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NASA NTRS1991

Design optimization of space structures

The topology-shape-size optimization of space structures is investigated through Kikuchi's homogenization method. The method starts from a 'design domain block,' which is a region of space into which the structure is to materialize. This domain is initially filled with a finite element mesh, typically regular. Force and displacement boundary conditions corresponding to applied loads and supports are applied at specific points in the domain. An optimal structure is to be 'carved out' of the design under two conditions: (1) a cost function is to be minimized, and (2) equality or inequality constraints are to be satisfied. The 'carving' process is accomplished by letting microstructure holes develop and grow in elements during the optimization process. These holes have a rectangular shape in two dimensions and a cubical shape in three dimensions, and may also rotate with respect to the reference axes. The properties of the perforated element are obtained through an homogenization procedure. Once a hole reaches the volume of the element, that element effectively disappears. The project has two phases. In the first phase the method was implemented as the combination of two computer programs: a finite element module, and an optimization driver. In the second part, focus is on the application of this technique to planetary structures. The finite element part of the method was programmed for the two-dimensional case using four-node quadrilateral elements to cover the design domain. An element homogenization technique different from that of Kikuchi and coworkers was implemented. The optimization driver is based on an augmented Lagrangian optimizer, with the volume constraint treated as a Courant penalty function. The optimizer has to be especially tuned to this type of optimization because the number of design variables can reach into the thousands. The driver is presently under development.

Felippa, Carlos↗

NASA NTRS1991

Interlaminar stress analysis at the skin-stiffener interface of a grid-stiffened composite panel

Results are presented of an analysis of the interlaminar stress components at the skin-wrap, skin-core, and wrap-core interfaces for an advanced-concept stiffened panel using a global/local finite element procedure. The procedure consists of a global model of two-dimensional shell elements that is used to design a grid-stiffened panel with blade-type stiffeners, a local model of three-dimensional solid elements that is used to compute interlaminar stress components, and a scheme devised to assign displacement boundary conditions for the local model that are derived from displacement and rotation data of a few nodes of the global model. The interlaminar stresses for this panel design were found to be well below typical tensile normal and shearing strengths of a graphite-epoxy material.

Wiggenraad, J. F. M.↗

NASA NTRS1993

Laplace's equation and the Dirichlet-Neumann map in multiply connected domains

A variety of problems in material science and fluid dynamics require the solution of Laplace's equation in multiply connected domains. Integral equation methods are natural candidates for such problems, since they discretize the boundary alone, require no special effort for free boundaries, and achieve superalgebraic convergence rates on sufficiently smooth domains in two space dimensions, regardless of shape. Current integral equation methods for the Dirichlet problem, however, require the solution of M independent problems of dimension N, where M is the number of boundary components and N is the total number of points in the discretization. In this paper, we present a new boundary integral equation approach, valid for both interior and exterior problems, which requires the solution of a single linear system of dimension N + M. We solve this system by making use of an iterative method (GMRES) combined with the last multipole method for the rapid calculation of the necessary matrix vector products. For a two-dimensional system with 200 components and 100 points on each boundary, we gain a speedup of a factor of 100 from the new analytic formulation and a factor of 50 from the fast multipole method. The resulting scheme brings large scale calculations in extremely complex domains within practical reach.

Greenbaum, A.↗

NASA NTRS1993

Strain energy of thermally stressed multilayer panels and its sensitivity coefficients

A study is made of the effect of lamination and material parameters of thermally stressed multilayer composite panels on the strain energy and its sensitivity coefficients obtained by the three-dimensional thermoelasticity model. The sensitivity coefficients measure the sensitivity of the strain energy to variations in the different lamination and material parameters of the panel. The strain energy and sensitivity coefficients obtained by the three-dimensional model are used as the basis for assessing the accuracy of the corresponding quantities obtained by two-dimensional first-order shear deformation theory. Numerical results are presented for antisymmetrically laminated angle-ply panels subjected to linear temperature variation through the thickness. The numerical results demonstrate the accuracy of the strain energy and its sensitivity coefficients obtained by the first-order shear deformation theory, for the range of parameters considered, and the importance of the particular terms in the strain energy, which vanish for single-layer panels.

