ALBERT

Description: The objectives of this program are as follows: modelling of guided waves in fiber-reinforced plates in terms of different modes; and analysis of scattering by transverse cracks using modal representation. A hybrid numerical method combining the finite element representation of a region around the crack with the modal representation in the exterior region will be used in this program. Modes will be obtained using the through-the-thickness discretization of the displacement field.

Description: The low-g fluids management group with the Center for Space Construction is engaged in active research on the following topics: gauging; venting; controlling contamination; sloshing; transfer; acquisition; and two-phase flow. Our basic understanding of each of these topics at present is inadequate to design space structures optimally. A brief report is presented on each topic showing the present status, recent accomplishings by our group and our plans for future research. Reports are presented in graphic and outline form.

Description: Experimental and theoretical studies have been conducted to determine critical parameters at the onset of nonlinear counterflow in He II below the lambda point of He-4. Critical temperature differences have been measured in porous media for zero net mass flow and for Darcy permeabilities in the order of magnitude range from 10 to the -10th to 10 to the -8th sq cm. The normalized critical temperature gradients, which covered the liquid temperature range of 1.5 K to the lambda temperature, are found to vary with T proportional to the ratio of the superfluid density to the normal fluid density. This liquid temperature dependence appears to be consistent with duct data which are limited at low temperature by a Reynolds number criterion.

Description: An analysis is made based upon the concept that the velocity fluctuations, and therefore, the Reynolds stresses, driven by the instability of the original flow grow until a new stable state is approached. The Reynolds stresses incorporated into the Orr-Sommerfeld equation are coupled with the main flow such that all the imaginary parts of the complex eigenvalues vanish, i.e., the original instability is eliminated. Using this stabilization principle, it is possible to find the Reynolds stresses as well as the mean velocity for plane Poiseuille flow with the Reynolds number slightly higher than the critical.

Description: This paper considers complex transcendental eigenvalue problems where one is interested in pairs of eigenvalues that are restricted to take real values only. Such eigenvalue problems arise in dynamic stability analysis of nonconservative physical systems, i.e., flutter analysis of aeroelastic systems. Some available solution methods are discussed and a new method is presented. Two computational approaches are described for analytical evaluation of the sensitivities of these eigenvalues when they are dependent on other parameters. The algorithms presented are illustrated through examples.

Description: The behavior of the reverse flow ceiling jet against the ventilation flow from 0.58 to 0.87 m/s was investigated in a 1/3 scale model of a wide body aircraft interior. For all tests, strong reverse-flow ceiling jets of hot gases were detected well upstream of the fire. Both thicknesses of the reverse-flow ceiling jet and the smoke layer increased with the fire-crossflow parameter. The thickness of the smoke layer where the smoke flows along the main flow below the reverse-flow ceiling jet was almost twice that of the reverse-flow ceiling jet. Detailed spatial and time-varying temperatures of the gas in the test section were measured, and velocity profiles were also measured using a temperature compensated hot film.

Description: Certain theoretical studies of boundary-layer transition are described, based on high Reynolds numbers and with attention drawn to the various nonlinear interactions and scales present. The article concentrates in particular on theories for which the mean-flow profile is completely altered from its original state. Two- and three-dimensional flow theory and conjectures on turbulent-boundary-layer structures are included. Specific recent findings noted, and in qualitative agreement with experiments, are: nonlinear finite-time break-ups in unsteady interactive boundary layers; strong vortex/wave interactions; and prediction of turbulent boundary-layer displacement- and stress sublayer-thicknesses.

Description: Delamination growth caused by local buckling of a delaminated group of plies was investigated. Delamination growth was assumed to be governed by the strain energy release rates, G(1), G(2) and G(3). The strain energy release rates were calculated using a geometrically nonlinear three-dimensional finite element analysis. The program is described and several checks of the analysis are discussed. Based on a limited parametric study, the following conclusions were reached: (1) the problem is definitely mixed mode (in some cases G(1) is larger than G(2), for other cases the opposite is true); (2) in general, there is a large gradient in the strain energy release rates along the delamination front; (3) the locations of maximum G(1) and G(2) depend on the delamination shape and the applied strain; (4) the mode 3 component was negligible for all cases considered; and (5) the analysis predicted that parts of the delamination would overlap. The results presented did not impose contact constraints to prevent overlapping. Further work is needed to determine the effects of allowing the overlapping.

Description: This paper presents the application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems. The methods consists of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line- or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to those of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.

Description: The propagation of elastic waves of the type induced by impact are studied for a special class of cylinders. In this class are thin finite cylinders, for which Mindlin's equations are appropriate, on which point masses are attached. An approximation is derived valid for frequencies below cutoff of the lowest shear mode. An eigenfunction expansion is used to compute the transient response of the coupled system.

Description: The method of boundary elements is adapted to the dynamics of elastic axisymmetric solids. Three scalar potentials are used, each satisfying the Helmholtz equation and each represented by its own source distribution. The sources are distributed over a surface enclosing the solid boundary. Stress or displacement conditions on the boundary are realized by third-order derivatives of the potentials. Discrete ring elements on the source enclosure combine their influences at discrete ring elements on the solid boundary.

Description: Rapid distortion theory is applied to study distortion of homogeneous turbulence subject to two different axisymmetric strain modes: the axisymmetric contraction (AC, nozzle-type flow), and the axisymmetric expansion (AE, diffuser-type flow). The paper explores the differences in effects of the two axisymmetric strain modes on the anisotropy of correlations and structures of turbulence; examines the effect of dilatation on the distortion of turbulence; and provides a theoretical background for turbulence model development. It is found that velocity and vorticity fluctuations are enhanced more efficiently by contraction than by expansion; contraction produces much higher anisotropy in velocity and vorticity than expansion; root-mean-square pressure is slightly reduced during contraction, whereas it increases rapidly during expansion; and vortical structures of rodlike shape develop in a contraction flow, while disklike structures develop in an expansion flow. A simple model that reflects the dependence of turbulence evolution on structural parameters such as the Reynolds-stress anisotropy and total strain is proposed, and is shown to outperform all other models for all cases examined, regardless of the mean strain rate.

Description: While the standard mode acceleration formulation in structural dynamics has often been interpreted to suggest that the reason for improved convergence obtainable is that the dynamic correction factor is divided by the modal frequencies-squared, an alternative formulation is presented which clearly indicates that the only difference between mode acceleration and mode displacement data recovery is the addition of a static correction term. Attention is given to the advantages in numerical implementation associated with this alternative, as well as to an illustrative example.

Description: A key step in the application of formal automated design techniques to structures under transient loading is the calculation of sensitivities of response quantities to the design parameters. This paper considers response quantities to the design parameters. This paper considers structures with general forms of damping acted on by general transient loading and addresses issues of computational errors and computational efficiency. The equations of motion are reduced using the traditional basis of vibration modes and then integrated using a highly accurate, explicit integration technique. A critical point constraint formulation is used to place constraints on the magnitude of each response quantity as a function of time. Three different techniques for calculating sensitivities of the critical point constraints are presented. The first two are based on the straightforward application of the forward and central difference operators, respectively. The third is based on explicit differentiation of the equations of motion. Condition errors, finite difference truncation errors, and modal convergence errors for the three techniques are compared by applying them to a simple five-span-beam problem. Sensitivity results are presented for two different transient loading conditions and for both damped and undamped cases.

