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NASA NTRS1975

A method for the dynamic and thermal stress analysis of space shuttle surface insulation

The thermal protection system of the space shuttle consists of thousands of separate insulation tiles bonded to the orbiter's surface through a soft strain-isolation layer. The individual tiles are relatively thick and possess nonuniform properties. Therefore, each is idealized by finite-element assemblages containing up to 2500 degrees of freedom. Since the tiles affixed to a given structural panel will, in general, interact with one another, application of the standard direct-stiffness method would require equation systems involving excessive numbers of unknowns. This paper presents a method which overcomes this problem through an efficient iterative procedure which requires treatment of only a single tile at any given time. Results of associated static, dynamic, and thermal stress analyses and sufficient conditions for convergence of the iterative solution method are given.

Ojalvo, I. U.↗

NASA NTRS1975

Simultaneous calculation of aircraft design loads and structural member sizes

A design process which accounts for the interaction between aerodynamic loads and changes in member sizes during sizing of aircraft structures is described. A simultaneous iteration procedure is used wherein both design loads and member sizes are updated during each cycle yielding converged, compatible loads and member sizes. A description is also given of a system of programs which incorporates this process using lifting surface theory to calculate aerodynamic pressure distributions, using a finite-element method for structural analysis, and using a fully stressed design technique to size structural members. This system is tailored to perform the entire process with computational efficiency in a single computer run so that it can be used effectively during preliminary design. Selected results, considering maneuver, taxi, and fatigue design conditions, are presented to illustrate convergence characteristics of this iterative procedure.

Giles, G. L.↗

NASA NTRS1975

Application of an advanced computerized structural design system to an arrow-wing supersonic cruise aircraft

A structural design study of an arrow-wing supersonic cruise aircraft has been made using the integrated design system, ATLAS, and a relatively large analytical finite-element model containing 8500 degrees of freedom. This paper focuses on structural design methods developed and used in support of the study with emphasis on aeroelasticity. The use of ATLAS permitted (1) automatic resizing of the wing structure for multiple load conditions, (2) rapid evaluation of aeroelastic effects, and (3) an iterative approach to the correction of flutter deficiencies. The significant results of the study are discussed along with the advantages derived from the use of an advanced structural design system in preliminary design studies.

Robinson, J. C.↗

NASA NTRS1975

Finite element techniques applied to cracks interacting with selected singularities

The finite-element method for computing the extensional stress-intensity factor for cracks approaching selected singularities of varied geometry is described. Stress-intensity factors are generated using both displacement and J-integral techniques, and numerical results are compared to those obtained experimentally in a photoelastic investigation. The selected singularities considered are a colinear crack, a circular penetration, and a notched circular penetration. Results indicate that singularities greatly influence the crack-tip stress-intensity factor as the crack approaches the singularity. In addition, the degree of influence can be regulated by varying the overall geometry of the singularity. Local changes in singularity geometry have little effect on the stress-intensity factor for the cases investigated.

Conway, J. C.↗

NASA NTRS1975

Analytical study of mixing and reacting three-dimensional supersonic combustor flow fields

An analytical investigation is presented of mixing and reacting hydrogen jets injected from multiple orifices transverse and parallel to a supersonic airstream. The COMOC computer program, based upon a finite-element solution algorithm, was developed to solve the governing equations for three-dimensional, turbulent, reacting, boundary-region, and confined flow fields. The computational results provide a three-dimensional description of the velocity, temperature, and species-concentration fields downstream of hydrogen injection. Detailed comparisons between cold-flow data and results of the computational analysis have established validity of the turbulent-mixing model based on the elementary mixing-length hypothesis. A method is established to initiate computations for reacting flow fields based upon cold-flow correlations and the appropriate experimental parameters of Mach number, injector spacing, and pressure ratio. Key analytical observations on mixing and combustion efficiency for reacting flows are presented and discussed.

Baker, A. J.↗

NASA NTRS1975

An investigation of several numerical procedures for time-asymptotic compressible Navier-Stokes solutions

The status of an investigation of four numerical techniques for the time-dependent compressible Navier-Stokes equations is presented. Results for free shear layer calculations in the Reynolds number range from 1000 to 81000 indicate that a sequential alternating-direction implicit (ADI) finite-difference procedure requires longer computing times to reach steady state than a low-storage hopscotch finite-difference procedure. A finite-element method with cubic approximating functions was found to require excessive computer storage and computation times. A fourth method, an alternating-direction cubic spline technique which is still being tested, is also described.