Noor, Ahmed K.↗

NASA NTRS1993

Modal element method for scattering and absorbing of sound by two-dimensional bodies

The modal element method for acoustic scattering from a 2-D body is presented. The body may be acoustically soft (absorbing) or hard (reflecting). The infinite computational region is divided into two subdomains - the bounded finite element domain, which is characterized by complicated geometry and/or variable material properties, and the surrounding unbounded homogeneous domain. The acoustic pressure field is represented approximately in the finite element domain by a finite element solution, and is represented analytically by an eigenfunction expansion in the homogeneous domain. The two solutions are coupled by the continuity of pressure and velocity across the interface between the two subdomains. Also, for hard bodies, a compact modal ring grid system is introduced for which computing requirements are drastically reduced. Analysis for 2-D scattering from solid and coated (acoustically treated) bodies is presented, and several simple numerical examples are discussed. In addition, criteria are presented for determining the number of modes to accurately resolve the scattered pressure field from a solid cylinder as a function of the frequency of the incoming wave and the radius of the cylinder.

Baumeister, K. J.↗

NASA NTRS1956

Theoretical investigation of flutter of two-dimensional flat panels with one surface exposed to supersonic potential flow

A Rayleigh type analysis involving chosen modes of the panel as degrees of freedom is used to treat the flutter of a two-dimensional flat panel supported at its leading and trailing edges and subjected to a middle-plane tensile force. The panel has a supersonic stream passing over its upper surface and still air below. The aerodynamic forces due to the supersonic stream are obtained from the theory for linearized two-dimensional unsteady flow and the forces due to the still air are obtained from acoustical theory. In order to study the effect of increasing the number of modes in the analysis, two and then four modes are employed. The modes used are the first four natural modes of the panel in a vacuum with no tensile force acting. The analysis includes these variables: Mach number, structural damping, tensile force, density of the still air, and edge fixity (clamped and pinned). For certain combinations of these variables, stability boundaries are obtained which can be used to determine the panel thickness required to prevent flutter for any panel material and altitude.

Nelson, Herbert C↗

NASA NTRS1991

Failure prediction of thin beryllium sheets used in spacecraft structures

The primary objective of this study is to develop a method for prediction of failure of thin beryllium sheets that undergo complex states of stress. Major components of the research include experimental evaluation of strength parameters for cross-rolled beryllium sheet, application of the Tsai-Wu failure criterion to plate bending problems, development of a high order failure criterion, application of the new criterion to a variety of structures, and incorporation of both failure criteria into a finite element code. A Tsai-Wu failure model for SR-200 sheet material is developed from available tensile data, experiments carried out by NASA on two circular plates, and compression and off-axis experiments performed in this study. The failure surface obtained from the resulting criterion forms an ellipsoid. By supplementing experimental data used in the the two-dimensional criterion and modifying previously suggested failure criteria, a multi-dimensional failure surface is proposed for thin beryllium structures. The new criterion for orthotropic material is represented by a failure surface in six-dimensional stress space. In order to determine coefficients of the governing equation, a number of uniaxial, biaxial, and triaxial experiments are required. Details of these experiments and a complementary ultrasonic investigation are described in detail. Finally, validity of the criterion and newly determined mechanical properties is established through experiments on structures composed of SR200 sheet material. These experiments include a plate-plug arrangement under a complex state of stress and a series of plates with an out-of-plane central point load. Both criteria have been incorporated into a general purpose finite element analysis code. Numerical simulation incrementally applied loads to a structural component that is being designed and checks each nodal point in the model for exceedance of a failure criterion. If stresses at all locations do not exceed the failure criterion, the load is increased and the process is repeated. Failure results for the plate-plug and clamped plate tests are accurate to within 2 percent.