Description: A new and simple method of finite-element grid improvement is presented. The objective is to improve the accuracy of the analysis. The procedure is based on a minimization of the trace of the stiffness matrix. For a broad class of problems this minimization is seen to be equivalent to minimizing the potential energy. The method is illustrated with the classical tapered bar problem examined earlier by Prager and Masur. Identical results are obtained.

Description: Numerical studies of turbulent flow in an axisymmetric 45-deg-expansion combustor and bifurcated diffuser are presented. The Navier-Stokes equations incorporating a k-epsilon model were solved in a nonorthogonal curvilinear coordinate system. A zonal-grid method, where the flow field was divided into several subsections, was developed. This approach permitted different computational schemes to be used in the various zones. In addition, grid generation was made a more simple task. Boundary overlap and interpolating techniques were used, and an adjustment of the flow variables was required to assure conservation of mass flux. Three finite-differencing methods (hybrid, quadratic upwind, and skew upwind) were used to represent the convection terms. Results were compared with existing experimental data. In general, good agreement between predicted and measured values was obtained.

Description: Assuming a single-mode transverse displacement, a simple formula is derived for the transverse load-displacement relationship of a plate under in-plane compression. The formula is used to derive a simple analytical expression for the nonlinear dynamic response of postbuckled plates under sinusoidal or random excitation. The highly nonlinear motion of snap-through can be easily interpreted using the single-mode formula. Experimental results are obtained with buckled and cylindrical aluminum panels using discrete frequency and broadband excitation of mechanical and acoustic forces. Some important effects of the snap-through motion on the dynamic response of the postbuckled plates are described. Static tests were used to identify the deformation shape during snap-through.

Description: An experimental investigation of composite to composite bonded joints was undertaken to study the effect of bond thickness on debond growth rate under cyclic loading and critical strain energy release rate under static loading. Double cantilever beam specimens of graphite/epoxy adherends bonded with EC 3445 were tested under mode I loading. A different behavior of fracture and fatigue strength was observed with variation of bondline thickness.

Description: The feasibility of using a viscoplastic model developed by Robinson to perform a nonlinear structural analysis was investigated. The paper presents analytical solutions for three classical problems: (1) a pressurized thick-walled cylinder, (2) a thin rotating disk, and (3) a pressurized thick-walled sphere. The analytical expressions derived for the stress and the strain rates for these components are general in nature as they consider both the mechanical and thermal loadings to be time-dependent. A computer program VISTAN (VIscoplastic STructural ANalyzer) was developed to obtain the stress and strain distributions. The finite element solutions for these problems are also presented. The numerical results pertaining to isothermal loading conditions are provided. The results obtained demonstrate the feasibility of using the viscoplastic model developed by Robinson to perform nonlinear structural analyses.

Description: A numerical procedure in which the Navier-Stokes equations are discretized using tightly coupled discretizations of pressure derivatives and continuity equations is used here to extend the range of known terminal velocities of gaseous bubbles in liquids well beyond that in previous investigations. Computations performed for Reynolds numbers up to 2000 and Marangoni numbers up to 1000 show only a modest variation of the scaled bubble velocity between 0.16 and 0.5. The bubble velocity is influenced more by the Marangoni number than by the Reynolds number.

Description: A numerical analysis is performed on thermocapillary buoyancy convection induced by phase change in a liquid droplet. A finite-difference code is developed using an alternating-direction implicit (ADI) scheme. The intercoupling relation between thermocapillary force, buoyancy force, fluid property, heat transfer, and phase change, along with their effects on the induced flow patterns, are disclosed. The flow is classified into three types: thermocapillary, buoyancy, and combined convection. Among the three mechanisms, the combined convection simulates the experimental observations quite well, and the basic mechanism of the observed convection inside evaporating sessile drops is thus identified. It is disclosed that evaporation initiates unstable convection, while condensation always brings about a stable density distribution which eventually damps out all fluid disturbances. Another numerical model is presented to study the effect of boundary recession due to evaporation, and the 'peeling-off' effect (the removal of the surface layer of fluid by evaporation) is shown to be relevant.

Description: Two-dimensional solidification influenced by anisotropic heat conduction has been considered. The interfacial energy balance was derived to account for the heat transfer in one direction (x or y) depending on the temperature gradient in both the x and y directions. A parametric study was made to determine the effects of the Stefan number, aspect ratio, initial superheat, and thermal conductivity ratios on the solidification rate. Because of the imposed boundary conditions, the interface became skewed and sometimes was not a straight line between the interface position at the upper and lower adiabatic walls (spatially nonlinear along the height). This skewness depends on the thermal conductivity ratio k(yy)/k(yx). The nonlinearity of the interface is influenced by the solidification rate, aspect ratio, and k(yy/k(yx).

Description: A multiple-time-scale turbulence model of a single point closure and a simplified split-spectrum method is presented. In the model, the effect of the ratio of the production rate to the dissipation rate on eddy viscosity is modeled by use of the multiple-time-scales and a variable partitioning of the turbulent kinetic energy spectrum. The concept of a variable partitioning of the turbulent kinetic energy spectrum and the rest of the model details are based on the previously reported algebraic stress turbulence model. Example problems considered include: a fully developed channel flow, a plane jet exhausting into a moving stream, a wall jet flow, and a weakly coupled wake-boundary layer interaction flow. The computational results compared favorably with those obtained by using the algebraic stress turbulence model as well as experimental data. The present turbulence model, as well as the algebraic stress turbulence model, yielded significantly improved computational results for the complex turbulent boundary layer flows, such as the wall jet flow and the wake boundary layer interaction flow, compared with available computational results obtained by using the standard kappa-epsilon turbulence model.

Description: A combined experimental and analytical study of bearing and bypass loading on single-fastener specimens of a 16-ply, quasi-isotropic T300/5208 graphite/epoxy laminate with a centrally located hole is reported. The specimens were loaded in either tension or compression, and onset damage, ultimate strengths, and corresponding failure modes were determined. The tension data showed the expected linear interaction for combined bearing-bypass loading with damage developing in the net-section tension mode. However, the bearing-onset strengths showed an unexpected interaction of the bearing and compressive bypass loads in which the latter reduced the bearing-onset strength. A linear finite element analysis showed that bearing-bypass loading had a marked influence on the bolt-hole contact which in turn had a significant effect on local stresses.

Description: A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite rectangular thin plates. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite rectangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, different boundary conditions, aspect ratios, lamination angles and number of plies are presented. The finite element results are compared with available approximate continuum solutions.

Description: The emission from a gray radiating medium is analyzed for transient cooling in surroundings at a low temperature. The medium is rectangular with no variations in the direction normal to the cross section. The integral equation for the transient temperature distribution is solved numerically using a two-dimensional Gaussian integration subroutine. The emissive ability for a rectangle at uniform temperature is compared with that for transient cooling where the temperature distribution of the region has reached a fully developed shape, as shown by a separation of variables solution. The two solutions provide the upper and lower bounds for the emittance of a rectangle during transient cooling. The emittances for various aspect ratios are presented as a function of the mean length of the rectangle and are compared with results for a plane layer and a cylinder.

