A quadrilateral element based on refined global-local higher-order theory for coupling bending and extension thermo-elastic multilayered plates

In this paper a refined higher-order global-local theory is presented to analyze the laminated plates coupled bending and extension under thermo-mechanical loading. The in-plane displacement fields are composed of a third-order polynomial of global coordinate z in the thickness direction and 1,2–3 order power series of local coordinate ζ_k in the thickness direction of each layer, which is identical to the 1,2–3 global-local higher-order theory by Li and Liu [Li, X.Y., Liu, D., 1997. Generalized laminate theories based on double superposition hypothesis. Int. J. Numer. Methods Eng. 40, 1197–1212] Moreover, a second-order polynomial of global coordinate z in the thickness direction is chosen as transverse displacement field. The transverse shear stresses can satisfy continuity at interfaces, and the number of unknowns does not depend on the layer numbers of the laminate.Based on this theory, a quadrilateral laminated plate element satisfying the requirement of C¹ continuity is presented. By solving both bending and thermal expansion problems of laminates, it can be found that the present refined theory is very accurate and obviously superior to the existing 1,2–3 global-local higher-order theory. The most attractive feature of this theory is that the transverse shear stresses can be accurately predicted from direct use of constitutive equations without any post-processing method. It is also shown that the present quadrilateral element possesses higher accuracy.     

FLOW-INDUCED MULTIPLE-MODE VIBRATIONS OF GATES WITH SUBMERGED DISCHARGE

An experimental investigation of flow-induced vibrations of gates with multiple degrees of freedom is presented. An underflown vertical gate plate with submerged discharge was allowed to oscillate both in the cross-flow (z -) and in the streamwise (x -) direction. The two purposes of the investigation were to further the insight into the hydrodynamic coupling mechanisms of the two vibration modes and to determine the interaction of the unsteady lift and drag forces. Self-excited vibration tests were run with reduced velocities V_rzandV_rx from 0·8 to 14, covering a range in which the instability-induced excitation (IIE) due to impinging-leading-edge vortices (ILEV) as well as the transition to galloping (MIE) occurred. The ratio of the natural frequencies of the two vibration modes f_{x 0}/f_{z 0}, the gate opening ratios /d, and the submergence of the gate plate were varied. Depending on the ranges of reduced velocities and frequency ratios, a complex interaction of two different kinds of instability-induced excitation was detected. Furthermore, it was found that streamwise IIE-excitation and cross-flow galloping coexist. To assess the relevant fluid dynamic amplification and attenuation mechanisms, simultaneous body response and flow velocity measurements were carried out.     

Hysteresis in transverse galloping: The role of the inflection points

Transverse galloping is here considered as a one-degree-of-freedom oscillator subjected to aerodynamic forces, which are described by using the quasi-steady hypothesis. The hysteresis of transverse galloping is also analyzed. Approximate solutions of the model are obtained by assuming that the aerodynamic and damping forces are much smaller than the inertial and stiffness ones. The analysis of the approximate solution, which is obtained by means of the method of Krylov–Bogoliubov, reveals the existing link between the hysteresis phenomenon and the number of inflection points at the aerodynamic force coefficient curve, C_y(α); C_y and α being, respectively, the force coefficient normal to the incident flow and the angle of attack. The influence of the position of these inflection points on the range of flow velocities in which hysteresis takes place is also analyzed.     

NEAR-WAKE FLOW STRUCTURE OF A CYLINDER WITH A HELICAL SURFACE PERTURBATION

The near-wake of a circular cylinder having a helical wire pattern about its surface is characterized using a technique of high-image-density velocimetry. Patterns of vorticity in three orthogonal planes show substantial influence of a wire having a diameter an order of magnitude smaller than the cylinder diameter. The distinctive patterns of vorticity in these three planes are associated with lack of formation of large-scale Kármán-like clusters of vorticity (ω_z) in the near-wake region of the cylinder. The instantaneous structure of the separating spanwise vorticity (ω_z) layers on either side of the cylinder involve small-scale concentrations of vorticity analogous to the well-known Kelvin–Helmholtz vortices from a smooth cylinder. Moreover, a dual vorticity layer, i.e., two adjacent layers of like vorticity (ω_z), can form from one side of the cylinder. Along the span of the cylinder, distributions of instantaneous velocity and transverse vorticity (ω_y) show a spatially periodic sequence of wake-like patterns, each of which has features in common with the very near-wake of a two-dimensional bluff body, including a large velocity defect bounded by vorticity layers with embedded small-scale vorticity concentrations. In the cross-flow plane of the wake, patterns of streamwise vorticity (ω_x) show small-scale, counter-rotating pairs of vorticity concentrations (ω_x) emanating from the inclined helical perturbation, rather than isolated concentrations of vorticity of like sign, which would indicate single streamwise vortices. All of the aforementioned patterns of small-scale vorticity concentrations are scaled according to the local wake width/local pitch of the helical wire pattern in the respective plane of observation.     

