Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “stiff problem”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14

Current research in oxidation-resistant carbon-carbon composites at NASA. Langley Research Center

The significant potential of carbon-carbon composites for high-temperature structural applications is well established. For hypersonic vehicle applications, desirable properties include low density, high specific strength and stiffness, low coefficients of thermal expansion, and retention of mechanical properties above 3000 F. A significant problem associated with carbon materials, however, is that they oxidize rapidly in air at temperatures above about 800 F, and therefore must be protected from oxidation. Successful development of effective methods of oxidation protection is key to the eventual utilization of carbon-carbon composites on hypersonic vehicles such as NASP. In this presentation, the basic elements of an oxidation-protection system are described. Results from oxidation-performance evaluations of state-of-the-art ACC-4 type material in simulated airframe vehicle environments (temperature, pressure, and time) conducted at NASA Langley are also presented. NASA Langley has an active research effort to improve the oxidation resistance of carbon-carbon materials for airframe structural and vehicle thermal protection applications. Conversion coating and sealant development research is highlighted.

Ohlhorst, Craig W.↗

Genetic Optimization of a Tensegrity Structure

Marshall Space Flight Center (MSFC) is charged with developing advanced technologies for space telescopes. The next generation of space optics will be very large and lightweight. Tensegrity structures are built of compressive members (bars), and tensile members (strings). For most materials, the tensile strength of a longitudinal member is larger than its buckling strength; therefore a large stiffness to mass ratio can be achieved by increasing the use of tensile members. Tensegrities are the epitome of lightweight structures, since they take advantage of the larger tensile strength of materials. The compressive members of tensegrity structures are disjoint allowing compact storage of the structure. The structure has the potential to eliminate the requirement for assembly by man in space; it can be deployed by adjustments in its cable tension. A tensegrity structure can be more reliably modeled since none of the individual members experience bending moments. (Members that experience deformation in more than one dimension are much harder to model.) Structures that can be more precisely modeled can be more precisely controlled. Furthermore, an astoundingly wide variety of natural systems, including carbon atoms, water molecules, proteins, viruses, cells, tissues and even human and other living creatures are tensegrity structures. Through the process of evolution, nature continually improves the design of living creatures for the environment they live in. Since tensegrities are nature's structure of choice, it is conceivable that they have other benefits we are unaware of. A. Keane and S. Brown designed a satellite boom truss system with an enhanced vibration performance. They started with a standard truss system, then used a genetic algorithm to alter the design, while optimizing the vibration performance. An improvement of over 20,000% in frequency-averaged energy levels was obtained using this approach. In this report an introduction to tensegrity structures is given, along with a description of how to generate the nodal coordinates and connectivity of a multiple stage cylindrical tensegrity structure. A description of how finite elements can be used to develop a stiffness and mass matrix so that the modes of vibration can be determined from the eigenvalue problem is shown. A brief description of a micro genetic algorithm is then presented.

Jaime R. Taylor↗

Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure

A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.

Tsiveriotis, K.↗

Efficient discontinuous Galerkin implementations and preconditioners for implicit unsteady compressible flow simulations

This work presents and compares efficient implementations of high-order discontinuous Galerkin methods: a modal matrix-free discontinuous Galerkin (DG) method, a hybridizable discontinuous Galerkin (HDG) method, and a primal formulation of HDG, applied to the implicit solution of unsteady compressible flows. The matrix-free implementation allows for a reduction of the memory footprint of the solver when dealing with implicit time-accurate discretizations. HDG reduces the number of globally-coupled degrees of freedom relative to DG, at high order, by statically condensing element-interior degrees of freedom from the system in favor of face unknowns. The primal formulation further reduces the element-interior degrees of freedom by eliminating the gradient as a separate unknown. This paper introduces a p-multigrid preconditioner implementation for these discretizations and presents results for various flow problems. Benefits of the p-multigrid strategy relative to simpler, less expensive, preconditioners are observed for stiff systems, such as those arising from low-Mach number flows at high-order approximation. The p-multigrid preconditioner also shows excellent scalability for parallel computations. Finally, additional savings in both speed and memory occur with a matrix-free/reduced version of the preconditioner.