Description: Calculations for n-decane drops evaporating in a spherical cluster surrounded by unvitiated ambient air at atmospheric pressure were performed using two previously proposed cluster models. Both cluster models predict that turbulent transport effects are more important in the case of small clusters. This is due to the smaller volume to surface ratio and thus to the greater transport of hot unvitiated gas to the drops in order to promote evaporation. The results obtained are compared with those of two turbulent models for each one of the 'trapping factors' and similarity models.

Description: The objectives are to present the derivation of the new virtual crack closure technique, evaluate the accuracy of the technique, and finally to present the results of a limited parametric study of laminates with a postbuckled delamination. Although the new virtual crack closure technique is general, only homogeneous, isotropic laminates were analyzed. This was to eliminate the variation of flexural stiffness with orientation, which occurs even for quasi-isotropic laminates. This made it easier to identify the effect of geometrical parameters on G. The new virtual crack closure technique is derived. Then the specimen configurations are described. Next, the stress analyses is discussed. Finally, the virtual crack closure technique is evaluated and then used to calculate the distribution of G along the delamination front of several laminates with a postbuckled delamination.

Description: The effects of critical layer nonlinearity are considered on spatially growing oblique instability waves on nominally two-dimensional shear layers between parallel streams. The analysis shows that three-dimensional effects cause nonlinearity to occur at much smaller amplitudes than it does in two-dimensional flows. The nonlinear instability wave amplitude is determined by an integro-differential equation with cubic type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. The numerical solutions always end in a singularity at a finite downstream distance.

Description: The effects of critical-layer nonlinearity on spatially growing oblique instability waves on compressible shear layers between two parallel streams are considered. The analysis shows that mean temperature nonuniformities cause nonlinearity to occur at much smaller amplitudes than it does when the flow is isothermal. The nonlinear instability wave growth rate effects are described by an integrodifferential equation which bears some resemblance to the Landau equation, in that it involves a cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. Inviscid solutions always end in a singularity at a finite downstream distance, but viscosity can eliminate this singularity for certain parameter ranges.

Description: A simulation is performed of a passive scalar field convected by a rapidly fluctuating velocity field whose correlation time approaches zero. By using a code proposed in a previous study (Chasnov et al., 1988), the turbulence spectrum of the passive temperature field in the conductive subrange is determined. A theoretical model is proposed which explains the result obtained by representing the transfer of scalar variance by an eddy conductivity, whose correlation time is limited by the correlation time of the velocity field.

Description: A description of the finite element implementation of Robinson's unified viscoplastic model into the General Purpose Finite Element Program (MARC) is presented. To demonstrate its application, the implementation is applied to some uniaxial and multiaxial problems. A comparison of the results for the multiaxial problem of a thick internally pressurized cylinder, obtained using the finite element implementation and an analytical solution, is also presented. The excellent agreement obtained confirms the correct finite element implementation of Robinson's model.

Description: In the dynamic formulation of holonomic and nonholonomic systems based on D'Alembert-Lagrange equation, the forces of constraints are maintained in the dynamic equations by introducing auxiliary variables, called Lagrange multipliers. This approach introduces a set of generalized reaction forces associated with the system generalized coordinates. Different sets of variables can be used as generalized coordinates and accordingly, the generalized reactions associated with these generalized coordinates may not be the actual reaction forces at the joints. In rigid body dynamics, the generalized reaction forces and the actual reaction forces at the joints represent equipollent systems of forces since they produce the same total forces and moments at and about any point on the rigid body. This is not, however, the case in deformable body analyses wherein the generalized reaction forces depend on the system generalized reference and elastic coordinates. In this paper, a method for determining the actual reaction forces at the joints from the generalized reaction forces in deformable multibody systems is presented.

Description: Long's self-similar vortex is known to have two solutions for each supercritical value of the flow force. Each of those solutions is shown to have a double structure if the flow force is large. The inertial instabilities of one of those large-flow-force limit solutions are investigated, showing that they are related to the instabilities of the Bickley jet in one regime. However, the swirl in the vortex becomes important for long waves, very strongly modifying the sinuous and varicose, Bickley modes. The asymptotic results obtained agree well with the numerical solutions for the sinuous mode, but not for the varicose mode, the difficulty in the latter case being apparently due to mode jumping.

Description: Numerical techniques are developed to solve the Navier-Stokes equations for unsteady incompressible flow. The extension of the finite-difference Galerkin (FDG) method of Stephens et al. (1984) to the continuous-time case in two or three space dimensions is explained, and the numerical implementation of the method is discussed with particular attention to the staggered-MAC-grid primitive-variable discretization, the application of discrete mass balance to avoid problems inherent in FDG schemes, the direct interpretation of the FDG expansion variables as a discrete streamfunction, and a mass-balance approach to two-dimensional problems with throughflow or obstacles. Numerical results are presented graphically for the evolution of asymptotic steady flow in a driven cavity at Reynolds number 400, 1000, or 3200; good agreement with published experimental data is demonstrated, with accurate predictions of secondary-vortex formation from wall bubble recirculations at Reynolds number 1000.

Description: The Boundary Force Method (BFM), a form of indirect boundary element method, is used to analyze composite laminates with cracks. The BFM uses the orthotropic elasticity solution for a concentrated horizontal and vertical force and a moment applied at a point in a cracked, infinite sheet as the fundamental solution. The necessary stress functions for this fundamental solution were formulated using the complex variables theory of orthotropic elasticity. The current method is an improvement over a previous method using only forces and no moment. The improved method was verified by comparing it to accepted solutions for a finite-width, center-crack specimen subjected to uniaxial tension. Four graphite/epoxy laminates were used: (0 + or - 45/90)sub s, (0), (+ or - 45)sub s, and (+ or - 30)sub s. The BFM results agreed well with accepted solutions. Convergence studies showed that with the addition of the moment in the fundamental solution, the number of boundary elements required for a converged solution was significantly reduced. Parametric studies were done for two configurations for which no orthotropic solutions are currently available; a single edge crack and an inclined single edge crack.

Description: Flow-field measurements of unsteady turbulent flow downstream of a rotating spoked-wheel wake generator were performed in a short-duration light-piston tunnel, and the instantaneous-velocity data were phase averaged based on a signal synchronized with the bar-passing frequency. Mean axial velocities were found to agree well with those obtained from measurements behind a stationary cylinder and to be independent of both Reynolds and bar-passing Strouhal numbers. Reynolds stresses were found to be consistent with related cylinder-wake measurements, but were significantly higher than corresponding measurements obtained in large-scale research turbomachines. Phase-averaged triple velocity correlations were calculated from the digital velocity records, revealing the sign and the magnitude of skewness in the velocity probability density distributions for the two components.

Description: The bifurcation diagram corresponding to the Eckhaus stability curve has been constructed for the one-dimensional Swift-Hohenberg equation in a finite domain. Finite-amplitude solutions with particular spatial wavelength recover linear stability, as predicted by the Eckhaus curve, after a sequence of secondary bifurcations from the branch of solutions with this wavelength. No connectivity between the primary-solution branches is admissible if the stability predicted by this bifurcation diagram is to correspond to the prediction of the Eckhaus analysis. The Eckhaus curve does not exist if nonlinear couplings destroy this pattern. This is demonstrated by analysis of a coupled pair of Swift-Hohenberg equations.

