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Mass and strength analyses and system requirements identified titanium-box-stiffened-skin wall candidate for lightweight fuselage of pressurized vehicle. Photoelastic models of stiffener-to-skin joint used to identify quickly modifications to joint that lowers severity of stress concentration. Results with various photoelastic models cut from polyurethane sheet led to novel diffusion-bond joint with reduced stress concentration.
Work was carried out to extend the near-wall models formulated for the incompressible Reynolds stress equations to compressible flows. The idea of splitting the compressible dissipation function into a solenoidal part that is not sensitive to changes of compressibility indicators and a compressible part that is directly affected by these changes is adopted. This means that all models involving the dissipation rate could be expressed in terms of the solenoidal dissipation rate and an equation governing its transport could be formulated to close the set of compressible Reynolds stress equations. The near-wall modelling of the dissipation rate equation is investigated and its behavior near a wall is studied in detail using k-epsilon closure. It is found that all existing modelled equations give the wrong behavior for the dissipation rate near a wall. Improvements are suggested and the resultant behavior is found to be in good agreement with near-wall data. Furthermore, the present modified k-epsilon closure is used too calculate a flat plate boundary layer and the results are compared with four existing k-epsilon closures. These comparisons show that all closures tested give essentially the same flow properties, except in a region very close to the wall. In this region, the present k-epsilon closure calculations are in better agreement with measurements and direct simulation data; in particular, the behavior of the dissipation rate.
Stress states, structure deformation, failure criteria and constitutive relations in structural design noting tensile, strip and lap shear test and continuum model
The objective of this paper is to demonstrate the applicability of a currently proposed model, with minimum empiricism, for calculation of the Reynolds stresses and other turbulence structural quantities in a channel. The current Large-Eddy Interaction Model not only yields Reynolds stresses but also presents an opportunity to illuminate typical characteristic motions of large-scale turbulence and the phenomenological aspects of engineering models for two Reynolds numbers.
A mechanistically consistent model for indentation damage based on elastic failure at tensile or shear overloads, is proposed. The model accommodates arbitrary crack orientation, stress relaxation, reduction and recovery of stiffness due to crack opening and closure, and interfacial friction due to backward sliding of closed cracks. This elastic failure model was implemented by an axisymmetric finite element program which was used to simulate progressive damage in a silicon nitride plate indented by a tungsten carbide sphere. The predicted damage patterns and the permanent impression matched those observed experimentally. The validation of this elastic failure model shows that the plastic deformation postulated by others is not necessary to replicate the indentation damage of brittle structural ceramics.
A set of three-dimensional failure criteria for laminated fiber-reinforced composites, denoted LaRC04, is proposed. The criteria are based on physical models for each failure mode and take into consideration non-linear matrix shear behaviour. The model for matrix compressive failure is based on the Mohr-Coulomb criterion and it predicts the fracture angle. Fiber kinking is triggered by an initial fiber misalignment angle and by the rotation of the fibers during compressive loading. The plane of fiber kinking is predicted by the model. LaRC04 consists of 6 expressions that can be used directly for design purposes. Several applications involving a broad range of load combinations are presented and compared to experimental data and other existing criteria. Predictions using LaRC04 correlate well with the experimental data, arguably better than most existing criteria. The good correlation seems to be attributable to the physical soundness of the underlying failure models.
