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At least 253 records · Page 14

Innovative design of composite structures: The use of curvilinear fiber format in composite structure design

The gains in structural efficiency are investigated that can be achieved by aligning the fibers in some or all of the layers in a laminate with the principal stress directions in those layers. The name curvilinear fiber format is given to this idea. The problem studied is a plate with a central circular hole subjected to a uniaxial tensile load. An iteration scheme is used to find the fiber directions at each point in the laminate. Two failure criteria are used to evaluate the tensile load capacity of the plates with a curvilinear format, and for comparison, counterpart plates with a conventional straightline fiber format. The curvilinear designs for improved tensile capacity are then checked for buckling resistance. It is concluded that gains in efficiency can be realized with the curvilinear format.

Hyer, M. W.↗

Shear buckling of specially orthotropic plates with centrally located cutouts

The shear loading of a composite rectangular plate with a centrally located circular cutout was analyzed in order to predict the buckling load of the plate. The first step in this analysis is to calculare the in-plane stress distribution of the plate prior to buckling. This problem can be solved using finite element methods, but a quicker and more cost efficient method is desired. The method chosen to determine the pre-buckling stresses is that of boundary collocation using complex variables. The real valued force functions are written in terms of two complex valued functions, each of which is a function of a different complex variable. The solution of the generalized biharmonic function is a superposition of functions of these two complex variables. For this analysis, the force functions are represented with a Laurent series. The constants in these series are found using boundary collocation. Two force equations for complex variables are satisfied over the plate boundaries to obtain these constants. The stresses in the plate are then known for any particular locations on the plate given the applied shear on the edges of the plate.

Klang, Eric C.↗

A Measurement of Atmospheric Circular Polarization with POLARBEAR

At millimeter wavelengths, the atmospheric emission is circularly polarized owing to the Zeeman splitting of molecular oxygen by the Earth's magnetic field. We report a measurement of the signal in the 150 GHz band using 3 yr of observational data with the POLARBEAR project. Nonidealities of a continuously rotating half-wave plate (HWP) partially convert circularly polarized light to linearly polarized light. While POLARBEAR detectors are sensitive to linear polarization, this effect makes them sensitive to circular polarization. Although this was not the intended use, we utilized this conversion to measure circular polarization. We reconstruct the azimuthal gradient of the circular polarization signal and measure its dependency from the scanning direction and the detector bandpass. We compare the signal with a simulation based on atmospheric emission theory, the detector bandpass, and the HWP leakage spectrum model. We find the ratio of the observed azimuthal slope to the simulated slope is 0.92 ± 0.01(stat) ± 0.07(sys). This ratio corresponds to a brightness temperature of 3.8 mK at the effective band center of 121.8 GHz and bandwidth of 3.5 GHz estimated from representative detector bandpass and the spectrum of Zeeman emission. This result validates our understanding of the instrument and reinforces the feasibility of measuring the circular polarization using the imperfection of continuously rotating HWP. Continuously rotating HWP is popular in ongoing and future cosmic microwave background experiments to modulate the polarized signal. This work shows a method for signal extraction and leakage subtraction that can help measure circular polarization in such experiments.

79 ASTRONOMY AND ASTROPHYSICS↗

Innovative design of composite structures: Use of curvilinear fiber format to improve structural efficiency

To increase the effectiveness and efficiency of fiber-reinforced materials, the use of fibers in a curvilinear rather than the traditional straightline format is explored. The capacity of a laminated square plate with a central circular hole loaded in tension is investigated. The orientation of the fibers is chosen so that the fibers in a particular layer are aligned with the principle stress directions in that layer. Finite elements and an iteration scheme are used to find the fiber orientation. A noninteracting maximum strain criterion is used to predict load capacity. The load capacities of several plates with different curvilinear fibers format are compared with the capacities of more conventional straightline format designs. It is found that the most practical curvilinear design sandwiches a group of fibers in a curvilinear format between a pair of +/-45 degree layers. This design has a 60% greater load capacity than a conventional quasi-isotropic design with the same number of layers. The +/-45 degree layers are necessary to prevent matrix cracking in the curvilinear layers due to stresses perpendicular to the fibers in those layers. Greater efficiencies are achievable with composite structures than now realized.