Description: The fundamental relationship between the morphology of a composite laminate and the resulting free edge effects is explored and related to delamination failures. Cross-ply, angle-ply, and quasi-isotropic laminates are discussed in detail. It is shown that the local mismatch in elastic properties of adjacent layers and the global stacking sequence of a laminate both have a significant influence on the interlaminar stresses and delamination failures.

Description: The effects of asymmetry in furnace temperature profile and pulling velocity on the crystal interface shape are demonstrated while neglecting the latent heat of solidification. It is seen that the furnace temperature profile may be varied in order to influence the shape of the melt-crystal interface. An exact thermal analysis is then performed on the Bridgman technique by including the latent heat of solidification as a source term. The exact temperature field required for yielding a flat melt-crystal interface is obtained. The earlier observation regarding the influence of furnace temperature profile on the interface shape is confirmed and a criterion for achieving a flat interface is obtained. Various furnace temperature profiles are selected and their corresponding melt-crystal interface results are presented.

Description: A method is developed for the optimal design of composite links based on dynamic performance criteria directly related to structural modal damping and dynamic stiffness. An integrated mechanics theory correlates structural composite damping to the parameters of basic composite material systems, laminate parameters, link shape, and modal deformations. The inclusion of modal properties allows the selective minimization of vibrations associated with specific modes. Ply angles and fiber volumes are tailored to obtain optimal combinations of damping and stiffness. Applications to simple composite links indicate wide margins for trade-offs and illustrate the importance of various design variables to the optimal design.

Description: Transient cooling by radiation is analyzed for a cylindrical region filled with axially flowing streams of drops that are becoming solidified. This is of interest for the dissipation of waste heat from orbiting power system in space. The drops absorb, emit, and scatter radiation, and the surroundings are at a lower uniform temperature. The radiative properties are assumed gray, and the scattering is isotropic. The radiating region is a two-phase mixture that remains at the melting temperature of the drops. Its temperature uniformity maintains a high emissive power as energy is lost. This is an advantage over a sensible heat radiator in which the temperature decreases, thereby reducing the emissive power. The results provide the axial length that remains two-phase and the fraction of energy dissipated within this length in which the emissive power has not decreased because of sensible cooling. It is also shown how the radial distribution of the axial velocity of the drops can be modified to increase this energy fraction.

Description: A number of successful applications of a spectral collocation method extended by a multi-domain patching technique are shown. The multi-domain technique can be used to improve resolution for problems with widely disparate scales, and to reduce the ill-conditioning of the spectral operators for problems in which a large number of points are required for distributed resolution. A new nonreflecting outflow boundary treatment for unsteady transition-to-turbulence simulations is also presented, which relies on the multi-domain technique. The role of multi-domain in improving the efficiency of such calculations is discussed.

Description: Spectral element methods are high-order weighted residual techniques based on spectral expansions of variables and geometry for the Navier-Stokes (NS) and transport equations. Here, practical aspects of these methods and their efficient implementation are examined, and several examples of flows in truly complex geometries are presented. The spectral element discretization for NS equations is introduced, and the convergence of the method is addressed. An efficient data management scheme is discussed in the context of parallel processing computations. The method is validated by comparing the spectral element solutions with the exact eigensolutions for the Orr-Sommerfeld equations in two and three dimensions. Computer-aided flow visualizations are presented for an impulsive flow past a sharp edge wedge. Three-dimensional states of channel flow disrupted by an array of cylindrical eddy promoters are studied, and the results of a direct simulation of the turbulent flow in a plane channel are presented.

Description: Local buckling can cause large interlaminar stresses along the delamination front, which can lead to delamination growth. This paper examines several methods of calculating strain-energy release rates, which are often used to predict delamination growth. The thin-film plate analysis, which was least expensive, calculated the total strain-energy release rate G(T) quite accurately. However, the stress field along the delamination front is highly mixed-mode and has no fixed ratio of G(I) to G(II). Since plate analysis can only calculate G(T), it would not be useful for accurate predictions of delamination growth if mode mix is important.

Description: A description of the Axial Flow Turbine Research Facility (AFTRF) being built at the Turbomachinery Laboratory of the Pennsylvania State University is presented. The purpose of the research to be performed in this facility is to obtain a better understanding of the rotor/stator interaction, three dimensional viscous flow field in nozzle and rotor blade passages, spanwise mixing and losses in these blade rows, transport of wake through rotor passage, and unsteady aerodynamics and heat transfer of rotor blade row. The experimental results will directly feed and support the analytical and the computational tool development. This large scale low speed facility is heavily instrumented with pressure and temperature probes and has provision for flow visualization and laser Doppler anemometer measurement. The facility design permits extensive use of the high frequency response instrumentation on the stationary vanes and more importantly on the rotating blades. Furthermore it facilitates detailed nozzle wake, rotor wake, and boundary layer surveys. The large size of the rig also has the advantage of operating at Reynolds numbers representative of the engine environment.

Description: Over the years, NASA has been conducting the Advanced Earth-to-Orbit (AETO) Propulsion Technology Program to provide the knowledge, understanding, and design methodology that will allow the development of advanced Earth-to-orbit propulsion systems with high performance, extended service life, automated operations, and diagnostics for in-flight health monitoring. The objective of the Aerothermodynamic Loads Definition Study is to develop methods to more accurately predict the operating environment in AETO propulsion systems, such as the Space Shuttle Main Engine (SSME) powerhead. The approach taken consists of 2 parts: to modify, apply, and disseminate existing computational fluid dynamics tools in response to current needs and to develop new technology that will enable more accurate computation of the time averaged and unsteady aerothermodynamic loads in the SSME powerhead. The software tools are detailed. Significant progress was made in the area of turbomachinery, where there is an overlap between the AETO efforts and research in the aeronautical gas turbine field.

Description: The purpose of the Probabilistic Structural Analysis Method (PSAM) project is to develop structural analysis capabilities for the design analysis of advanced space propulsion system hardware. The boundary element method (BEM) is used as the basis of the Probabilistic Advanced Analysis Methods (PADAM) which is discussed. The probabilistic BEM code (PBEM) is used to obtain the structural response and sensitivity results to a set of random variables. As such, PBEM performs analogous to other structural analysis codes such as finite elements in the PSAM system. For linear problems, unlike the finite element method (FEM), the BEM governing equations are written at the boundary of the body only, thus, the method eliminates the need to model the volume of the body. However, for general body force problems, a direct condensation of the governing equations to the boundary of the body is not possible and therefore volume modeling is generally required.

Description: A major research and technology program in Probabilistic Structural Analysis Methods (PSAM) is currently being sponsored by the NASA Lewis Research Center with Southwest Research Institute as the prime contractor. This program is motivated by the need to accurately predict structural response in an environment where the loadings, the material properties, and even the structure may be considered random. The heart of PSAM is a software package which combines advanced structural analysis codes with a fast probability integration (FPI) algorithm for the efficient calculation of stochastic structural response. The basic idea of PAAM is simple: make an approximate calculation of system response, including calculation of the associated probabilities, with minimal computation time and cost, based on a simplified representation of the geometry, loads, and material. The deterministic solution resulting should give a reasonable and realistic description of performance-limiting system responses, although some error will be inevitable. If the simple model has correctly captured the basic mechanics of the system, however, including the proper functional dependence of stress, frequency, etc. on design parameters, then the response sensitivities calculated may be of significantly higher accuracy.