Rudy, D. H.↗

NASA NTRS1974

The 3.3K thrust chamber life prediction

The cause of low-cycle fatigue failure of the 3.3K Thrust Chamber was investigated. This thrust chamber typifies the current trend in rocket nozzle design which calls for high performance coupled with weight and volume limitations as well as the requirement of reusability. The analysis was performed with the BOPACE finite-element computer program which provides capability to determine viscoplastic response of a structure subjected to cyclic thermal and mechanical loading. Results are presented which show the critical region for low-cycle fatigue and the history of strain within that region for each thermo-mechanical loading cycle in the 3.3K thrust chamber. The predicted behavior was used to evaluate the low-cycle fatigue life near the throat plane of the chamber. The results show that BOPACE provides an extremely accurate prediction of structural behavior; the critical region was identified and the life determined from computed strains was within 154 cycles of the observed failure at 1013 cycles.

Armstrong, W. H.↗

NASA NTRS1975

Analytical and experimental vibration studies of a 1/8-scale shuttle orbiter

Natural frequencies and mode shapes for four symmetric vibration modes and four antisymmetric modes are compared with predictions based on NASTRAN finite-element analyses. Initial predictions gave poor agreement with test data; an extensive investigation revealed that the major factors influencing agreement were out-of-plane imperfections in fuselage panels and a soft fin-fuselage connection. Computations with a more refined analysis indicated satisfactory frequency predictions for all modes studied, within 11 percent of experimental values.

Pinson, L. D.↗

NASA NTRS1975

Fully unsteady subsonic and supersonic potential aerodynamics for complex aircraft configurations for flutter applications

A general theory for study, oscillatory or fully unsteady potential compressible aerodynamics around complex configurations is presented. Using the finite-element method to discretize the space problem, one obtains a set of differential-delay equations in time relating the potential to its normal derivative which is expressed in terms of the generalized coordinates of the structure. For oscillatory flow, the motion consists of sinusoidal oscillations around a steady, subsonic or supersonic flow. For fully unsteady flow, the motion is assumed to consist of constant subsonic or supersonic speed for time t or = 0 and of small perturbations around the steady state for time t 0.

Tseng, K.↗

NASA NTRS1976

A computer program for anisotropic shallow-shell finite elements using symbolic integration

A FORTRAN computer program for anisotropic shallow-shell finite elements with variable curvature is described. A listing of the program is presented together with printed output for a sample case. Computation times and central memory requirements are given for several different elements. The program is based on a stiffness (displacement) finite-element model in which the fundamental unknowns consist of both the displacement and the rotation components of the reference surface of the shell. Two triangular and four quadrilateral elements are implemented in the program. The triangular elements have 6 or 10 nodes, and the quadrilateral elements have 4 or 8 nodes. Two of the quadrilateral elements have internal degrees of freedom associated with displacement modes which vanish along the edges of the elements (bubble modes). The triangular elements and the remaining two quadrilateral elements do not have bubble modes. The output from the program consists of arrays corresponding to the stiffness, the geometric stiffness, the consistent mass, and the consistent load matrices for individual elements. The integrals required for the generation of these arrays are evaluated by using symbolic (or analytic) integration in conjunction with certain group-theoretic techniques. The analytic expressions for the integrals are exact and were developed using the symbolic and algebraic manipulation language.

Andersen, C. M.↗

NASA NTRS1975

Remote sensing applied to numerical modelling

Progress and remaining difficulties in the construction of predictive mathematical models of large bodies of water as ecosystems are reviewed. Surface temperature is at present the only variable than can be measured accurately and reliably by remote sensing techniques, but satellite infrared data are of sufficient resolution for macro-scale modeling of oceans and large lakes, and airborne radiometers are useful in meso-scale analysis (of lakes, bays, and thermal plumes). Finite-element and finite-difference techniques applied to the solution of relevant coupled time-dependent nonlinear partial differential equations are compared, and the specific problem of the Biscayne Bay and environs ecosystem is tackled in a finite-differences treatment using the rigid-lid model and a rigid-line grid system.

Sengupta, S.↗

NASA NTRS1975

Program design by a multidisciplinary team

The use of software engineering aids in the design of a structural finite-element analysis computer program for the STAR-100 computer is described. Nested functional diagrams to aid in communication among design team members were used, and a standardized specification format to describe modules designed by various members was adopted. This is a report of current work in which use of the functional diagrams provided continuity and helped resolve some of the problems arising in this long-running part-time project.