Roschke, Paul N.↗

NASA NTRS1991

Development of a portable multispectral thermal infrared camera

The purpose of this research and development effort was to design and build a prototype instrument designated the 'Thermal Infrared Multispectral Camera' (TIRC). The Phase 2 effort was a continuation of the Phase 1 feasibility study and preliminary design for such an instrument. The completed instrument designated AA465 has application in the field of geologic remote sensing and exploration. The AA465 Thermal Infrared Camera (TIRC) System is a field-portable multispectral thermal infrared camera operating over the 8.0 - 13.0 micron wavelength range. Its primary function is to acquire two-dimensional thermal infrared images of user-selected scenes. Thermal infrared energy emitted by the scene is collected, dispersed into ten 0.5 micron wide channels, and then measured and recorded by the AA465 System. This multispectral information is presented in real time on a color display to be used by the operator to identify spectral and spatial variations in the scenes emissivity and/or irradiance. This fundamental instrument capability has a wide variety of commercial and research applications. While ideally suited for two-man operation in the field, the AA465 System can be transported and operated effectively by a single user. Functionally, the instrument operates as if it were a single exposure camera. System measurement sensitivity requirements dictate relatively long (several minutes) instrument exposure times. As such, the instrument is not suited for recording time-variant information. The AA465 was fabricated, assembled, tested, and documented during this Phase 2 work period. The detailed design and fabrication of the instrument was performed during the period of June 1989 to July 1990. The software development effort and instrument integration/test extended from July 1990 to February 1991. Software development included an operator interface/menu structure, instrument internal control functions, DSP image processing code, and a display algorithm coding program. The instrument was delivered to NASA in March 1991. Potential commercial and research uses for this instrument are in its primary application as a field geologists exploration tool. Other applications have been suggested but not investigated in depth. These are measurements of process control in commercial materials processing and quality control functions which require information on surface heterogeneity.

Osterwisch, Frederick G.↗

NASA NTRS1994

Variations of a global constraint factor in cracked bodies under tension and bending loads

Elastic-plastic finite-element analyses were used to calculate stresses and displacements around a crack in finite-thickness plates for an elastic-perfectly plastic material. Middle- and edge-crack specimens were analyzed under tension and bending loads. Specimens were 1.25 to 20 mm thick with various widths and crack lengths. A global constraint factor alpha(sub g), an averaged normal-stress to flow-stress ratio over the plastic region, was defined to simulate three-dimensional (3D) effects in two-dimensional (2D) models. For crack lengths and uncracked ligament lengths greater than four times the thickness, the global constraint factor was found to be nearly a unique function of a normalized stress-intensity factor (related to plastic-zone size to thickness ratio) from small- to large-scale yielding conditions for various specimen types and thickness. For crack length-to-thickness ratios less than four, the global constraint factor was specimen type, crack length and thickness dependent. Using a 2D strip-yield model and the global constraint factors, plastic-zone sizes and crack-tip displacements agreed reasonably well with the 3D analyses. For a thin sheet aluminum alloy, the critical crack-tip-opening angle during stable tearing was found to be independent of specimen type and crack length for crack length-to-thickness ratios greater than 4.

Newman, J. C., Jr.↗

NASA NTRS1994

Optimal experimental designs for the estimation of thermal properties of composite materials

Reliable estimation of thermal properties is extremely important in the utilization of new advanced materials, such as composite materials. The accuracy of these estimates can be increased if the experiments are designed carefully. The objectives of this study are to design optimal experiments to be used in the prediction of these thermal properties and to then utilize these designs in the development of an estimation procedure to determine the effective thermal properties (thermal conductivity and volumetric heat capacity). The experiments were optimized by choosing experimental parameters that maximize the temperature derivatives with respect to all of the unknown thermal properties. This procedure has the effect of minimizing the confidence intervals of the resulting thermal property estimates. Both one-dimensional and two-dimensional experimental designs were optimized. A heat flux boundary condition is required in both analyses for the simultaneous estimation of the thermal properties. For the one-dimensional experiment, the parameters optimized were the heating time of the applied heat flux, the temperature sensor location, and the experimental time. In addition to these parameters, the optimal location of the heat flux was also determined for the two-dimensional experiments. Utilizing the optimal one-dimensional experiment, the effective thermal conductivity perpendicular to the fibers and the effective volumetric heat capacity were then estimated for an IM7-Bismaleimide composite material. The estimation procedure used is based on the minimization of a least squares function which incorporates both calculated and measured temperatures and allows for the parameters to be estimated simultaneously.

Scott, Elaine P.↗

NASA NTRS1994

Test methods for textile composites

Various test methods commonly used for measuring properties of tape laminate composites were evaluated to determine their suitability for the testing of textile composites. Three different types of textile composites were utilized in this investigation: two-dimensional (2-D) triaxial braids, stitched uniweave fabric, and three-dimensional (3-D) interlock woven fabric. Four 2-D braid architectures, five stitched laminates, and six 3-D woven architectures were tested. All preforms used AS4 fibers and were resin-transfer-molded with Shell RSL-1895 epoxy resin. Ten categories of material properties were investigated: tension, open-hole tension, compression, open-hole compression, in-plane shear, filled-hole tension, bolt bearing, interlaminar tension, interlaminar shear, and interlaminar fracture toughness. Different test methods and specimen sizes were considered for each category of test. Strength and stiffness properties obtained with each of these methods are documented in this report for all the material systems mentioned above.