Description: Two-dimensional optical strain measurements on high temperature test specimens are presented. This two-dimensional capability is implemented through a rotatable sensitive strain axis. Three components of surface strain can be measured automatically, from which the first and second principal strains are calculated. One- and two-dimensional strain measurements at temperatures beyond 750 C with a resolution of 15 microstrain are demonstrated. The system is based on a one-dimensional speckle shift technique. The speckle shift technique makes use of the linear relationship between surface strain and the differential shift of laser speckle patterns in the diffraction plane. Laser speckle is a phase effect that occurs when spatially coherent light interacts with an optically rough surface. Since speckle is generated by any diffusely reflecting surface, no specimen preparation is needed to obtain a good signal. Testing was done at room temperature on a flat specimen of Inconel 600 mounted in a fatigue testing machine. A load cell measured the stress on the specimen before and after acquiring the speckle data. Strain components were measured at 0 C (parallel to the load axis) and at plus or minus 45 C, and plots indicate the calculated values of the first and second principal strains. The measured values of Young's modulus and Poisson's ratio are in good agreement with handbook values. Good linearity of the principal strain moduli at high temperatures indicate precision and stability of the system. However, a systematic error in the high-temperature test setup introduced a scale factor in the slopes of the two-dimensional stress-strain curves. No high temperature effects, however, have been observed to degrade speckle correlation.

Description: A quasi-three-dimensional analysis has been developed for unsteady rotor-stator interaction in turbomachinery. The analysis solves the unsteady Euler or thin-layer Navier-Stokes equations in a body-fitted coordinate system. It accounts for the effects of rotation, radius change, and stress-surface thickness. The Baldwin-Lomax eddy-viscosity model is used for turbulent flows. The equations are integrated in time using an explicit four-stage Runge-Kutta scheme with a constant time step. Implicit residual smoothing is used to increase the stability limit of the time-accurate computations. The scheme is described, and stability and accuracy analyses are given.

Description: The fusion of the probabilistic finite element method (PFEM) and reliability analysis for probabilistic fracture mechanics (PFM) is presented. A comprehensive method for determining the probability of fatigue failure for curved crack growth was developed. The criterion for failure or performance function is stated as: the fatigue life of a component must exceed the service life of the component; otherwise failure will occur. An enriched element that has the near-crack-tip singular strain field embedded in the element is used to formulate the equilibrium equation and solve for the stress intensity factors at the crack-tip. Performance and accuracy of the method is demonstrated on a classical mode 1 fatigue problem.

Description: A 3-D model was developed for simulating multistage turbomachinery flows using supercomputers. This average passage flow model described the time averaged flow field within a typical passage of a bladed wheel within a multistage configuration. To date, a number of inviscid simulations were executed to assess the resolution capabilities of the model. Recently, the viscous terms associated with the average passage model were incorporated into the inviscid computer code along with an algebraic turbulence model. A simulation of a stage-and-one-half, low speed turbine was executed. The results of this simulation, including a comparison with experimental data, is discussed.

Description: The probabilistic structural analysis method (PSAM) was developed to analyze the effects of fluctuating loads, variable material properties, and uncertain analytical models especially for high performance structures such as the Space Shuttle Main Engine turbopump blades. Risk is calculated after expensive service experience. However, probabilistic structural analysis provides a rational alternative method to quantify uncertainties in the structural performance and durability. NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) was developed as a probabilistic structural analysis computer code which integrates finite element methods and reliability algorithms, capable to predicting the probability distributions of structural response variables such as stress, displacement, natural frequencies, and buckling loads. This computer code is detailed.

Description: The Probabilistic Structural Analysis Methods (PSAM) project developed at the Southwest Research Institute integrates state-of-the-art structural analysis techniques with probability theory for the design and analysis of complex large-scale engineering structures. An advanced efficient software system (NESSUS) capable of performing complex probabilistic analysis has been developed. NESSUS contains a number of software components to perform probabilistic analysis of structures. These components include: an expert system, a probabilistic finite element code, a probabilistic boundary element code and a fast probability integrator. The NESSUS software system is shown. An expert system is included to capture and utilize PSAM knowledge and experience. NESSUS/EXPERT is an interactive menu-driven expert system that provides information to assist in the use of the probabilistic finite element code NESSUS/FEM and the fast probability integrator (FPI). The expert system menu structure is summarized. The NESSUS system contains a state-of-the-art nonlinear probabilistic finite element code, NESSUS/FEM, to determine the structural response and sensitivities. A broad range of analysis capabilities and an extensive element library is present.

Description: Constitutive and life prediction models are developed and verified for materials typically used in hot gas path components of reusable space propulsion systems over the range of relevant operating environments. The efforts were centered on the development of crack initiation life prediction methods, while the efforts of a counterpart group were centered on the development of cyclic crack propagation life prediction methods. The complexion of the active tasks are presented. A significant new task started this year will incorporate the various material constitutive and life prediction models developed in this program into a comprehensive creep-fatigue damage analysis and life assessment computer code. The program will function as a postprocessor to general structural analysis programs (such as finite element or boundary element codes) using the output of such analyses (stress, strain, and temperature fields as functions of time) as the input to the damage analysis and life assessment code. The code will be designed to execute on engineering/scientific workstations and will feature a windowing, mouse-driven user interface. Current plans call for the code to be finished and made available for use in mid 1991.

Description: A multiphase turbulence closure model is presented which employs one transport equation, namely the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A mass/time averaging procedure for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less retrictive assumptions comparative to previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.

Description: Generally, two types of theory are used to describe the field equations for suspensions. The so-called postulated equations are based on the kinetic theory of mixtures, which logically should give reasonable equations for solutions. The basis for the use of such theory for suspensions is tenuous, though it at least gives a logical path for mathematical arguments. It has the disadvantage that it leads to a system of equations which is underdetermined, in a sense that can be made precise. On the other hand, the so-called averaging theory starts with a determined system, but the very process of averaging renders the resulting system underdetermined. A third type of theory is proposed in which the kinetic theory of gases is used to motivate continuum equations for the suspended particles. This entails an interpretation of the stress in the particles that is different from the usual one. Classical theory is used to describe the motion of the suspending medium. The result is a determined system for a dilute suspension. Extension of the theory to more concentrated systems is discussed.

Description: In structural analysis the amount of computational time necessary for a solution is proportional to the number of degrees of freedom times the bandwidth squared. In implicit time analysis, this must be done at each discrete point in time. If, in addition, the problem is nonlinear, then this solution must be iterated at each point in time. If the bandwidth is large, the size of the problem that can be analyzed is severely limited. The multi-grid method is a possible algorithm which can make this solution much more computationally efficient. This method has been used for years in computational fluid mechanics. It works on the fact that relaxation is very efficient on the high frequency components of the solution (nearest neighbor interactions) and not very good on low frequency components of the solution (far interactions). The multi-grid method is then to relax the solution on a particular model until the residual stops changing. This indicates that the solution contains the higher frequency components. A coarse model is then generated for the lower frequency components to the solution. The model is then relaxed for the lower frequency components of the solution. These lower frequency components are then interpolated to the fine model. In computational fluid mechanics the equations are usually expressed as finite differences.

