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The functions and operating rules of the SPAR system, which is a group of computer programs used primarily to perform stress, buckling, and vibrational analyses of linear finite element systems, were given. The following subject areas were discussed: basic information, structure definition, format system matrix processors, utility programs, static solutions, stresses, sparse matrix eigensolver, dynamic response, graphics, and substructure processors.
A composite wing with spars, bulkheads and built-in sensor/control devices is probabilistically configured with a methodology for the probabilistic assessment of smart composite structures. Structural responses such as changes in angle of attack, vertical displacements and stresses in the non-control and control plies are probabilistically assessed to quantify their respective scatter ranges. Sensitivity factors are evaluated to identify those parameters that have the greatest influence on a specific structural response. Results show that smart composite structures can be configured to control distortions and ply stresses, and to have specified scatter ranges in the frequencies, buckling loads in the presence of defects to satisfy specified design requirements.
Ameron International Protective Coatings Group developed a special coating for NASA that would withstand the high temperatures generated by the Space Shuttle rocket engines. The coating remains intact for at least 10 minutes, and insulates the launch pad so that it does not exceed 150 degrees and buckle. The NASA formulation was from Ameron's Engineered Siloxane (PSX) chemistry, which employs an inorganic silicon-oxygen structure which the company states is stronger and more reliable than organic polymers. Some of Ameron's PSX product line is based on the NASA technology, used for everything from industrial equipment to bridges.
Experimental and numerical work was conducted to better understand composite shell response to transverse loadings which simulate damage-causing impact events. The quasi-static, centered, transverse loading response of laminated graphite/epoxy shells in a [+/-45(sub n)/O(sub n)](sub s) layup having geometric characteristics of a commercial fuselage are studied. The singly-curved composite shell structures are hinged along the straight circumferential edges and are either free or simply supported along the curved axial edges. Key components of the shell response are response instabilities due to limit-point and/or bifurcation buckling. Experimentally, deflection-controlled shell response is characterized via load-deflection data, deformation-shape evolutions, and the resulting damage state. Finite element models are used to study the kinematically nonlinear shell response, including bifurcation, limit-points, and postbuckling. A novel technique is developed for evaluating bifurcation from nonlinear prebuckling states utilizing asymmetric spatial discretization to introduce numerical perturbations. Advantages of the asymmetric meshing technique (AMT) over traditional techniques include efficiency, robustness, ease of application, and solution of the actual (not modified) problems. The AMT is validated by comparison to traditional numerical analysis of a benchmark problem and verified by comparison to experimental data. Applying the technique, bifurcation in a benchmark shell-buckling problem is correctly identified. Excellent agreement between the numerical and experimental results are obtained for a number of composite shells although predictive capability decreases for stiffer (thicker) specimens which is attributed to compliance of the test fixture. Restraining the axial edge (simple support) has the effect of creating a more complex response which involves unstable bifurcation, limit-point buckling, and dynamic collapse. Such shells were noted to bifurcate into asymmetric deformation modes but were undamaged during testing. Shells in this study which were damaged were not observed to bifurcate. Thus, a direct link between bifurcation and atypical damage could not be established although the mechanism (bifurcation) was identified. Recommendations for further work in these related areas are provided and include extensions of the AMT to other shell geometries and structural problems.
An extension of the program STARS (a general-purpose structural analysis program) has been developed; this extension implements a complete aeroservoelastic analysis capability. Previous capabilities included finite-element modeling as well as statics, buckling, vibration, dynamic response, and flutter analyses. This paper presents a description and the formulation of STARS in its current state along with example dynamic, aeroelastic, and aeroservoelastic analyses pertaining to the X-29A aircraft. These examples include vibration analysis results as well as flutter analysis results obtained by the conventional k method and the velocity root-contour solution. Finally, selected open- and closed-loop aeroservoelastic analysis results based on a hybrid formulation are compared to illustrate, using the calculated frequency responses, the interactions of structures, aerodynamics, and flight controls.
