SEARCH · Search NASA

Results for “Stiff”

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.

SourceResearch connectionFrom yearThrough year

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

At least 289 records · Page 16

All sources NASA NTRS DOE OSTI

NASA NTRS1989

Internal state variable approach for predicting stiffness reductions in fibrous laminated composites with matrix cracks

A mathematical model utilizing the internal state variable concept is proposed for predicting the upper bound of the reduced axial stiffnesses in cross-ply laminates with matrix cracks. The axial crack opening displacement is explicitly expressed in terms of the observable axial strain and the undamaged material properties. A crack parameter representing the effect of matrix cracks on the observable axial Young's modulus is calculated for glass/epoxy and graphite/epoxy material systems. The results show that the matrix crack opening displacement and the effective Young's modulus depend not on the crack length, but on its ratio to the crack spacing.

Lee, Jong-Won↗

NASA NTRS1990

A study of numerical methods for hyperbolic conservation laws with stiff source terms

In the present study of the behavior of typical numerical methods in the case of a model advection equation having a parameter-dependent source term, two approaches to the incorporation of the source terms are used: MacCormack-type predictor-corrector methods with flux limiters, and splitting methods in which the fluid dynamics and chemistry are handled in separate steps. The latter are found to perform slightly better. The model scalar equation is used to show that the incorrectness of the propagation speeds of discontinuities observed in the stiff case is due to the introduction of nonequilibrium values through numerical dissipation in the advection step.

Leveque, R. J.↗

NASA NTRS1990

Derivatives of buckling loads and vibration frequencies with respect to stiffness and initial strain parameters

A uniform variational approach to sensitivity analysis of vibration frequencies and bifurcation loads of nonlinear structures is developed. Two methods of calculating the sensitivities of bifurcation buckling loads and vibration frequencies of nonlinear structures, with respect to stiffness and initial strain parameters, are presented. A direct method requires calculation of derivatives of the prebuckling state with respect to these parameters. An adjoint method bypasses the need for these derivatives by using instead the strain field associated with the second-order postbuckling state. An operator notation is used and the derivation is based on the principle of virtual work. The derivative computations are easily implemented in structural analysis programs. This is demonstrated by examples using a general purpose, finite element program and a shell-of-revolution program.

Haftka, Raphael T.↗

NASA NTRS1990

Stiffness-matrix condition number and shape sensitivity errors

This paper derives an error magnification index for assessing the sensitivity of the displacement field to errors in the load vector. It is shown that the error magnification index is less conservative than the stiffness-matrix condition number and that, for some cases, no error magnification occurs even when the condition number is very high. The proposed index was used to calculate the derivatives of beam response to changes in the beam structural parameters, using a semianalytical method. It is shown that the proposed index discriminates well between the calculation of the derivative with respect to length, which is very sensitive to errors, and the calculation of the derivative with respect to cross-sectional height, which is not sensitive.

Haftka, Raphael T.↗

NASA NTRS1991

On the application of ENO scheme with subcell resolution to conservation laws with stiff source terms

Two approaches are used to extend the essentially non-oscillatory (ENO) schemes to treat conservation laws with stiff source terms. One approach is the application of the Strang time-splitting method. Here the basic ENO scheme and the Harten modification using subcell resolution (SR), ENO/SR scheme, are extended this way. The other approach is a direct method and a modification of the ENO/SR. Here the technique of ENO reconstruction with subcell resolution is used to locate the discontinuity within a cell and the time evolution is then accomplished by solving the differential equation along characteristics locally and advancing in the characteristic direction. This scheme is denoted ENO/SRCD (subcell resolution - characteristic direction). All the schemes are tested on the equation of LeVeque and Yee (NASA-TM-100075, 1988) modeling reacting flow problems. Numerical results show that these schemes handle this intriguing model problem very well, especially with ENO/SRCD which produces perfect resolution at the discontinuity.

Chang, Shih-Hung↗

NASA NTRS1991

A fully Galerkin method for the recovery of stiffness and damping parameters in Euler-Bernoulli beam models

A fully Sinc-Galerkin method for recovering the spatially varying stiffness and damping parameters in Euler-Bernoulli beam models is presented. The forward problems are discretized with a sinc basis in both the spatial and temporal domains thus yielding an approximate solution which converges exponentially and is valid on the infinite time interval. Hence the method avoids the time-stepping which is characteristic of many of the forward schemes which are used in parameter recovery algorithms. Tikhonov regularization is used to stabilize the resulting inverse problem, and the L-curve method for determining an appropriate value of the regularization parameter is briefly discussed. Numerical examples are given which demonstrate the applicability of the method for both individual and simultaneous recovery of the material parameters.

