences in the boundary behaviors of solutions to equations posed with these different definitions. Through our efforts, we aim to further engage the research community in open problems and assist practitioners in identifying the most appropriate definition and computational approach to use for their mathematical models in addressing anomalous transport in diverse applications.

Regularity of solutions for a fourth‐order elliptic system via Conservation law

In this paper, we obtain interior Hölder continuity for solutions of the fourth-order elliptic system Δ 2 u = Δ ( V · ∇ u ) + div ( w ∇ u ) + W · ∇ u formulated by Lamm and Rivière [Comm. Partial Differential Equations 33 (2008) 245–262]. Boundary continuity is also obtained under a standard Dirichlet or Navier boundary condition. We also use conservation law to establish a weak compactness result which generalizes a result of Rivière for the second-order problem.

Fermionic Casimir effect in Horava–Lifshitz theories

In this paper, we analyze the fermionic Casimir effects associated with a massless quantum field in the context of Lorentz symmetry violation approach based on Horava–Lifshitz methodology. In order to obtain these observables, we impose the standard MIT bag boundary condition on the fields on two large and parallel plates. Our main objectives are to investigate how the Casimir energy and pressure depend on the parameter associated with the breaking of Lorentz symmetry.

Approximate analytic solutions for a chemical tubular reactor model using the Adomian decomposition method

The purpose of this paper is to apply the Adomian decomposition method to acquire the approximate analytical solutions for a chemical tubular reactor model composed of a system of strongly nonlinear second-order partial differential equations with standard boundary conditions. By properly assigning the dimensionless parameters in the model, the objective description of the solutions of temperature and process component concentration distributions can be obtained.

A shear flow problem for compressible viscous micropolar fluid: Uniqueness of a generalized solution

In this paper, we consider the nonstationary shear flow of a compressible, viscous, and heat‐conducting micropolar fluid. The mathematical model is set up in Lagrangian description in the form of initial‐boundary problem with inhomogeneous boundary conditions for velocity and standard homogeneous boundary conditions for microrotation and heat flux. Under the assumptions that this problem has a generalized solution and that the initial mass density, temperature, the velocity, and microrotation vectors are smooth enough functions, we prove that this solution is unique.

Variational nonlocal gradient elasticity for nano-beams

In the paper (Zaera, Serrano, & Fernández-Sáez, 2019) it is claimed that the nonlocal strain gradient theory (NSGT) leads to ill-posed structural problems. This conclusion was motivated by observing that Constitutive Boundary Conditions (CBC) conflict with non-standard Kinematic and Static Higher-Order Boundary Conditions (KHOBC) - (SHOBC). In the present study, it is shown that no ill-posedness holds if NSGT is established by an adequate variational formulation, with appropriate test fields. KHOBC and SHOBC have nothing to do with the proper mathematical formulation and thus they have not to be prescribed, while standard kinematic and static boundary conditions and CBC have to be imposed to close the relevant nonlocal gradient problem. This conclusion follows from a well-posed abstract variational scheme conceived for nonlocal gradient inflected beams. The treatment provides as special cases most of the size-dependent models adopted in Engineering Science to assess size-effects in nanostructures, such as NSGT, strain-driven and stress-driven local-nonlocal elasticity approaches. Additionally, a well-posed Nonlocal Stress Gradient (NStressG) model is presented, coupling the stress-driven nonlocal strategy (Romano and Barretta, 2017) with the stress gradient elasticity. The presented methodology is elucidated and validated by investigating the structural behavior of a variety of inflected nano-beams of nanotechnological interest, such as sensors and actuators. NStressG is able to predict both softening and hardening nonlocal responses and, unlike the special stress gradient elasticity model, leads to well-posed structural problems in Nanomechanics.