Hyer, M. W.↗

Use of curvilinear fiber format to increase structural efficiency

To increase the effectiveness and efficiency of fiber-reinforced materials, the use of fibers in a curvilinear rather than the traditional straightline format is explored. The capacity of a laminated square plate with a central circular hole loaded in tension is investigated. The orientation of the fibers is chosen so that the fibers in a particular layer are aligned with the principle stress directions in that layer. Finite elements and an iteration scheme are used to find the fiber orientation. A noninteracting maximum strain criterion is used to predict load capacity. The load capacities of several plates with different curvilinear fibers format are compared with the capacities of more conventional straightline format designs. It is found that the most practical curvilinear design sandwiches a group of fibers in a curvilinear format between a pair of +/-45 degree layers. This design has a 60 percent greater load capacity than a conventional quasi-isotropic design with the same number of layers. The +/-45 degree layers are necessary to prevent matrix cracking in the curvilinear layers due to stresses perpendicular to the fibers in those layers. Greater efficiencies are achievable with composite structures than now realized.

Hyer, M. W.↗

Supersonic separated flow past a cylindrical obstacle on a flat plate

An experimental investigation of three-dimensional boundary-layer separation on a flat plate ahead of a circular cylinder at Mach 2.36 was made. Emphasis was given to the laminar flow regime and to the flow region upstream of the cylinder. The heights and diameters of the cylinders used in the study were larger than the undisturbed boundary-layer thickness at the cylinder location. Data were obtained by oil flow visualization, Schlieren observations, static pressure measurements, and laser anemometry. Oil flow visualization revealed three separation lines on the flat plate ahead of the cylinder. A postulated flowfield structure, which was suggested by this skin-friction pattern, could not be confirmed by the velocity measurements. Velocity measurements indicated an unsteady flow structure.

Ozcan, O.↗

Stress intensity factors for long, deep surface flaws in plates under extensional fields

Using a singular solution for a part circular crack, a Taylor Series Correction Method (TSCM) was verified for extracting stress intensity factors from photoelastic data. Photoelastic experiments were then conducted on plates with part circular and flat bottomed cracks for flaw depth to thickness ratios of 0.25, 0.50 and 0.75 and for equivalent flaw depth to equivalent ellipse length values ranging from 0.066 to 0.319. Experimental results agreed well with the Smith theory but indicated that the use of the ''equivalent'' semi-elliptical flaw results was not valid for a/2c less than 0.20. Best overall agreement for the moderate (a/t approximately 0.5) to deep flaws (a/t approximatelly 0.75) and a/2c greater than 0.15 was found with a semi-empirical theory, when compared on the basis of equivalent flaw depth and area.

Harms, A. E.↗

Stress intensity factors for long, deep surface flaws in plates under extensional fields

Using a singular solution for a part circular crack by Smith, a Taylor Series Correction Method (TSCM) was verified for extracting stress intensity factors (SIFs) from photoelastic data. Photoelastic experiments were then conducted on plates with part circular and flat bottomed cracks for flaw depth to thickness ratios of 0.25, 0.50, and 0.75 and for equivalent flaw depth to equivalent ellipse length values ranging from 0.066 to 0.319. Experimental results agreed well with the Smith theory but indicated that the use of the 'equivalent' semi-elliptical flaw for correlating the part circular flaw results with semi-elliptical flaw results was not valid for a/2c much less than 0.20. Best overall agreement for the moderate (a/t about 0.5) to deep flaws (a/t about 0.75) and a/2c greater than 0.15 was found with a semi-empirical theory due to Newman when compared on the basis of equivalent flaw depth and area. The Smith theory, when correlated on the basis of flaw depth and area, appears to yield reasonable estimates (within 10%) of the SIF for flat bottomed flaws for the geometries studied here.

Harms, A. E.↗

Experimental and theoretical investigation of stress wave attenuation in fiber reinforced composites.

The propagation of an initialrcidrical pressure pulse through a linear elastic fiber reinforced composite medium is analysed, both experimentally and analytically. In the experiment, tests were performed on plates with single and multiple circular inclusions embedded in a matrix of lower characteristic impedance. Sharp compression pulses were generated at an edge of the plate. Strain gages were mounted on various positions of the plate to determine the attenuation of the transient stress in the fiber reinforced composite. The qualitative analytical treatment is based on the methods of propagating stress discontinuities. Computer programs were written to numerically determine the changes in the shape of the leading wave front and the stresses immediately behind it. Experimental results for the attenuation of stress wave on steel-aluminum and steel-brass fiber-matrix composites compared very well with the computed analytical results when the applied pressure is generated by small explosive charges. The results did not compare well when the applied pressure is generated by projectile impact.