Description: The deployment, assembly and mission-oriented maneuvering of space structures in orbit will trigger large motions of flexible, truss-type structures. In addition, the presence of on-board controls both for attitude stabilization and specified vibration tolerance requirements may further complicate the dynamic behavior of the orbiting structures. Because of safety and cost considerations, the dynamic response of the combined structural and control systems must be predicted reliably. This need can only be met through the development of reliable and efficient simulation capabilities, since there is general agreement that on-orbit experiments should be limited because of cost, time and facility constraints. The long-term objective of this research effort is to develop a next-generation computer simulator for the dynamics and control of large space structures. The simulator will be based on integrating four research thrusts: a new multibody dynamics formulation methodology, modeling capabilities in long/slender truss-beam components with realistic joints, efficient computational procedures that can be implemented either in sequential or concurrent computers, and prototype simulation modules that can be easily processed into a modern large-scale engineering software system such as the NASA/Computational Structural Mechanics (CSM) testbed.

Description: The 3-D inelastic analysis method is a focused program with the objective to develop computationally effective analysis methods and attendant computer codes for three-dimensional, nonlinear time and temperature dependent problems present in the hot section of turbojet engine structures. Development of these methods was a major part of the Hot Section Technology (HOST) program over the past five years at Lewis Research Center.

Description: A summary of the status of this five-year project which is now in its third year of research and development is presented. The goal of the project is the development of several methodologies for probabilistic structural modeling. Probabilistic structural modeling consists of stochastic models of material properties, part geometries, boundary conditions, as well as loading conditions. The current presentation focuses on one methodology - coupling of an advanced finite element structural analysis code with probabilistic modeling strategies. The essential algorithm developments for combining the finite element and probabilistic analysis methods are reported. The validity of the resulting probabilistic structural analysis method is confirmed through a series of test problems with exact results based on Monte Carlo simulations. Additionally, the applicability of the method to a Space Propulsion System (a turbine blade) is demonstrated for static stresses.

Description: This project supports the conversion of codes in Computational Structural Mechanics (CSM) to a parallel form which will efficiently exploit the computational power available from multiprocessors. The work is a part of a comprehensive, FORTRAN-based system to form a basis for a parallel version of the NICE/SPAR combination which will form the CSM Testbed. The software is macro-based and rests on the force methodology developed by the principal investigator in connection with an early scientific multiprocessor. Machine independence is an important characteristic of the system so that retargeting it to the Flex/32, or any other multiprocessor on which NICE/SPAR might be imnplemented, is well supported. The principal investigator has experience in producing parallel software for both full and sparse systems of linear equations using the force macros. Other researchers have used the Force in finite element programs. It has been possible to rapidly develop software which performs at maximum efficiency on a multiprocessor. The inherent machine independence of the system also means that the parallelization will not be limited to a specific multiprocessor.

Description: A new numerical algorithm for the solution of large-order eigenproblems typically encountered in linear elastic finite element systems is presented. The architecture of parallel processing is utilized in the algorithm to achieve increased speed and efficiency of calculations. The algorithm is based on the frontal technique for the solution of linear simultaneous equations and the modified subspace eigenanalysis method for the solution of the eigenproblem. Assembly, elimination and back-substitution of degrees of freedom are performed concurrently, using a number of fronts. All fronts converge to and diverge from a predefined global front during elimination and back-substitution, respectively. In the meantime, reduction of the stiffness and mass matrices required by the modified subspace method can be completed during the convergence/divergence cycle and an estimate of the required eigenpairs obtained. Successive cycles of convergence and divergence are repeated until the desired accuracy of calculations is achieved. The advantages of this new algorithm in parallel computer architecture are discussed.

Description: The overall objective of this research is to develop efficient methods for the solution of linear and nonlinear systems of equations on parallel and supercomputers, and to apply these methods to the solution of problems in structural analysis. Attention has been given so far only to linear equations. The methods considered for the solution of the stiffness equation Kx=f have been Choleski factorization and the conjugate gradient iteration with SSOR and Incomplete Choleski preconditioning. More detail on these methods will be given on subsequent slides. These methods have been used to solve for the static displacements for the mast and panel focus problems in conjunction with the CSM testbed system based on NICE/SPAR.

Description: The background for the CSM Testbed Architecture and a description of the three architecture related tasks under the NASA/Langley CSM contract (NAS1-18444) are given. For each task the objectives, subtasks chosen to achieve the objectives, and the accomplishments are presented. For Task 2, Near-Term Enhancements to the CSM Testbed Architecture, the primary objectives are to quickly correct: (1) inefficiency in the GAL data manager, and (2) deficiency in the CLIP-interpreted command language, CLAMP. The corresponding modifications should preserve upward-compatibility to a reasonable extent, while at the same time increasing the flexibility and extensibility of the CSM Testbed. Researchers have increased the efficiency of GAL by a factor of 2+ and have made several improvements in CLIP. For Task 5, Matrix Algebra Methods and Utilities, the goal is to investigate the current capabilities of the CSM Testbed and the required improvements to the CSM Testbed for performing the matrix algebraic operations required for the analysis of present and future CSM focal problems using advanced methods. Researchers have made an extensive study of the matrix algebra functions in SPAR that includes documenting these routines and supplying inline comments.

Description: The PISCES project started in 1984 under the sponsorship of the NASA Computational Structural Mechanics (CSM) program. A PISCES 1 programming environment and parallel FORTRAN were implemented in 1984 for the DEC VAX (using UNIX processes to simulate parallel processes). This system was used for experimentation with parallel programs for scientific applications and AI (dynamic scene analysis) applications. PISCES 1 was ported to a network of Apollo workstations by N. Fitzgerald.

Description: In January 1987, SPARTA received a Phase I SBIR award from the NASA Lewis Research Center to investigate the feasibility of a finite element solver implemented on multiple VLSI processors. The transputer was chosen as the processor for the feasibility study since it combined low cost with high performance and was specifically designed to directly link with other transputers to form networks of multiple processors. A brief description of transputers, a summary of the SBIR feasibility study, and a discussion of issues concerning a large scale transputer based finite element solver (TBFES) and the performance levels which can be expected are discussed.

Description: Damage assessment of structural assemblies is treated as an identification problem. A brief review of identification methods is first presented with particular focus on the output error approach. The use of numerical optimization methods in identifying the location and extent of damage in structures is studied. The influence of damage on eigenmode shapes and static displacements is explored as a means of formulating a measure of damage in the structure. Preliminary results obtained in this study are presented and special attention is directed at the shortcomings associated with the nonlinear programming approach to solving the optimization problem.