97 MATHEMATICS AND COMPUTING↗

Coupled flap-lag-torsional dynamics of hingeless rotor blades in forward flight

The aeroelastic stability and response problem of the coupled flap-lag-torsional dynamics of an isolated hingeless rotor blade in forward flight is considered. Linear, quasi-steady aerodynamics below stall is included. The spatial dependence of the partial differential nonliner equations of motion is discretized using a multimodal Galerkin method. The nonlinear time dependent equilibrium position (steady state response) about which the equations are linearized is obtained by solving a sequence of linear periodic response problems (quasilinearization). Results illustrating blade behavior in forward flight for both soft-in-plane and stiff-in-plane designs are presented. Quasilinearization provides a clear indication of the cases when nonlinear terms due to moderate deflections are important. The results indicate that nonlinearities affect system stability much more than system response. This implies that for obtaining blade vibrations and loads, approximate analytical models based on linearized formulations could be employed, whereas for determining blade stability a more accurate nonlinear analysis would be required.

Friedmann, P. P.↗

A mixed formulaton of C(0)-linear triangular plate/shell element - The role of edge shear constraints

A simple and effective linear C(0)-tiangular element for plates and shells is developed on the basis of the Hellinger-Reissner mixed variational principle with independently assumed stress and displacement fields. Two main features are emphasized in this development concerning the assumed transverse shear stress field. First, this assumption results in edge-type penalty constraints in the thin plate/shell regimes. Second, the element is used in the form of a four-triangle, cross-diagonal macroelement mesh. As a result, the element is shown to be free from shear locking in thin plate/shell applications, and it satisfies all the appropriate patch tests required for Kirchhoff plate models. In addition, the element exhibits good overall convergence properties in a variety of test problems for plates and shells. Finally, from the computational standpoint, the element is very efficient since all stiffness component matrices are derived in explicit forms.

Saleeb, A. F.↗

Pressure distribution under flexible polishing tools. II - Cylindrical (conical) optics

A previously developed eigenvalue model is extended to determine polishing pressure distribution by rectangular tools with unequal stiffness in two directions on cylindrical optics. Tool misfit is divided into two simplified one-dimensional problems and one simplified two-dimensional problem. Tools with nonuniform cross-sections are treated with a new one-dimensional eigenvalue algorithm, permitting evaluation of tool designs where the edge is more flexible than the interior. This maintains edge pressure variations within acceptable parameters. Finite element modeling is employed to resolve upper bounds, which handle pressure changes in the two-dimensional misfit element. Paraboloids and hyperboloids from the NASA AXAF system are treated with the AXAFPOD software for this method, and are verified with NASTRAN finite element analyses. The maximum deviation from the one-dimensional azimuthal pressure variation is predicted to be 10 percent and 20 percent for paraboloids and hyperboloids, respectively.

Mehta, Pravin K.↗

Effects of fiber and interfacial layer architectures on the thermoplastic response of metal matrix composites

Examined here is the effect of fiber and interfacial layer morphologies on thermal fields in metal matrix composites (MMCs). A micromechanics model based on an arbitrarily layered concentric cylinder configuration is used to calculate thermal stress fields in MMCs subjected to spatially uniform temperature changes. The fiber is modelled as a layered material with isotropic or orthotropic elastic layers, whereas the surrounding matrix, including interfacial layers, is treated as a strain-hardening, elastoplastic, von Mises solid with temperature-dependent parameters. The solution to the boundary-value problem of an arbitrarily layered concentric cylinder under the prescribed thermal loading is obtained using the local/global stiffness matrix formulation originally developed for stress analysis of multilayered elastic media. Examples are provided that illustrate how the morphology of the SCS6 silicon carbide fiber and the use of multiple compliant layers at the fiber/matrix interface affect the evolution of residual stresses in SiC/Ti composites during fabrication cool-down.

Pindera, Marek-Jerzy↗

Adaptive Force Control in Compliant Motion

This paper addresses the problem of controlling a manipulator in compliant motion while in contact with an environment having an unknown stiffness. Two classes of solutions are discussed: adaptive admittance control and adaptive compliance control. In both admittance and compliance control schemes, compensator adaptation is used to ensure a stable and uniform system performance.

manipulators↗

ISOFINEL: Isoparametric finite element code for elastic analysis of two-dimensional bodies

A formulation is presented for the development of a finite element program for the elastic analysis of two-dimensional bodies using the eight-node isoparametric quadrilateral. The program solves for both plane stress and plane strain problems. The finite element formulation based on the isoparametric displacement functions is presented. The program structure is given in the form of flow diagrams with descriptions of the numerical procedure used to obtain the element stiffness matrix, and the solution method employed to solve for nodal displacements. Three numerical examples (a plate under uniaxial tension, a plate under pure shear, and a beam under pure bending) are presented to illustrate the capability and limitations of the element implementation. The first problem is solved exactly by the element, as predicted by the form of its displacement functions. In the other two problems the accuracy of the solution is highly dependent upon the slenderness of the element, the number of elements in the map, and the numerical integration scheme used to build the element stiffness matrix.