Stochastic finite element nonlinear free vibration analysis of piezoelectric functionally graded materials beam subjected to thermo-piezoelectric loadings with material uncertainties

In this paper, second order statistics of large amplitude free flexural vibration of shear deformable functionally graded materials (FGMs) beams with surface-bonded piezoelectric layers subjected to thermopiezoelectric loadings with random material properties are studied. The material properties such as Young’s modulus, shear modulus, Poisson’s ratio and thermal expansion coefficients of FGMs and piezoelectric materials with volume fraction exponent are modeled as independent random variables. The temperature field considered is assumed to be uniform and non-uniform distribution over the plate thickness and electric field is assumed to be the transverse components E _z only. The mechanical properties are assumed to be temperature dependent (TD) and temperature independent (TID). The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear strain kinematics. A C ⁰ nonlinear finite element method (FEM) based on direct iterative approach combined with mean centered first order perturbation technique (FOPT) is developed for the solution of random eigenvalue problem. Comparison studies have been carried out with those results available in the literature and Monte Carlo simulation (MCS) through normal Gaussian probability density function.     

Stability of Periodic Clusters in Globally Coupled Maps

The phenomenon of partial synchronization, or clustering, in a system of globally coupled C ¹-smooth maps is analyzed. We prove the stability of equally populated K-clustered states with n-periodic temporal dynamics, referred to as P _n C _K-states. For this purpose, we first obtain formulas giving a relation between longitudinal and transverse multipliers of the in-cluster periodic orbits, and then, using these formulas, we find exact parameter intervals for transverse stability. We conclude that, typically, for symmetric P _n C _K-states, in-cluster stability implies transverse stability. Moreover, transverse stability can take place even if in-cluster dynamics are unstable.     

Some analytic solutions for a simple model of microwave absorber

An absorber, whose permittivity is a continuous function of the wave propagation direction z only, is placed between two planes, z = 0 and z = L, in a straight waveguide with a uniform cross section and perfectly conducting walls. Solutions of Maxwell's equations for the region occupied by the absorber, are given as transverse electric and transverse magnetic waves, and expressed in terms of known functions for certain choices of permittivity. Expressions for reflection and transmission coefficients are deduced.     

Calibration of a four-hole pyramid probe and area traverse measurements in a short-duration transonic turbine cascade tunnel

A four-hole pyramid probe has been calibrated for use in a short-duration transonic turbine cascade tunnel. The probe is used to create area traverse maps of total and static pressure, and pitch and yaw angles of the flow downstream of a transonic annular cascade. This data is unusual in that it was acquired in a short-duration (5 s of run time) annular cascade blowdown tunnel. A four-hole pyramid probe was used which has a 2.5 mm section head, and has the side faces inclined at 60° to the flow to improve transonic performance. The probe was calibrated in an ejector driven, perforated wall transonic tunnel over the Mach number range 0.5–1.2, with pitch angles from -20° to + 20° and yaw angles from-23° to +23°. A computer driven automatic traversing mechanism and data collection system was used to acquire a large probe calibration matrix (～ 10,000 readings) of non dimensional pitch, yaw, Mach number, and total pressure calibration coefficients. A novel method was used to transform the probe calibration matrix of the raw coefficients into a probe application matrix of the physical flow variables (pitch, yaw, Mach number etc.). The probe application matrix is then used as a fast look-up table to process probe results. With negligible loss of accuracy, this method is faster by two orders of magnitude than the alternative of global interpolation on the raw probe calibration matrix. The blowdown tunnel (mean nozzle guide vane blade ring diameter 1.1 m) creates engine representative Reynolds numbers, transonic Mach numbers and high levels (≈ 13%) of inlet turbulence intensity. Contours of experimental measurements at three different engine relevant conditions and two axial positions have been obtained. An analysis of the data is presented which includes a necessary correction for the finite velocity of the probe. Such a correction is non trivial for the case of fast moving probes in compressible flow.     