Description: Within the past several years, the Jet Propulsion Laboratory has designed and built major ground antenna structures in Spain, Australia, and California. One of the antennas at each location is a 70 meter-diameter structure that is a retrofit of the existing 64 meter antenna. The 64 meter existing antennas were first stripped back to a 34 meter interior and then completely new construction with deeper trusses was added to extend the interior to 70 meters. The 70 meter project included the rare opportunity to collect field data to compare with predictions of the finite-element analytical models. The new quadripod design was tested for its lower mode natural frequencies and the main reflector was measured by theodolite to determine deflections of subsets of the backup-structure deformations under load. The emphasis here is to examine measurement results and possibly provide some appreciation of the relationship of predictions made from the design model to actual measurements.

Description: The application of a generalized optimality criteria to framed structures is presented. The optimality conditions, Lagrangian multipliers, resizing algorithm, and scaling procedures are all represented as a function of the objective and constraint functions along with their respective gradients. The optimization of two plane frames under multiple loading conditions subject to stress, displacement, generalized stiffness, and side constraints is presented. These results are compared to those found by optimizing the frames using a nonlinear mathematical programming technique.

Description: Recent developments in multilevel optimization are briefly reviewed. The general nature of the multilevel design task, the use of approximations to develop and solve the analysis design task, the structure of the formal multidiscipline optimization problem, a simple cantilevered beam which demonstrates the concepts of multilevel design and the basic mathematical details of the optimization task and the system level are among the topics discussed.

Description: A two-level design optimization metholology is described. A progress report of its application to Printed Wiring Board (PWB) assembly examples is given. The design of PWB assemblies is a complex task which is generally conducted as a sequential process. Individual PWBs are usually designed first, followed by the composition of the PWBs into an assembly. As a result, optimizing design considerations such as assembly reliability cannot be accomplished. This study showed that a two-level decomposition method can be employed to optimize for reliability at both the PWB- and the assembly-level in a coupled manner. The two-level decomposition method also resolved the mixed-integer nonlinear programming nature of the problem rather easily.

Description: Independent Modal Space Control (IMSC) is a technique that is often used for the control of large order structural systems. The pertinent optimization problem in the simultaneous design and control of structures is a min - min problem that minimizes with respect to the structural design variables, the minimum value of the performance index with respect to the control forces obtained using the IMSC technique. The minimization process requires derivatives of eigenvalues and eigenvectors with respect to the design variables. These derivatives can be computed by a rather involved analytical procedure or a relatively simple finite difference procedure. The computer cost effectiveness of these two procedures for the derivative calculations is examined.

Description: The objective of this presentation is to introduce the attendees to the DYSCO program. The emphasis will be on the features which make it multidisciplinary. DYSCO is a very general and versatile software program which couples and solves dynamic systems. It was initiated in the late 1970's in response to a helicopter analysis requirement. The system development, however, resulted in an executive which was completely separated from any particular area of technology, except that of second order ordinary differential equations. During the course of its development, it was funded by the Army Aviation Applied Technology Directorate, the Air Force Wright Aeronautical Laboratories, and by the Kaman Aerospace Corporation. It is completely written in FORTRAN and is operational on IBM and VAX computers.

Description: A numerical method is presented for design sensitivity analysis, using an iterative-method reanalysis of the structure generated by a small perturbation in the design variable; a forward-difference scheme is then employed to obtain the approximate sensitivity. Algorithms are developed for displacement and stress sensitivity, as well as for eignevalues and eigenvector sensitivity, and the iterative schemes are modified so that the coefficient matrices are constant and therefore decomposed only once.

Description: The considerations and the resultant approach used to implement design sensitivity capability for grids into a large scale, general purpose finite element system (MSC/NASTRAN) are presented. The design variables are grid perturbations with a rather general linking capability. Moreover, shape and sizing variables may be linked together. The design is general enough to facilitate geometric modeling techniques for generating design variable linking schemes in an easy and straightforward manner. Test cases have been run and validated by comparison with the overall finite difference method. The linking of a design sensitivity capability for shape variables in MSC/NASTRAN with an optimizer would give designers a powerful, automated tool to carry out practical optimization design of real life, complicated structures.

Description: Structural optimization has been available to the structural analysis community as a tool for many years. The popular use of displacement method finite-element techniques to analyze linearly elastic structures has resulted in an ability to calculate the weight and constraint gradients inexpensively for numerical optimization of structures. Here, recent experiences in the investigation and use of structural optimization are discussed. In particular, experience with the commercially available ADS/NASOPT code is addressed. An overview of the ADS/NASOPT procedure and how it was implemented is given. Two example problems are also discussed.

Description: ASTROS (Automated Structural Optimization System) is a finite-element-based multidisciplinary structural optimization procedure developed under Air Force sponsorship to perform automated preliminary structural design. The design task is the determination of the structural sizes that provide an optimal structure while satisfying numerous constraints from many disciplines. In addition to its automated design features, ASTROS provides a general transient and frequency response capability, as well as a special feature to perform a transient analysis of a vehicle subjected to a nuclear blast. The motivation for the development of a single multidisciplinary design tool is that such a tool can provide improved structural designs in less time than is currently needed. The role of such a tool is even more apparent as modern materials come into widespread use. Balancing conflicting requirements for the structure's strength and stiffness while exploiting the benefits of material anisotropy is perhaps an impossible task without assistance from an automated design tool. Finally, the use of a single tool can bring the design task into better focus among design team members, thereby improving their insight into the overall task.

Description: Large space structures (LSSs) and other dynamical systems of current interest are often extremely complex assemblies of rigid and flexible bodies subjected to kinematical constraints. A formulation is presented for the governing equations of constrained multibody systems via the application of singular value decomposition (SVD). The resulting equations of motion are shown to be of minimum dimension.

Description: A recently developed finite-element capability for general nonlinear shell analysis, featuring the use of three-dimensional constitutive equations within an efficient resultant-oriented framework, is employed to simulate the postbuckling response of an axially compressed composite cylindrical panel with a circular cutout. The problem is a generic example of modern composite aircraft components for which postbuckling strength (i.e., fail-safety) is desired in the presence of local discontinuities such as holes and cracked stiffeners. While the computational software does a reasonable job of predicting both the buckling load and the qualitative aspects of postbuckling (compared both with experiment and another code) there are some discrepancies due to: (1) uncertainties in the nominal layer material properties, (2) structural sensitivity to initial imperfections, and (3) the neglect of dynamic and local material delamination effects in the numerical model. Corresponding refinements are suggested for the realistic continuation of this type of analysis.

Description: The development of commercial finite element software is addressed. This software provides practical tools that are used in an astonishingly wide range of engineering applications that include critical aspects of the safety evaluation of nuclear power plants or of heavily loaded offshore structures in the hostile environments of the North Sea or the Arctic, major design activities associated with the development of airframes for high strength and minimum weight, thermal analysis of electronic components, and the design of sports equipment. In the more advanced application areas, the effectiveness of the product depends critically on the quality of the mechanics and mechanics related algorithms that are implemented. Algorithmic robustness is of primary concern. Those methods that should be chosen will maximize reliability with minimal understanding on the part of the user. Computational efficiency is also important because there are always limited resources, and hence problems that are too time consuming or costly. Finally, some areas where research work will provide new methods and improvements is discussed.