The development and description of a test fixture designed to restrict out-of-plane motion in the center region of tension-loaded carbon-epoxy panels are presented herein. The test fixture was used to impose displacement conditions consistent with those in an analytical tool being developed to predict panel behavior in the vicinity of a central notch, which included the assumption that there would be no out-of-plane displacement and no buckling. However, pretest analysis using finite element models for a panel loaded without any out-of-plane restraint in the region of the notch indicated that with an imperfection magnitude equal to 20 percent of the thickness of the thin-skin panel, an unacceptable amount of out-of-plane deformation would occur as Poisson effects induced compression loads in the region of the notch. Therefore, to validate this tool in a test program, a restraint fixture which would suppress out-of-plane motion was required. The panel could not be encased in restraining plates because instrumentation and visibility were required in the vicinity of the notch. Therefore, a fixture that would restrict out-of-plane motion while still allowing access to the surface of the panel at the notch edges for instrumentation and line-of-sight access for cameras was required. To satisfy these requirements, a fixture was designed to restrict only out-of-plane motion near the center of the notch. Two 1.78-m-long test panels were loaded in tension to failure using this fixture. Out-of-plane deformations were not directly measured during testing, so back-to-back strain gages were used to obtain an indication of buckling. Strain results indicated that the restraint fixture performed as designed and buckling did not occur.
A design for a Mars mission aerobrake with rib-stringer construction coupled with a generic shell using composite materials, which is shown to produce a feasible alternative to propulsive braking, is presented. For the case of a spherical shell subjected to a uniform pressure loading the membrane stress state is isotropic and independent of material properties. The stresses due to bending are significant and dominate only near the attachment points. The addition of meridional stiffeners increased the buckling load and absorbed a large portion of the stresses near the attachment points. The final design employed a high modulus graphite/epoxy composite material. The final weight of the structure when subjected to a 2.0 psi stagnation pressure loading was about 42,000 pounds. This constituted 9 percent of the total spacecraft weight, well below the 15 percent upper limit. It is concluded that aerobraking is a feasible alternative to a propulsive braking system. A rib-stringer shell composition coupled with composite materials is a viable configuration for an aerobrake structure.
The rational use of optimality criteria was investigated for a class of structural synthesis problems where materials, configuration and applied load conditions are specified, and the minimum weight design is to be determined. The potential of hybrid methods of structural optimization for dealing with relatively large design problems involving practical complexity was explored. The reduced basis concept in design space was used to decrease the number of generalized design variables dealt with by the mathematical programming algorithm. Optimality criteria methods for obtaining design vectors associated with displacement, system buckling and natural frequency constraints are presented. A stress ratio method was used to generate a basis design vector representing the stress constraints. The finite element displacement method was used as the basic structural analysis tool. Results for several examples of truss systems subject to stress, displacement and minimum size constraints are presented. An assessment of these results indicates the effectiveness of the hybrid method developed.
The state of the art of automated structural design through the use of optimality criteria, with emphasis on aerospace applications is reviewed. Constraints on stresses, displacements, and buckling strengths under static loading, as well as lower bound limits on natural frequencies and flutter speeds are presented. It is presumed that the reader is experienced in finite element methods of analysis, but is not familiar with optimal design techniques.
Physical characteristics of large skeletal frameworks for space applications are investigated by analyzing one concept: the tetrahedral truss, which is idealized as a sandwich plate with isotropic faces. Appropriate analytical relations are presented in terms of the truss column-element properties, which for calculations were taken as slender graphite/epoxy tubes. Column loads, resulting from gravity-gradient control and orbital transfer, are found to be small for the class structure investigated. Fundamental frequencies of large truss structures are shown to be an order of magnitude lower than large earth-based structures. Permissible loads are shown to result in small lateral deflections of the truss due to low strain at Euler buckling of the slender graphite/epoxy truss column elements. Lateral thermal deflections are found to be a fraction of the truss depth using graphite/epoxy columns.
The results of a stability design study are presented for a slender column with curved longitudinal stiffeners for large space structure applications. Linear stability analyses are performed using a link-plate representation of the stiffeners to determine stiffener local buckling stresses. Results from a set of parametric analyses are used to determine an approximate explicit expression for stiffener local buckling in terms of its geometric parameters. This expression along with other equations governing column stability and mass are assembled into a determinate system describing minimum mass stiffened column design. An iterative solution is determined to solve this system and a computer program incorporating this routine is presented. Example design problems are presented which verify the solution accuracy and illustrate the implementation of the solution routine. Also, observations are made which lead to a greatly simplified first iteration design equation relating the percent increase in column mass to the percent increase in column buckling load. From this, generalizations are drawn as to the mass savings offered by the stiffened column concept. Finally, the percent increase in fundamental column vibration frequency due to the addition of deployable stiffeners is studied.
Recent developments in two areas of structural sensitivity analysis are reviewed. These are the sensitivity of static and transient response, and the sensitivity of vibration and buckling eigenproblems. Recent developments from the point of view of computational cost, accuracy, and ease of implementation are considered.
STAGS models complex thin shell structures including separate shell branches or segments connected along their boundaries. Options include static stress and vibration, transient, and bifurcation buckling analysis. Also useful for submarine design.