A study of two-dimensional dispersion in unconsolidated porous media

An experimental and numerical investigation into the magnitude of longitudinal and transverse dispersion in a two-dimensional flow field over a particle Peclet number range of 50–8500 is reported. Numerical modelling using a Galerkin finite element method is used to test various models, notably those of Fried and combarnous and Koch and Brady. Dispersion at low Peclet numbers (< 200) is found to be described adequately by either model, which at large Peclet, the degree of dispersion is significantly underestimated. An improved dispersion model for Peclet numbers greater than 200 is proposed. The transverse dispersion term and the choice of inlet boundary condition are found to have a negligible effect on the shape of the breakthrough curve.Nomenclature A (z) Polynomial in the z plane - B (z) Polynomial in the z plane - C Concentration - C _f Feed concentration - C _o Concentration at the entrance - D Dispersion tensor - D _f Molecular diffusion coefficient - D ₁ Longitudinal dispersion coefficient - D _p Particle diameter - D _t Transverse dispersion coefficient - k Permeability/viscosity - k Dimensionless permiability in the Koch and Brady model - P Pressure - Pe _k Modified Peclet number, Pe _p k - Pe _p Particle Peclet number vD _p /D _f - v Velocity - z Axial coordinate or complex variable Greek letters Solution domain - Boundary - Porosity     

A numerical study of rotational and transverse galloping rectangular bodies

In this paper we investigate rotational and translational galloping instabilities due to fluid/structure interaction using a previously developed algorithm. This numerical technique utilizes a two-dimensional spectral/hp element method and a frame of reference transformation to ensure efficient computations. Both transverse and rotational motion of rectangular sections of varying aspect ratio are simulated for a Reynolds number of 250 and at reduced velocities which promote a galloping response. Qualitative comparisons with quasi-steady theory and experimental data are found to be favourable.     

An approach to characterization of the agricultural self-propelled machines stability

This paper presents an analytical algorithm with appropriate software specified for the approximation of the allowed critical slope of the solid flat terrain that guarantees static and/or dynamic stability of the specified self-propelled agricultural machines and their aggregates. This algorithm assumes machine as a rigid body, having 3 or 4 contact points (defined by wheels or crawlers), under uniform motion at different constant velocities and radii of curvature trajectories. Using this algorithm, based on the principles of theoretical mechanics combined with 3D analytical geometry, the computer program SSPM (stability of the self-propelled agricultural machines) has been coded. This software is intended to facilitate the analysis, comparison and optimization of different configurations of self-propelled agricultural machines in operation on horizontal and sloped flat terrains at constant velocities and radii of trajectory with respect to their static and dynamic stability. It calculates critical pitch and roll angles of the self-propelled machine and the maximum allowed slope of the flat terrain under the given conditions. The algorithm and the appropriate SSPM software were experimentally verified using the platform and low-scale tractor model. Average difference between calculated and experimental critical values of roll and pitch angles were about 4°     

Accurate transverse stress evaluation in composite/sandwich thick laminates using a C0 HSDT and a novel post-processing technique

An efficient method for accurate evaluation of through-the-thickness distribution of transverse stresses in thick composite and sandwich laminates, using a displacement-based C⁰ higher-order shear deformation theory (HSDT), is presented. The technique involves a least square of error (LSE) method applied to the 3D equilibrium equations at the post-processing phase, after a primary finite element analysis is performed using the HSDT. This is distinctly different from the conventional method of integrating the 3D equilibrium equations, for transverse stress recovery in composite laminates during post-processing. Competence of the technique is demonstrated in the numerical examples through comparison with results from first-order shear deformation theory (FSDT), another HSDT and those from analytical and 3D elasticity solutions available in literature.     

Stress functions for a heterogeneous section of a tree

Consider a tree that is composed of wood, which is orthotropic with respect to the cylindrical coordinate axes, where the z-axis is directed up the center of the tree. When a section of a tree is considered as a Relaxed Saint-Venant's Problem the stresses in the plane of a transverse cross section will equal zero. By allowing some of, or all of the compliance coefficients to be functions of the radial coordinate r, the structure of the stress functions can be fundamentally altered. If the compliance coefficient in the z-direction (S₃₃₃₃) is allowed to remain constant, the S_rz and S_θz shear stresses will be functions of the coordinates, dimensions, applied loads, and compliance coefficients, while the other stresses will only be functions of the coordinates, dimensions and applied loads. If S₃₃₃₃ is also allowed to be a function of r, then all the nonzero stresses will be functions of the coordinates, dimensions, applied loads, and compliance coefficients.     