The new topography and gravitational field data for Venus expressed in spherical harmonics of degree and order up to 50 allow us to analyze the crust-mantle boundary relief and stress state of the Venusian lithosphere. In these models, we consider models in which convection is confined beneath a thick, buoyant lithosphere. We divide the convection regime into an upper mantle and lower mantle component. The lateral scales are smaller than on Earth. In these models, relative to Earth, convection is reflected in higher order terms of the gravitational field. On Venus geoid height and topography are highly correlated, although the topography appears to be largely compensated. We hypothesize that Venus topography for those wavelengths that correlate well with the geoid is partly compensated at the crust-mantle boundary, while for the others compensation may be distributed over the whole mantle. In turn the strong sensitivity of the stresses to parameters of the models of the external layers of Venus together with geological mapping allows us to begin investigations of the tectonics and geodynamics of the planet. For stress calculations we use a new technique of space- and time-dependent Green's response functions using Venus models with rheologically stratified lithosphere and mantle and a ductile lower crust. In the basic model of Venus the mean crust is 50-70 km thick, the density contrast across the crust-mantle boundary is in the range from 0.3 to 0.4 g/cm(exp -3). The thickness of a weak mantle zone may be from 350 to 1000 km. Strong sensitivity of calculated stress to various parameters of the layered model of Venus together with geological mapping and analysis of surface tectonic patterns allow us to investigate the tectonics and geodynamics of the planet. The results are presented in the form of maps of compression-extension and maximum shear stresses in the lithosphere and maps of crust-mantle boundary relief, which can be presented as a function of time. We have modeled the region of Western Aphrodite and the Niobe plains to get reasonable depths of compensation. Crust mantle boundary relief is calculated for Western Aphrodite-Niobe relative to a mean crustal thickness of 50 km. The calculations include the consequences of simple crust models and more complicated models with a weak, ductile lower crust, a strong upper mantle and a weak lower mantle layer.
In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented.
The heat flux and Reynolds stress budgets are presented for a buoyant plume. The terms involving pressure correlations are obtained as the closing terms in these budgets. Despite certain measurement errors, these budgets provide useful information about how various phenomena contribute to the transport of second moments. These experimental results are used to assess the local equilibrium assumption and to investigate why the mechanical to thermal time scale ratio for a buoyant plume is different than the commonly recommended value. Analysis show that this departure is a consequence of the local equilibrium assumption being not satisfied in the present experiment.
Several two-equation turbulence models are compared to data from direct numerical simulations (DNS) of the homogeneous elliptic streamline flow, which combines rotation and strain. The models considered include standard two-equation models and models with corrections for rotational effects. Most of the rotational corrections modify the dissipation rate equation to account for the reduced dissipation rate in rotating turbulent flows, however, the DNS data shows that the production term in the turbulent kinetic energy equation is not modeled correctly by these models. Nonlinear relations for the Reynolds stresses are considered as a means of modifying the production term. Implications for the modeling of turbulent vortices will be discussed.
The effect of solute additions on the steady-state creep behavior of coarse-grained dispersion-strengthened aluminum alloys was studied. Recrystallized dispersion-strengthened solid solutions were found to have stress and temperature sensitivities quite unlike those observed in single-phase solid solutions having the same composition and grain size. The addition of magnesium or copper to the matrix of a recrystallized dispersion-strengthened aluminum causes a decrease in the steady-state creep rate which is much smaller than that caused by similar amounts of solute in single-phase solid solutions. All alloys exhibited essentially a 4.0 power stress exponent in agreement with the model of Ansell and Weertman. The activation energy for steady-state creep in dispersion-strengthened Al-Mg alloys, as well as the stress dependence, was in agreement with the physical model of dislocation climb over the dispersed particles.
Some new developments in two equation models and second order closure models are presented. In this paper, modified two equation models are proposed to remove shortcomings such as computing flows over complex geometries and the ad hoc treatment near the separation and reattachment points. The calculations using various two equation models are compared with direct numerical solutions of channel flows and flat plate boundary layers. Development of second order closure models will also be discussed with emphasis on the modeling of pressure related correlation terms and dissipation rates in the second moment equations. All existing models poorly predict the normal stresses near the wall and fail to predict the three dimensional effect of mean flow on the turbulence. The newly developed second order near-wall turbulence model to be described in this paper is capable of capturing the near-wall behavior of turbulence as well as the effect of three dimension mean flow on the turbulence.
Flexible manufacturing methods are needed to reduce the cost of using advanced composites in structural applications. One method that allows for this is the stretch forming of long discontinuous fiber materials with thermoplastic matrices. In order to exploit this flexibility in an economical way, a thorough understanding of the relationship between manufacturing and component performance must be developed. This paper reviews some of the recent work geared toward establishing this understanding. Micromechanics models have been developed to predict the formability of the material during processing. The latest improvement of these models includes the viscoelastic nature of the matrix and comparison with experimental data. A finite element scheme is described which can be used to model the forming process. This model uses equivalent anisotropic viscosities from the micromechanics models and predicts the microstructure in the formed part. In addition, structural models have been built to account for the material property gradients that can result from the manufacturing procedures. Recent developments in this area include the analysis of stress concentrations and a failure model each accounting for the heterogeneous material fields.
