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NASA NTRS1991

Analysis of shell-type structures subjected to time-dependent mechanical and thermal loading

This report deals with the development of a general mathematical model and solution methodology for analyzing the structural response of thin, metallic shell-like structures under dynamic and/or static thermomechanical loads. In the mathematical model, geometric as well as the material-type of nonlinearities are considered. Traditional as well as novel approaches are reported and detailed applications are presented in the appendices. The emphasis for the mathematical model, the related solution schemes, and the applications, is on thermal viscoelastic and viscoplastic phenomena, which can predict creep and ratchetting.

Simitses, G. J.↗

NASA NTRS1991

Formulation of the nonlinear analysis of shell-like structures, subjected to time-dependent mechanical and thermal loading

The object of the research reported herein was to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. The methodology is demonstrated through different problems of extension, shear, and of planar curved beams. Moreover, importance of the inclusion of large strain is clearly demonstrated, through the chosen applications.

Simitses, George J.↗

NASA NTRS1992

Accuracy of the TRIA3 thick shell element

The accuracy of the new TRIA3 thick shell element is assessed via comparison with a theoretical solution for thick homogeneous and honeycomb flat simply supported plates under the action of a uniform pressure load. The theoretical thick plate solution is based on the theory developed by Reissner and includes the effects of transverse shear flexibility which are not included in the thin plate solutions based on Kirchoff plate theory. In addition, the TRIA3 is assessed using a set of finite element test problems developed by the MacNeal-Schwendler Corp. (MSC). Comparison of the COSMIC TRIA3 element as well as those from MSC and Universal Analytics Inc. (UAI) for these problems is presented. The current COSMIC TRIA3 element is shown to have excellent comparison with both the theoretical solutions and also those from the two commercial versions of NASTRAN with which it is compared.

Case, William R.↗

NASA NTRS1991

A geometric nonlinear degenerated shell element using a mixed formulation with independently assumed strain fields

A mixed formulation is chosen to overcome deficiencies of the standard displacement-based shell model. Element development is traced from the incremental variational principle on through to the final set of equilibrium equations. Particular attention is paid to developing specific guidelines for selecting the optimal set of strain parameters. A discussion of constraint index concepts and their predictive capability related to locking is included. Performance characteristics of the elements are assessed in a wide variety of linear and nonlinear plate/shell problems. Despite limiting the study to geometric nonlinear analysis, a substantial amount of additional insight concerning the finite element modeling of thin plate/shell structures is provided. For example, in nonlinear analysis, given the same mesh and load step size, mixed elements converge in fewer iterations than equivalent displacement-based models. It is also demonstrated that, in mixed formulations, lower order elements are preferred. Additionally, meshes used to obtain accurate linear solutions do not necessarily converge to the correct nonlinear solution. Finally, a new form of locking was identified associated with employing elements designed for biaxial bending in uniaxial bending applications.

Graf, Wiley E.↗

NASA NTRS1990

Fluid dynamics and solidification of levitated drops and shells

The fluid dynamic investigaton of simple free liquid drops is described based on ground-based and low-gravity experimental results. The behavior of compound drops and liquid shells as described in recent theoretical and experimental studies is discussed. Experimental investigations using both levitation devices and drop tubes are considered in the case of 1-g laboratory investigations, highlighting the advantages and drawbacks of both techniques.

Trinh, E. H.↗

NASA NTRS1992

An assumed-stress hybrid 4-node shell element with drilling degrees of freedom

An assumed-stress hybrid/mixed 4-node quadrilateral shell element is introduced that alleviates most of the deficiencies associated with such elements. The formulation of the element is based on the assumed-stress hybrid/mixed method using the Hellinger-Reissner variational principle. The membrane part of the element has 12 degrees of freedom including rotational or 'drilling' degrees of freedom at the nodes. The bending part of the element also has 12 degrees of freedom. The bending part of the element uses the Reissner-Mindlin plate theory which takes into account the transverse shear contributions. The element formulation is derived from an 8-node isoparametric element by expressing the midside displacement degrees of freedom in terms of displacement and rotational degrees of freedom at corner nodes. The element passes the patch test, is nearly insensitive to mesh distortion, does not 'lock', possesses the desirable invariance properties, has no hidden spurious modes, and for the majority of test cases used in this paper produces more accurate results than the other elements employed herein for comparison.

Aminpour, M. A.↗

NASA NTRS1992

The semicircular shell of CTB 109

The radio and X-ray images of the supernova remnant CTB 109 have the morphology of a semicircular shell. It is shown that such a structure is a natural result of a supernova explosion that occurred 3,000 yr ago near an interface between the diffuse interstellar medium and a dense molecular cloud. The calculated X-ray, infrared, and radio fluxes agree fairly well with the observed values.