Turbulence modulation in a particle-laden flow over a hemisphere-roughened wall

Turbulence modulation by the inertia particles in a spatially developing turbulent boundary layer flow over a hemisphere-roughened wall was investigated using the direct numerical simulation method. The Eulerian and Lagrangian approaches were used for the gas- and particle-phases, respectively. An immersed boundary method was employed to resolve the hemispherical roughness element. The hemispheres were staggered in the downstream direction and arranged periodically in the streamwise and spanwise directions with spacing of p_x/d= 4 and p_z/d= 2 (where p_x and p_z are the streamwise and spanwise spacing of the hemispheres, and d is the diameter). The effects of particles on the turbulent coherent structures, turbulent statistics and quadrant events were analyzed. The results show that the addition of particles significantly damps the vortices structures and increases the length scales of streak structures. Compared with the particle-laden flow over the smooth wall, the existence of the wall roughness decreases the mean streamwise velocity in the near wall region, and makes the peaks of Reynolds stresses profiles shift up. In addition, the existence of particles also increases the percentage contributions to Reynolds shear stress from the Q4 events, however, decreases the percentage contributions from other quadrant events.     

Characterization of Anisotropic Polymeric Foam Under Static and Dynamic Loading

An orthotropic polymeric foam with transverse isotropy (Divinycell H250) used in composite sandwich structures was characterized at various strain rates. Uniaxial experiments were conducted along principal material axes as well as along off-axis directions under tension, compression, and shear to determine engineering constants, such as Young??s and shear moduli. Uniaxial strain experiments were conducted to determine mathematical stiffness constants, i. e., C _ij . An optimum specimen aspect ratio for these tests was selected by means of finite element analysis. Quasi-static and intermediate strain rate tests were conducted in a servo-hydraulic testing machine. High strain rate tests were conducted using a split Hopkinson Pressure Bar system built for the purpose using polymeric (polycarbonate) bars. The polycarbonate material has an impedance that is closer to that of foam than metals and results in lower noise to signal ratios and longer loading pulses. It was determined by analysis and verified experimentally that the loading pulses applied, propagated along the polycarbonate rods at nearly constant phase velocity with very low attenuation and dispersion. Material properties of the foam were obtained at three strain rates, quasi-static (10^?4 s^?1), intermediate (1 s^?1), and high (10³ s^?1) strain rates. A simple model proposed for the Young??s modulus of the foam was in very good agreement with the present and published experimental results.     

Low Reynolds number airfoil aerodynamic loads determination via line integral of velocity obtained with particle image velocimetry

The small magnitude lift forces generated by both a NACA 0012 airfoil and a thin flat plate at Re?=?29,000 and 54,000 were determined through the line integral of velocity, obtained with particle image velocimetry, via the application of the Kutta–Joukowsky theorem. Surface pressure measurements of the NACA0012 airfoil were also obtained to validate the lift coefficient C _l. The bound circulation was found to be insensitive to the size and aspect ratio of the rectangular integration loop for pre-stall angles. The present C _l data were also found to agree very well with the surface pressure-determined lift coefficient for pre-stall conditions. A large variation in C _l with the loop size and aspect ratio for post-stall conditions was, however, observed. Nevertheless, the present flat-plate C _l data were also found to collectively agree with the published force-balance measurements at small angles of attack, despite the large disparity exhibited among the various published data at high angles. Finally, the ensemble-averaged wake velocity profiles were also used to compute the drag coefficient and, subsequently, the lift-to-drag ratio.     

State of stress at the vertex of a quarter-infinite crack in a half-space

Spherical coordinates are r, θ, φ. The half-space extends in θ < π/2. The crack occurs along φ = 0. The region to be investigated is the solid space-triangle (or cone) between the three planes θ = π/2, φ = +0 and φ = 2π ? 0, which planes are to be taken stress-free.In this space-angle a state of stress is considered in terms of the cartesian stress components σ_xx = r^λ?_xx(λ, θ, φ); σ_xy = r^λ(λ, θ, φ); etc. Possible values λ are determined from a characteristic (or eigenvalue) equation, expressing the condition that a determinant of infinite order is equal to zero. The root of λ which gives the most serious state of stress in the vertex region (the region r → 0) is the root closest to the limiting value Re λ > ?3/2. Knowledge of this state of stress, or at least of this value of λ is essential in the determination of the three-dimensional state of stress around a crack in a plate for distances of order of the plate thickenss.Along the front of the quarter-infinite crack (z-axis) the so called stress-intensity factor behaves like z^λ+½ (z → 0) and thus tends to zero, respectively to infinity, accordingly to Re λ being >?½ or <?½. But in the region z → 0 the notion stress-intensity factor loses its meaning. The required state of stress passes into the well-known state of plane strain around a crack tip if Poisson's ratio (v) tends to zero. The computed state of stress for the incompressible medium (v = ½) is confirmed by experiment.