Closed form and finite element models are developed to predict the device response of aluminum electrostatic torsion micro-mirrors fabricated on silicon substrate for space applications at operating temperatures of 30K. Initially, closed form expressions for electrostatic pressure arid mechanical restoring torque are used to predict the pull-in and release voltages at room temperature. Subsequently, a detailed mechanical finite element model is developed to predict stresses and vertical beam deflection induced by the electrostatic and thermal loads. An incremental and iterative solution method is used in conjunction with the nonlinear finite element model and closed form electrostatic equations to solve. the coupled electro-thermo-mechanical problem. The simulation results are compared with experimental measurements at room temperature of fabricated micro-mirror devices.
The reliability of brittle materials under a generalized state of stress is analyzed using the Batdorf model. The model is modified to include the reduction in shear due to the effect of the compressive stress on the microscopic crack faces. The combined effect of both surface and volume flaws is included. Due to the nature of fracture of brittle materials under compressive loading, the component is modeled as a series system in order to establish bounds on the probability of failure. A computer program was written to determine the probability of failure employing data from a finite element analysis. The analysis showed that for tensile loading a single crack will be the cause of total failure but under compressive loading a series of microscopic cracks must join together to form a dominant crack.
This paper examines the modeling of two-dimensional homogeneous stratified turbulent shear flows using the Reynolds-stress and Reynolds-heat-flux equations. Several closure models have been investigated-, the emphasis is placed on assessing the effect of modeling the dissipation rate tensor in the Reynolds-stress equation. Three different approaches are considered: one is an isotropic approach while the other two are anisotropic approaches. The isotropic approach is based on Kolmogorov's hypothesis and a dissipation rate equation modified to account for vortex stretching. One of the anisotropic approaches is based on an algebraic representation of the dissipation rate tensor, while another relies on solving a modeled transport equation for this tensor. In addition, within the former anisotropic approach, two different algebraic representations are examined one is a function of the Reynolds-stress anisotropy tensor, and the other is a function of' the mean velocity gradients. The performance of these closure models is evaluated against experimental and direct numerical simulation data of pure shear flows. pure buoyant flows and buoyant shear flows. Calculations have been carried out over a range of Richardson numbers (Ri) and two different Prandtl numbers (Pr); thus the effect of Pr on the development of counter-gradient heat flux in a stratified shear flow can be assessed. At low Ri, the isotropic model performs well in the predictions of stratified shear flows; however, its performance deteriorates as Ri increases. At high Ri, the transport equation model for the dissipation rate tensor gives the best result. Furthermore, the results also lend credence to the algebraic dissipation rate model based on the Reynolds stress anisotropy tensor. Finally, it is found that Pr has an effect on the development of counter-gradient heat flux. The calculations show that, under the action of shear, counter-gradient heat flux does not occur even at Ri = 1 in an air flow.
Numerical and analytical models are used to study the upper-ocean response to surface wind stress estimates from the tropical Atlantic and Pacific Oceans. These models are used to identify regions of important variability in the wind field, analyze the oceanic response, and demonstrate the applicability of remotely sensed vector wind stress and altimetry data. Both model and XBT depictions of the mean seasonal cycle, 1979 to 1981, were analyzed along the major ship tracks in the western, central, and eastern tropical Pacific. Model solutions were also used to address array design questions in observing system simulation experiments. Subsequent analyses of the 1982 to 1983 solutions will be performed with respect to differences from the mean seasonal cycle 1979 to 1981, as well as, differences in the three wind products.
The foreign object damage resistance of composite fan blades was studied. Edge impact stresses in an anisotropic plate were first calculated incorporating a constrained layer damping model. It is shown that a very thin damping layer can dramatically decrease the maximum normal impact stresses. A multilayer model of a composite plate is then presented which allows computation of the interlaminar normal and shear stresses. Results are presented for the stresses due to a line impact load normal to the plane of a composite plate. It is shown that significant interlaminar tensile stresses can develop during impact. A computer code was developed for this problem using the fast Fourier transform. A marker and cell computer code were also used to investigate the hydrodynamic impact of a fluid slug against a wall or turbine blade. Application of fluid modeling of bird impact is reviewed.