Minguet, Pierre J.↗

NASA NTRS1994

On the dynamics of a shock-bubble interaction

We present a detailed numerical study of the interaction of a weak shock wave with an isolated cylindrical gas inhomogenity. Such interactions have been studied experimentally in an attempt to elucidate the mechanisms whereby shock waves propagating through random media enhance mixing. Our study concentrates on the early phases of the interaction process which are dominated by repeated refractions of acoustic fronts at the bubble interface. Specifically, we have reproduced two of the experiments performed by Haas and Sturtevant : M(sub s) = 1.22 planar shock wave, moving through air, impinges on a cylindrical bubble which contains either helium or Refrigerant 22. These flows are modelled using the two-dimensional, compressible Euler equations for a two component fluid (air-helium or air-Refrigerant 22). Although simulations of shock wave phenomena are now fairly commonplace, they are mostly restricted to single component flows. Unfortunately, multi-component extensions of successful single component schemes often suffer from spurious oscillations which are generated at material interfaces. Here we avoid such problems by employing a novel, nonconservative shock-capturing scheme. In addition, we have utilized a sophisticated adaptive mesh refinement algorithm which enables extremely high resolution simulations to be performed relatively cheaply. Thus we have been able to reproduce numerically all the intricate mechanisms that were observed experimentally (e.g., transitions from regular to irregular refraction, cusp formation and shock wave focusing, multi-shock and Mach shock structures, jet formation, etc.), and we can now present an updated description for the dynamics of a shock-bubble interaction.

Quirk, James J.↗

NASA NTRS1995

Three-dimensional CTOA and constraint effects during stable tearing in a thin-sheet material

A small strain theory, three-dimensional elastic-plastic finite element analysis was used to simulate fracture in thin sheet 2024-T3 aluminum alloy in the T-L orientation. Both straight and tunneled cracks were modeled. The tunneled crack front shapes as a function of applied stress were obtained from the fracture surface of tested specimens. The stable crack growth behavior was measured at the specimen surface as a function of applied stress. The fracture simulation modeled the crack tunneling and extension as a function of applied stress. The results indicated that the global constraint factor, alpha(sub g), initially dropped during stable crack growth. After peak applied stress was achieved, alpha(sub g) began to increase slightly. The effect of crack front shape on alpha(sub g) was small, but the crack front shape did greatly influence the local constraint and through-thickness crack-tip opening angle (CTOA) behavior. The surface values of CTOA for the tunneled crack front model agreed well with experimental measurements, showing the same initial decrease from high values during the initial 3mm of crack growth at the specimen's surface. At the same time, the interior CTOA values increased from low angles. After the initial stable tearing region, the CTOA was constant through the thickness. The three-dimensional analysis appears to confirm the potential of CTOA as a two-dimensional fracture criterion.

Dawicke, D. S.↗

NASA NTRS1995

Assessment of computational models for thermoelectroelastic multilayered plates

A study is made of the accuracy of the steady-state (static) thermoelectroelastic response of multilayered hybrid composite plates predicted by five modeling approaches, based on two-dimensional plate theories. The plates consist of a combination of fiber-reinforced and piezothermoelastic layers. The standard of comparison is taken to be the exact three-dimensional thermoelectroelastic solutions, and the quantities compared include gross response characteristics (e.g., strain energy components, and average through-the-thickness displacements); detailed, through-the-thickness distributions of displacements and stresses; and sensitivity coefficients of the response quantities (derivatives of the response quantities with respect to material parameters of the plate). The modeling approaches considered include first-order theory; third-order theory; discrete-layer theory (with piecewise linear variation of the in-plane displacements, temperature and electric potential, in the thickness direction); and two predictor-corrector procedures.

Tang, Yvette T.↗

NASA NTRS1992

Effect of the fiber-matrix interphase on the transverse tensile strength of the unidirectional composite material

A simple one-dimensional fiber-matrix interphase model has been developed and analytical results obtained correlated well with available experimental data. It was found that by including the interphase between the fiber and matrix in the model, much better local stress results were obtained than with the model without the interphase. A more sophisticated two-dimensional micromechanical model, which included the interphase properties was also developed. Both one-dimensional and two-dimensional models were used to study the effect of the interphase properties on the local stresses at the fiber, interphase and matrix. From this study, it was found that interphase modulus and thickness have significant influence on the transverse tensile strength and mode of failure in fiber reinforced composites.