Wang, Zhenru↗

NASA NTRS1992

Mass loss from OH/IR stars - Models for the infrared emission of circumstellar dust shells

The IR emission of a sample of 24 OH/IR stars is modeled, and the properties of circumstellar dust and mass-loss rate of the central star are derived. It is shown that for some sources the observations of the far-IR emission is well fitted with a lambda exp -1 law, while some have a steeper index of 1.5. For a few sources, the presence of circumstellar ice grains is inferred from detailed studies of the observed 10-micron feature. Dust mass-loss rates are determined from detailed studies for all the stars in this sample. They range from 6.0 x 10 exp -10 solar mass/yr for an optically visible Mira to 2.2 x 10 exp -6 solar mass/yr for a heavily obscured OH/IR star. These dust mass-loss rates are compared to those calculated from IRAS photometry using 12-, 25-, and 60-micron fluxes. The dust mass-loss rates are also compared to gas mass-loss rates determined from OH and CO observations. For stars with tenuous shells, a dust-to-gas ratio of 0.001 is obtained.

Justtanont, K.↗

NASA NTRS1992

r-adaptive methods based on element-level error indicators for parallel analysis of plates and shells

The formulation and application of element-level error indicators based on parametrized variational principles are investigated. These indicators are ideally suited to drive adaptive mesh refinment on parallel computers where access to neighboring elements resident on different processors may incur significant computational overhead. Furthermore, such estimators are not affected by physical jumps at wavefronts or interfaces. An estimator derived from the higher-order element energy is applied to r adaptation of meshes in plates and shell structures where the exact solution is known.

Militello, Carmelo↗

NASA NTRS1992

Reliability analysis of laminated CMC components through shell subelement techniques

An updated version of the integrated design program C/CARES (composite ceramic analysis and reliability evaluation of structures) was developed for the reliability evaluation of CMC laminated shell components. The algorithm is now split in two modules: a finite-element data interface program and a reliability evaluation algorithm. More flexibility is achieved, allowing for easy implementation with various finite-element programs. The new interface program from the finite-element code MARC also includes the option of using hybrid laminates and allows for variations in temperature fields throughout the component.

Starlinger, A.↗

NASA NTRS1992

ANS shell elements with improved transverse shear accuracy

A method of forming assumed natural coordinate strain (ANS) plate and shell elements is presented. The ANS method uses equilibrium based constraints and kinematic constraints to eliminate hierarchical degrees of freedom which results in lower order elements with improved stress recovery and displacement convergence. These techniques make it possible to easily implement the element into the standard finite element software structure, and a modified shape function matrix can be used to create consistent nodal loads.

Jensen, Daniel D.↗

NASA NTRS1991

Gamma-rays from cosmic ray interactions in supernova shells

A model is presented for the transport and interaction of cosmic rays accelerated by a pulsar and confined inside an expanding supernova remnant. Assuming that protons are accelerated at the reverse shock in the confined pulsar wind and convected into the shell via the Rayleigh-Taylor instability, the diffusion and interaction of these protons in the expanding envelope is modeled. The resulting gamma-ray flux is lower than previous estimates due primarily to the inclusion of proton adiabatic losses in the expanding pulsar wind. Energy-dependent diffusion causes the higher energy gamma-ray light curves to decay faster than those at lower energy. The predicted flux from SN1987A, for proton luminosity less than 10 exp 40 erg/s, is below the present detector sensitivities at both GeV and TeV energies, although supernovae occurring within the Galaxy may be detectable.

Harding, A. K.↗

NASA NTRS1992

L-shell X-ray opacity of many-electron atoms

The study presents a formulation for obtaining the L-shell photoelectric cross section (sigma sub L) for many-electron atomic systems. A scaling law is suggested for the evaluation of the contribution to sigma sub L from 2s and 2p ejection from a general system in any ionization state. The formula is expressed in terms of the effective nuclear charge (Z sub 2s and Z sub 2p) seen by the corresponding bound electrons, with Z sub 2s and Z sub 2p, obtained from improved screening constants derived in a recent investigation. A comparison is made of Hartree-Fock and hydrogenic expressions for sigma sub L with experimental results for atomic neon at X-ray photon energies, providing the basis for the scaling law and an approximate energy dependence for the cross sections. The special case of sigma sub L for atomic Fe is considered in detail. This L edge has structure because of the different threshold for 2s and 2p photoejection; the latter has fine structure.