Marino, C.↗

Investigation of structural behavior of candidate Space Station structure

Quantitative evaluations of the structural loads, stiffness and deflections of an example Space Station truss due to a variety of influences, including manufacturing tolerances, assembly operations, and operational loading are reported. The example truss is a dual-keel design composed of 5-meter-cube modules. The truss is 21 modules high and 9 modules wide, with a transverse beam 15 modules long. One problem of concern is the amount of mismatch which will be expected when the truss is being erected on orbit. Worst-case thermal loading results in less than 0.5 inch of mismatch. The stiffness of the interface is shown to be less than 100 pounds per inch. Thus, only moderate loads will be required to overcome the mismatch. The problem of manufacturing imperfections is analyzed by the Monte Carlo approach. Deformations and internal loads are obtained for ensembles of 100 example trusses. All analyses are performed on a personal computer. The necessary routines required to supplement commercially available programs are described.

Hedgepeth, John M.↗

A multi-resolution approach to hydraulic fracture simulation

Abstract We present a multi-resolution approach for constructing model-based simulations of hydraulic fracturing, wherein flow through porous media is coupled with fluid-driven fracture. The approach consists of a hybrid scheme that couples a discrete crack representation in a global domain to a phase-field representation in a local subdomain near the crack tip. The multi-resolution approach addresses issues such as the computational expense of accurate hydraulic fracture simulations and the difficulties associated with reconstructing crack apertures from diffuse fracture representations. In the global domain, a coupled system of equations for displacements and pressures is considered. The crack geometry is assumed to be fixed and the displacement field is enriched with discontinuous functions. Around the crack tips in the local subdomains, phase-field sub-problems are instantiated on the fly to propagate fractures in arbitrary, mesh independent directions. The governing equations and fields in the global and local domains are approximated using a combination of finite-volume and finite element discretizations. The efficacy of the method is illustrated through various benchmark problems in hydraulic fracturing, as well as a new study of fluid-driven crack growth around a stiff inclusion.

58 GEOSCIENCES↗

Self-correcting incremental approach in nonlinear structural mechanics.

A self-correcting, incremental-solution procedure has been developed which seems to be promising in solving geometrically highly nonlinear problems. The procedure is also applicable to systems with many degrees of freedom where the bandwidth of the stiffness matrix is large compared with the narrow bandwidth for the shell of revolution.

Massett, D. A.↗

Effect of elastic end rings on the eigenfrequencies of thin cylinders

The effect of elastic end rings on the eigenfrequencies of thin cylindrical shells is studied by using an exact solution of the linear eigenvalue problem. The out-of-plane and torsional rigidities of the rings are responsible for the overall shell stiffness. Considerable mode interaction exists for modes with low circumferential wave numbers when the mass of the ring is comparable with that of the shell. The hypothetical simply supported and clamped boundary conditions are practically impossible to realize with a finite-mass ring for relatively short and thin shells.

El Raheb, M.↗

Characterization of Polyimide Matrix Resins and Prepregs

Graphite/polyimide composite materials are attractive candidates for a wide range of aerospace applications. They have many of the virtues of graphite/epoxies, i.e., high specific strengths and stiffness, and also outstanding thermal/oxidative stability. Yet they are not widely used in the aerospace industry due to problems of procesability. By their nature, modern addition polyimide (PI) resins and prepregs are more complex than epoxies; the key to processing lies in characterizing and understanding the materials. Chemical and rheological characterizations are carried out on several addition polyimide resins and graphite reinforced prepregs, including those based on PMR-15, LARC 160 (AP 22), LARC 160 (Curithane 103) and V378A. The use of a high range torque transducer with a Rheometrics mechanical spectrometer allows rheological data to be generated on prepreg materials as well as neat resins. The use of prepreg samples instead of neat resins eliminates the need for preimidization of the samples and the data correlates well with processing behavior found in the shop. Rheological characterization of the resins and prepregs finds significant differences not readily detected by conventional chemical characterization techniques.

Maximovich, M. G.↗

Progress with multigrid schemes for hypersonic flow problems

Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm uses upwind spatial discretization with explicit multistage time stepping. Two level versions of the various multigrid algorithms are applied to the two dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving three different hypersonic flow problems. Some new multigrid schemes based on semicoarsening strategies are shown to be quite effective in relieving the stiffness caused by the high aspect ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 x 10(exp 6) and Mach numbers up to 25.

Radespiel, R.↗