Tsai, H. C.↗

NASA NTRS1994

A new method for failure prediction of SR-200 beryllium sheet structures

Contemporary applications of failure criteria frequently incorporate two-dimensional or simplified three-dimensional methodologies for prediction of stresses. Motivation behind the development of a new multi-dimensional failure criterion is due mainly to the lack of a sufficiently accurate mathematical tool that accounts for the behavior of brittle material with anisotropic properties. Such a criterion should be able to provide a reliable maximum load estimate so that design of the structure is not penalized in terms of excessive weight requirements. The failure criterion developed is represented by a fracture surface in a six-dimensional stress space. The criterion is applied for failure prediction of SR-200 beryllium sheet structures, a non-homogeneous orthotropic material used widely in space applications. Two experiments are used to verify the criterion.

Papados, P. P.↗

NASA NTRS1995

Ignition and subsequent transition to flame spread in a microgravity environment

The fire safety strategy in a spacecraft is (1) to detect any fire as early as possible, (2) to keep any fire as small as possible, and (3) to extinguish any fire as quickly as possible. This suggests that a material which undergoes a momentary, localized ignition might be tolerable but a material which permits a transition to flame spread would significantly increase the fire hazard. Therefore, it is important to understand how the transition from localized ignition to flame spread occurs and what parameters significantly affect the transition. The fundamental processes involved in ignition and flame spread have been extensively studied, but they have been studied separately. Some of the steady state flame models start from ignition to reach a steady state, but since the objective of such a calculation is to obtain the steady state flame spread rate, the calculation through the transition process is made without high accuracy to save computational time. We have studied the transition from a small localized ignition at the center of a thermally thin paper in a microgravity environment. The configuration for that study was axisymmetric, but more general versions of the numerical scheme have been developed by including the effects of a slow, external flow in both two and three dimensions. By exploiting the non-buoyant nature of the flow, it is possible to achieve resolution of fractions of millimeters for 3D flow domains on the order of 10 centimeters. Because the calculations are time dependent, we can study the evolution of multiple flame fronts originating from a localized ignition source. The interaction of these fronts determines whether or not they will eventually achieve steady state spread. Most flame spread studies in microgravity consider two-dimensional flame spread initiated by ignition at one end of a sample strip with or against a slow external flow. In this configuration there is only one flame front. A more realistic scenario involves separate, oppositely directed fronts in two dimensions, or a continuous, radially directed front in three dimensions. We present here some results of both the two and three dimensional codes.

Kashiwagi, Takashi↗

NASA NTRS1994

Simulations of Titan's Brightness by a Two-Dimensional Haze Model

We have used a 2-D microphysics model to study the effects of atmospheric motions on the albedo of Titan's thick haze layer. We compare our results to the observed variations of Titan's brightness with season and latitude. We use two wind fields. The first is an analytic solution to the simplified equations of motion. The second is based on the preliminary results of a Titan GCM. Seasonally varying wind fields, of typical horizontal velocity 1 cm/ s at optical depth unity, are capable of producing the observed change in geometric albedo of about 10% over the Titan year. Neither of the two wind fields can adequately reproduce the latitudinal distribution of the contrast seen by Voyager. At visible wavelengths, where only haze opacity is radiatively important, upwelling produces darkening by increasing the particle size at optical depth unity. This is due to the suspension of larger particles as well as the removal of smaller particles from the top of the atmosphere. From our results it can be inferred that the circulation on Titan just prior to the time of Voyager was upwelling in the northern hemisphere and downwelling in the southern hemisphere with broad regions of uniform wind separated by a sharp transition at 10 deg. S. At UV wavelengths and at 0.89 microns the albedo is determined by the competing effects of the gas and the haze material. Gas is bright in the UV and dark at 0.89 microns. Haze transport at high altitudes controls the UV albedo and transport at low altitude controls the 0.89 microns albedo. Comparisons between the hemispheric contrast at UV and IR wavelengths can be diagnostic of the vertical structure of the wind field on Titan. Infrared albedo features, which are in the lower atmosphere and persist for many rotations could reflect the haze distribution set up by a seasonally varying circulation rather than surface features as assumed in some observational studies.

Hutzell, W.↗