Our search for large compressional structures similar to the Coprates rise reveals that the rise is part of a group of about three dozen structures (the 'Thaumasia fold belt') that encircles the southern part of the Tharsis region. Similar structures are scattered over Mars. All appear to be Noachian or Early Hesperian in age, suggesting that lithospheric-scale buckling was a common form of early Martian compressional deformation.
Interlaminar fracture mechanics has proven useful for characterizing the onset of delaminations in composites and has been used with limited success primarily to investigate onset in fracture toughness specimens and laboratory size coupon type specimens. Future acceptance of the methodology by industry and certification authorities however, requires the successful demonstration of the methodology on structural level. For this purpose a panel was selected that is reinforced with stringers. Shear loading causes the panel to buckle and the resulting out-of-plane deformations initiate skin/stringer separation at the location of an embedded defect. For finite element analysis, the panel and surrounding load fixture were modeled with shell elements. A small section of the stringer foot and the panel in the vicinity of the embedded defect were modeled with a local 3D solid model. Across the width of the stringer foot the mixed-mode strain energy release rates were calculated using the virtual crack closure technique. A failure index was calculated by correlating the results with the mixed-mode failure criterion of the graphite/epoxy material. For small applied loads the failure index is well below one across the entire width. With increasing load the failure index approaches one first near the edge of the stringer foot from which delamination is expected to grow. With increasing delamination lengths the buckling pattern of the panel changes and the failure index increases which suggests that rapid delamination growth from the initial defect is to be expected.
Interlaminar fracture mechanics has proven useful for characterizing the onset of delaminations in composites and has been used with limited success primarily to investigate onset in fracture toughness specimens and laboratory size coupon type specimens. Future acceptance of the methodology by industry and certification authorities however, requires the successful demonstration of the methodology on structural level. For this purpose a panel was selected that was reinforced with stringers. Shear loading cases the panel to buckle and the resulting out-of-plane deformations initiate skin/stringer separation at the location of an embedded defect. For finite element analysis, the panel and surrounding load fixture were modeled with shell element. A small section of the stringer foot and the panel in the vicinity of the embedded defect were modeled with a local 3D solid model. A failure index was calculated by correlating computed mixed-mode failure criterion of the graphite/epoxy material.
This paper summarizes a methodology developed at NASA Lewis Research Center which computationally simulates the structural, material, and load uncertainties associated with Space Shuttle Main Engine (SSME) components. The methodology was applied to evaluate the scatter in static, buckling, dynamic, fatigue, and damage behavior of the SSME turbo pump blade. Also calculated are the probability densities of typical critical blade responses, such as effective stress, natural frequency, damage initiation, most probable damage path, etc. Risk assessments were performed for different failure modes, and the effect of material degradation on the fatigue and damage behaviors of a blade were calculated using a multi-factor interaction equation. Failure probabilities for different fatigue cycles were computed and the uncertainties associated with damage initiation and damage propagation due to different load cycle were quantified. Evaluations on the effects of mistuned blades on a rotor were made; uncertainties in the excitation frequency were found to significantly amplify the blade responses of a mistuned rotor. The effects of the number of blades on a rotor were studied. The autocorrelation function of displacements and the probability density function of the first passage time for deterministic and random barriers for structures subjected to random processes also were computed. A brief discussion was included on the future direction of probabilistic structural analysis.
A preliminary study of structural concepts for noncircular fuselage configurations is presented. For an unconventional flying-wing type aircraft, in which the fuselage is inside the wing, multiple fuselage bays with non-circular sections need to be considered. In a conventional circular fuselage section, internal pressure is carried efficiently by a thin skin via hoop tension. If the section is non-circular, internal pressure loads also induce large bending stresses. The structure must also withstand additional bending and compression loads from aerodynamic and gravitational forces. Flat and vaulted shell structural configurations for such an unconventional, non-circular pressurized fuselage of a large flying-wing were studied. A deep honeycomb sandwich-shell and a ribbed double-wall shell construction were considered. Combinations of these structural concepts were analyzed using both analytical and simple finite element models of isolated sections for a comparative conceptual study. Weight, stress, and deflection results were compared to identify a suitable configuration for detailed analyses. The flat sandwich-shell concept was found preferable to the vaulted shell concept due to its superior buckling stiffness. Vaulted double-skin ribbed shell configurations were found to be superior due to their weight savings, load diffusion, and fail-safe features. The vaulted double-skin ribbed shell structure concept was also analyzed for an integrated wing-fuselage finite element model. Additional problem areas such as wing-fuselage junction and pressure-bearing spar were identified.