Jung, Young-Dae↗

NASA NTRS1992

SAPNEW: Parallel finite element code for thin shell structures on the Alliant FX/80

The results of a research activity aimed at providing a finite element capability for analyzing turbo-machinery bladed-disk assemblies in a vector/parallel processing environment are summarized. Analysis of aircraft turbofan engines is very computationally intensive. The performance limit of modern day computers with a single processing unit was estimated at 3 billions of floating point operations per second (3 gigaflops). In view of this limit of a sequential unit, performance rates higher than 3 gigaflops can be achieved only through vectorization and/or parallelization as on Alliant FX/80. Accordingly, the efforts of this critically needed research were geared towards developing and evaluating parallel finite element methods for static and vibration analysis. A special purpose code, named with the acronym SAPNEW, performs static and eigen analysis of multi-degree-of-freedom blade models built-up from flat thin shell elements.

Kamat, Manohar P.↗

NASA NTRS1992

Flexural models of trench/outer rise topography of coronae on Venus with axisymmetric spherical shell elastic plates

Magellan altimetry has revealed that many coronae on Venus have trenches or moats around their peripheries and rises outboard of the trenches. This trench/outer rise topographic signature is generally associated with the tectonic annulus of the corona. Sandwell and Schubert have interpreted the trench/outer rise topography and the associated tectonic annulus around coronae to be the result of elastic bending of the Venus lithosphere (though the tectonic structures are consequences of inelastic deformation of the lithosphere). They used two-dimensional elastic plate flexure theory to fit topographic profiles across a number of large coronae and inferred elastic lithosphere thicknesses between about 15 and 40 km, similar to inferred values of elastic thickness for the Earth's lithosphere at subduction zones around the Pacific Ocean. Here, we report the results of using axisymmetric elastic flexure theory for the deformation of thin spherical shell plates to interpret the trench/outer rise topography of the large coronae modeled by Sandwell and Schubert and of coronae as small as 250 km in diameter. In the case of a corona only a few hundred kilometers in diameter, the model accounts for the small planform radius of the moat and the nonradial orientation of altimetric traces across the corona. By fitting the flexural topography of coronae we determine the elastic thickness and loading necessary to account for the observed flexure. We calculate the associated bending moment and determine whether the corona interior topographic load can provide the required moment. We also calculate surface stresses and compare the stress distribution with the location of annular tectonic features.

Moore, W.↗

NASA NTRS1992

SAPNEW: Parallel finite element code for thin shell structures on the Alliant FX-80

The finite element method has proven to be an invaluable tool for analysis and design of complex, high performance systems, such as bladed-disk assemblies in aircraft turbofan engines. However, as the problem size increase, the computation time required by conventional computers can be prohibitively high. Parallel processing computers provide the means to overcome these computation time limits. This report summarizes the results of a research activity aimed at providing a finite element capability for analyzing turbomachinery bladed-disk assemblies in a vector/parallel processing environment. A special purpose code, named with the acronym SAPNEW, has been developed to perform static and eigen analysis of multi-degree-of-freedom blade models built-up from flat thin shell elements. SAPNEW provides a stand alone capability for static and eigen analysis on the Alliant FX/80, a parallel processing computer. A preprocessor, named with the acronym NTOS, has been developed to accept NASTRAN input decks and convert them to the SAPNEW format to make SAPNEW more readily used by researchers at NASA Lewis Research Center.

Kamat, Manohar P.↗

NASA NTRS1993

Preliminary analysis techniques for ring and stringer stiffened cylindrical shells

This report outlines methods of analysis for the buckling of thin-walled circumferentially and longitudinally stiffened cylindrical shells. Methods of analysis for the various failure modes are presented in one cohesive package. Where applicable, more than one method of analysis for a failure mode is presented along with standard practices. The results of this report are primarily intended for use in launch vehicle design in the elastic range. A Microsoft Excel worksheet with accompanying macros has been developed to automate the analysis procedures.

Graham, J.↗

NASA NTRS1992

Radiative equilibrium in rapidly expanding shells

The equation of radiative equilibrium for rapidly expanding spherical shells including the special relativistic terms is discussed, and a temperature-correction procedure for the solution of this equation is given. The temperature-correction scheme combines a partial linearization approach with the approximate Lambda-operator iteration method. For some test problems, the temperature structures of atmospheres in radiative equilibrium in the Lagrangian frame are calculated. The effects of the velocity field on the temperature stratification and the luminosity are also discussed. We find that the temperature structure of a moving photosphere in radiative equilibrium in the Lagrangian frame differs significantly from that of a static photosphere and that, at least, all first-order terms, in particular the advection and aberration terms, have to be included consistently both in the radiative transfer and the energy equation in studies of supernovae atmospheres and other high-speed radiating flows.

Hauschildt, P. H.↗