Voigt, S.↗

NASA NTRS1976

Modeling of three-dimensional mixing and reacting ducted flows

A computer code based on a finite-element solution algorithm is developed to perform an analytical investigation on the turbulent mixing and reaction of hydrogen jets injected from multiple orifices transverse and parallel to a supersonic airstream. A laser optical cavity flow field was also analyzed to demonstrate the generality of the proposed model. Computational results provide a three-dimensional description of velocity, temperature, and species-concentration fields downstream of injection. Major conclusions are that the analysis has immediate utility in evaluating the mixing effectiveness of transverse H2 injection data since it has been tested in its ability to model this type of data and that turbulent mixing length theory, constant effective Prandtl number, and a Lewis number of unity provide reasonable agreement with transverse H2 injection data downstream of the near-injection region. Efforts are presently being directed toward using the code in modeling laser and scramjet data for a wide range of flow conditions.

Zelazny, S. W.↗

NASA NTRS1976

On a numerical solution of the supersonic panel flutter eigenproblem

An automated digital computer procedure is presented in this paper which enables efficient solution of the eigenvalue problem associated with the supersonic panel flutter phenomena. The step-by-step incremental solution procedure is based on an inverse iteration technique which effectively utilizes solution results from the previous step in determining such results during the current solution step. Also, the computations are limited to the determination of a few specific roots only, which are expected to contain the flutter mode, and this is achieved at each step without having to compute any other root. The structural discretization achieved by the finite-element method yields highly banded stiffness, mass, and aerodynamic matrices; the aerodynamic matrix evaluated by the linearized piston theory is real but unsymmetric in nature. The solution algorithm presented in this paper fully exploits the banded form of the associated matrices, and the resulting computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most efficient and economical when compared to existing procedures of such analysis. Numerical results are presented for a two-dimensional panel flutter problem.

Gupta, K. K.↗

NASA NTRS1976

An advanced structural analysis/synthesis capability - ACCESS 2

An advanced automated design procedure for minimum-weight design of structures (ACCESS 2) is reported. Design variable linking, constraint deletion, and explicit constraint approximation are used to combine effectively finite-element and nonlinear mathematical programming techniques. The approximation-concepts approach to structural synthesis is extended to problems involving fiber composite structure, thermal effects, and natural frequency constraints in addition to the usual static stress and displacement limitations. Sample results illustrating these features are given.

Schmit, L. A.↗

NASA NTRS1976

On thermal edge effects in composite laminates

Results are presented for a finite-element investigation of the combined influence of edge effects due to mechanical and thermal mismatch in composite laminates with free edges. Laminates of unidirectional boron/epoxy symmetrically bonded to sheets of aluminum and titanium were studied. It is shown that interlaminar thermal stresses may be more significant than the interlaminar stresses due to loading only. In addition, the stresses due to thermal mismatch may be of the same sign as those due to Poisson's mismatch or they may be of opposite sign depending upon material properties, stacking sequence, and direction of loading. The paper concludes with a brief discussion of thermal stresses in all-composite laminates.

Herakovich, C. T.↗

NASA NTRS1976

Numerical studies of three-dimensional breakdown in trailing vortex wakes

The development of dangerous vortex wakes trailing between aircraft for appreciable distance downstream, and posing hazards to following aircraft, is calculated using finite-element three-dimensional relaxation methods. Near-wake, middle-wake, and far-wake conditions are delineated. Vortex system finite lifetimes can be calculated with greater facility owing to the inclusion of a self-induction term in the solution dependent upon local curvature and vortex core radius. Looping and convergence phenomena are studied for single vortex pairs, twin pairs, and multiple pairs. Proportions of flap span and wing span are shown to affect the time to convergence of vortex pairs. The self-induction term renders the convergence time of vortices a sensitive function of wavelength. Wakes trailing between wide-body ('Jumbo') aircraft are also examined.

Hackett, J. E.↗

NASA NTRS1976

Optimization of continuous one-dimensional structures under steady harmonic excitation

The paper examines some questions relating to the optimal design of continuous one-dimensional structures driven by harmonically oscillating loads. Optimal-control methods are applied to a cantilever bar driven sinusoidally by an axial force at its tip to illustrate the minimum-weight design of one-dimensional structures under dynamic excitation. Realistic constraints are imposed during the optimizations, including a maximum allowable stress amplitude at any point along the bar and a minimum cross-sectional area. It is shown that in the absence of damping, the design space may contain many disjoint feasible regions, and multiple optima can exist. Detailed solutions are obtained for continuous bars with an excitation frequency less than, and then greater than, the fundamental free-vibration frequency. It is found that above a certain excitation frequency, two or more arcs with different constraints characterize the optimal designs. It is concluded that when more than two different constrained arcs characterize the optimal solution, the continuum approach may be impractical, and finite-element approximations may offer the only alternative.

Johnson, E. H.↗