Description: An analytical method is being developed to determine the signature of an acoustic emission waveform from a growing crack and the results of this analysis are compared to experimentally obtained values. Within the assumptions of linear elastic fracture mechanics, a two dimensional model is developed to examine a semi-infinite crack that, after propagating with a constant velocity, suddenly stops. The analytical model employs an integral equation method for the analysis of problems of dynamic fracture mechanics. The experimental procedure uses an interferometric apparatus that makes very localized absolute measurements with very high fidelity and without acoustically loading the specimen.

Description: A computer program was developed to take a NASTRAN output file from a normal modes analysis and calculate the modal strain energies of selected elements. The FORTRAN program can determine the modal strain energies for CROD, CBAR, CELAS, CTRMEM, CQDMEM2, and CSHEAR elements. Modal strain energies are useful in estimating damping in structures.

Description: Many finite element preprocessors describe finite element model geometry with points, lines, surfaces and volumes. One method for describing these basic geometric entities is by use of parametric cubics which are useful for representing complex shapes. The lines, surfaces and volumes may be discretized for follow on finite element analysis. The ability to limit or selectively recover results from the finite element model is extremely important to the analyst. Equally important is the ability to easily apply boundary conditions. Although graphical preprocessors have made these tasks easier, model complexity may not lend itself to easily identify a group of grid points desired for data recovery or application of constraints. A methodology is presented which makes use of the assignment of grid point locations in parametric coordinates. The parametric coordinates provide a convenient ordering of the grid point locations and a method for retrieving the grid point ID's from the parent geometry. The selected grid points may then be used for the generation of the appropriate set and constraint cards.

Description: The DMAP coding was automated to such an extent by using the device of bubble vectors, that it is useable for analyses in its present form. This feasibility study demonstrates that the Ritz Method is so compelling as to warrant coding its modules in FORTRAN and organizing the resulting coding into a new Rigid Format. Even though this Ritz technique was developed for unsymmetric stiffness matrices, it offers advantages to problems with symmetric stiffnesses. If used for the symmetric case the solution would be simplified to one set of modes, because the adjoint would be the same as the primary. Its advantage in either type of symmetry over a classical eigenvalue modal expansion is that information density per Ritz mode is far richer than per eigenvalue mode; thus far fewer modes would be needed for the same accuracy and every mode would actively participate in the response. Considerable economy can be realized in adapting Ritz vectors for modal solutions. This new Ritz capability now makes NASTRAN even more powerful than before.

Description: A monolithic spatial light modulator chip was developed consisting of a large number of micrometer-scale mirror cells which can be rotated through an angle by application of an electrostatic field. The field is generated by electronics integral to the chip. The chip has application in photoreceptor based non-impact printing technologies. Chips containing over 16000 cells were fabricated, and were tested to several billions of cycles. Finite Element Analysis (FEA) of the device was used to model both the electrical and mechanical characteristics.

Description: The identification of power flow paths in dynamically loaded structures is an important, but currently unavailable, capability for the finite element analyst. For this reason, methods for calculating power flows and mechanical intensities in finite element models are developed here. Formulations for calculating input and output powers, power flows, mechanical intensities, and power dissipations for beam, plate, and solid element types are derived. NASTRAN is used to calculate the required velocity, force, and stress results of an analysis, which a post-processor then uses to calculate power flow quantities. The SDRC I-deas Supertab module is used to view the final results. Test models include a simple truss and a beam-stiffened cantilever plate. Both test cases showed reasonable power flow fields over low to medium frequencies, with accurate power balances. Future work will include testing with more complex models, developing an interactive graphics program to view easily and efficiently the analysis results, applying shape optimization methods to the problem with power flow variables as design constraints, and adding the power flow capability to NASTRAN.

Description: Numerical techniques for calculating the low frequency vibrational resonances of submerged structures are reviewed. Both finite element and boundary element approaches for calculating fully-coupled added mass matrices for use in NASTRAN analysis are described and illustrated. The finite element approach is implemented using existing capability in NASTRAN. The boundary element approach uses the NASHUA structural-acoustics program to compute the added mass matrix. The two procedures are compared to each other for the case of a submerged cylindrical shell with flat end closures. It is concluded that both procedures are capable of computing accurate submerged resonances and that the more elegant boundary element procedure is easier to use but may be more expensive computationally.

Description: The CONTINUE feature in transient analysis as implemented in the standard release of COSMIC/NASTRAN has inherent errors associated with it. As a consequence, the results obtained by a CONTINUEd restart run do not, in general, match the results that would be obtained in a single run without the CONTINUE feature. These inherent errors were eliminated by improvements to the restart logic that were developed by RPK Corporation and that are available on all RPK-supported versions of COSMIC/NASTRAN. These improvements ensure that the results of a CONTINUEd transient analysis run are the same as those of a non-CONTINUEd run. In addition, the CONTINUE feature was extended to transient analysis involving uncoupled modal equations. The improvements and enhancement were illustrated by examples.

Description: A modification to the NASTRAN solution sequence for transient analysis with direct time integration (COSMIC NASTRAN rigid format 9) was developed and incorporated into a DMAP alter. This DMAP alter calculates the buckling stability of a dynamically loaded structure, and is used to predict the onset of structural buckling under stress-wave loading conditions. The modified solution sequence incorporates the linear buckling analysis capability (rigid format 5) of NASTRAN into the existing Transient solution rigid format in such a way as to provide a time dependent eigensolution which is used to assess the buckling stability of the structure as it responds to the impulsive load. As a demonstration of the validity of this modified solution procedure, the dynamic buckling of a prismatic bar subjected to an impulsive longitudinal compression is analyzed and compared to the known theoretical solution. In addition, a dynamic buckling analysis is performed for the analytically less tractable problem of the localized dynamic buckling of an initially flawed composite laminate under transverse impact loading. The addition of this DMAP alter to the transient solution sequence in NASTRAN facilitates the computational prediction of both the time at which the onset of dynamic buckling occurs in an impulsively loaded structure, and the dynamic buckling mode shapes of that structure.

Description: A powerful enhancement to the DMAP alter capability was developed and is available on all RPK-supported versions of COSMIC/NASTRAN. This enhancement involves the addition of two alter control cards, called INSERT and DELETE, to the Executive Control Deck. These cards allow for DMAP alters to be made by referencing DMAP statements by their module names rather than by their statement numbers in the rigid format DMAP sequence. This allows for increased user convenience and flexibility and makes alters more meaningful to the user. In addition, DMAP alter packages employing the alter control cards will be much less susceptible to future changes in rigid format DMAPs than alter packages employing the standard ALTER control cards. The usage of the cards is illustrated by examples.

Description: Major improvements were made to the IBM version of COSMIC/NASTRAN by RPK Corporation under contract to IBM Corporation. These improvements will become part of COSMIC's IBM version and will be available in the second quarter of 1989. The first improvement is the inclusion of code to take advantage of IBM's new Vector Facility (VF) on its 3090 machines. The remaining improvements are modifications that will benefit all users as a result of the extended addressing capability provided by the MVS/XA operating system. These improvements include the availability of an in-memory data base that potentially eliminates the need for I/O to the PRIxx disk files. Another improvement is the elimination of multiple load modules that have to be loaded for every link switch within NASTRAN. The last improvement allows for NASTRAN to execute above the 16 mega-byte line. This improvement allows for NASTRAN to have access to 2 giga-bytes of memory for open core and the in-memory data base.