Yang, J. C. S.↗

Elasto-plastic bending of cracked plates, including the effects of crack closure

A capability for solving elasto-plastic plate bending problems is developed using assumptions consistent with Kirchhoff plate theory. Both bending and extensional modes of deformation are admitted with the two modes becoming coupled as yielding proceeds. Equilibrium solutions are obtained numerically by determination of the stationary point of a functional which is analogous to the potential strain energy. The stationary value of the functional for each load increment is efficiently obtained through use of the conjugate gradient. This technique is applied to the problem of a large centrally through cracked plate subject to remote circular bending. Comparison is drawn between two cases of the bending problem. The first neglects the possibility of crack face interference with bending, and the second includes a kinematic prohibition against the crack face from passing through the symmetry plane. Results are reported which isolate the effects of elastoplastic flow and crack closure.

Jones, D. P.↗

The influence of crack closure and elasto-plastic flow on the bending of a cracked plate

The influence of crack closure and elastoplastic flow on the bending behavior of thin cracked plates is investigated using an incremental elastoplastic plate bending finite element computer program. The finite element program was developed using assumptions consistent with Kirchhoff fourth-order plate theory while the material property treatment permits general isotropic work hardening with local elastic unloading. This technique is applied to the problem of a large centrally through cracked plate subject to remote circular bending. Comparison is drawn between two cases of the bending problem. The first neglects the possibility of crack face interference with bending, and the second includes a kinematic prohibition against the crack face from passing through the symmetry plane. Results are reported which isolate the effects of elastoplastic flow and crack closure.

Jones, D. P.↗

Stress-intensity factor equations for cracks in three-dimensional finite bodies subjected to tension and bending loads

Stress intensity factor equations are presented for an embedded elliptical crack, a semielliptical surface crack, a quarter elliptical corner crack, a semielliptical surface crack along the bore of a circular hole, and a quarter elliptical corner crack at the edge of a circular hole in finite plates. The plates were subjected to either remote tension or bending loads. The stress intensity factors used to develop these equations were obtained from previous three dimensional finite element analyses of these crack configurations. The equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and, where applicable, hole radius. The ratio of crack depth to plate thickness ranged from 0 to 1, the ratio of crack depth to crack length ranged from 0.2 to 2, and the ratio of hole radius to plate thickness ranged from 0.5 to 2. The effects of plate width on stress intensity variation along the crack front were also included.

Newman, J. C., Jr.↗

A linear aerodynamic analysis for unsteady transonic cascades

A potential flow analysis to predict unsteady airloads produced by the vibrations of turbomachinery blades operating at transonic Mach numbers is presented. The unsteady aerodynamic model includes the effects of blade geometry, finite mean pressure variation across the blade row, high frequency blade motion, and shock motion within the framework of a linearized, frequency domain formulation. The unsteady equations are solved implicit, least squares, finite difference approximation which is applicable on arbitrary grids. A numerical solution for the entire unsteady field is determined by matching a solution determined on a rectilinear type cascade mesh, which covers an extended blade passage region, to a solution determined on a detailed polar type local mesh, which covers and extends well beyond the supersonic region(s) adjacent to a blade surface. Cascades of double circular arc and flat plate blades demonstrate the unsteady analysis, and partially illustrate the effects of blade geometry, inlet Mach number, blade vibration frequency and shock motion on unsteady response.

Verdon, J. M.↗

A linearized unsteady aerodynamic analysis for transonic cascades

The unsteady airloads generated by the vibrations of turbomachine blades operating at transonic Mach numbers are predicted by a linearized potential flow analysis whose unsteady aerodynamics model encompasses the effects of blade geometry, nonzero mean pressure variation across the blade row, high frequency blade motion, and shock motion, all within the framework of a linearized frequency-domain formulation. A numerical solution for the entire unsteady flow field is determined by matching a solution covering an extended blade passage region to another covering, and extending beyond, the supersonic region(s) adjacent to a blade surface. Results are given for cascades of double circular arc and flat plate blades, in order to demonstrate the unsteady analysis and to partially illustrate the effects of blade geometry, inlet Mach number, vibration frequency and shock motion on unsteady response.

Verdon, J. M.↗

Navier-Stokes cascade analysis with a stiff Kappa-Epsilon turbulence solver

The two dimensional, compressible, thin layer Navier-Stokes equations with the Baldwin-Lomax turbulence model and the kinetic energy-energy dissipation (k-epsilon) model are solved numerically to simulate the flow through a cascade. The governing equations are solved for the entire flow domain, without the boundary layer assumptions. The stiffness of the k-epsilon equations is discussed. A semi-implicit, Runge-Kutta, time-marching scheme is developed to solve the k-epsilon equations. The impact of the k-epsilon solver on the explicit Runge-Kutta Navier-Stokes solver is discussed. Numerical solutions are presented for two dimensional turbulent flow over a flat plate and a double circular arc cascade and compared with experimental data.

Liu, Jong-Shang↗