Smith, R. C.↗

NASA NTRS1989

A method for exponential propagation of large systems of stiff nonlinear differential equations

A new time integrator for large, stiff systems of linear and nonlinear coupled differential equations is described. For linear systems, the method consists of forming a small (5-15-term) Krylov space using the Jacobian of the system and carrying out exact exponential propagation within this space. Nonlinear corrections are incorporated via a convolution integral formalism; the integral is evaluated via approximate Krylov methods as well. Gains in efficiency ranging from factors of 2 to 30 are demonstrated for several test problems as compared to a forward Euler scheme and to the integration package LSODE.

Friesner, Richard A.↗

NASA NTRS1991

Effect of stiffness characteristics on the response of composite grid-stiffened structures

A study of the effect of stiffness discontinuities and structural parameters on the response of continuous-filament grid-stiffened flat panels is presented. The buckling load degradation due to manufacturing-introduced stiffener discontinuities associated with a filament cut-and-add approach at the stiffener intersections is investigated. The degradation of buckling resistance in isogrid flat panels subjected to uni-axial compression and combined axial compression and shear loading conditions and induced damage is quantified using FEM. The combined loading case is the most critical one. Nonsolid stiffener cross sections, such as a foam-filled blade or hat with a 0-deg dominant cap, result in grid-stiffened structures that are structurally very efficient for wing and fuselage applications. The results of a study of the ability of grid-stiffened structural concepts to enhance the effective Poisson's ratio of a panel are presented. Grid-stiffened concepts create a highly effective Poisson's ratio, which can produce large camber deformations for certain elastic tailoring applications.

Ambur, Damodar R.↗

NASA NTRS1991

A parallel algorithm for generation and assembly of finite element stiffness and mass matrices

A new algorithm is proposed for parallel generation and assembly of the finite element stiffness and mass matrices. The proposed assembly algorithm is based on a node-by-node approach rather than the more conventional element-by-element approach. The new algorithm's generality and computation speed-up when using multiple processors are demonstrated for several practical applications on multi-processor Cray Y-MP and Cray 2 supercomputers.

Storaasli, O. O.↗

NASA NTRS1992

Effect of heat treatment on stiffness and damping of SiC/Ti-15-3

The effect of heat treatment on material properties of SiC/Ti-15-3 was measured by vibration tests. Heat treatment changes the microstructure, which was found to stiffen the matrix and reduce its damping capacity. Test results indicate how these changes in the matrix affect the corresponding properties of the composite. Measurements show that heat treatment affects damping properties of the composite to a greater extent than stiffness properties. The extent of change in mechanical properties is shown to depend on heat treatment temperature and exposure time.

Grady, Joseph E.↗

NASA NTRS1992

Time simulation of flutter with large stiffness changes

Time simulation of flutter, involving large local structural changes, is formulated with a state-space model that is based on a relatively small number of generalized coordinates. Free-free vibration modes are first calculated for a nominal finite-element model with relatively large fictitious masses located at the area of structural changes. A low-frequency subset of these modes is then transformed into a set of structural modal coordinates with which the entire simulation is performed. These generalized coordinates and the associated oscillatory aerodynamic force coefficient matrices are used to construct an efficient time-domain, state-space model for a basic aeroelastic case. The time simulation can then be performed by simply changing the mass, stiffness, and damping coupling terms when structural changes occur. It is shown that the size of the aeroelastic model required for time simulation with large structural changes at a few apriori known locations is similar to that required for direct analysis of a single structural case. The method is applied to the simulation of an aeroelastic wind-tunnel model. The diverging oscillations are followed by the activation of a tip-ballast decoupling mechanism that stabilizes the system but may cause significant transient overshoots.

Karpel, Mordechay↗

NASA NTRS1992

Active control of sound transmission through stiff lightweight composite fuselage constructions

Work was performed on the active control of sound transmission in composite structures. First, a model was outlined of a vibrating plate with arbitrary boundary conditions. Second, the far field was minimized to radiate acoustic power using secondary force inputs. Third, a model of a simple case of freely mounted stiff lightweight panels was used. Fourth, experimental results for aluminum honeycomb composite panels is presented. Fifth, experimental results are presented for the combination of a clamped steel plate and an aluminum honeycomb panel with secondary forces acting between the partitions. Finally, experimental results for the combination of a clamped steel plate with four secondary aluminum honeycomb panels is presented. All materials are shown in viewgraph format.

Thomas, D. R.↗

NASA NTRS1992

Time simulation of flutter with large stiffness changes

Time simulation of flutter, involving large local structural changes, is formulated with a state-space model that is based on a relatively small number of generalized coordinates. Free-free vibration modes are first calculated for a nominal finite-element model with relatively large fictitious masses located at the area of structural changes. A low-frequency subset of these modes is then transformed into a set of structural modal coordinates with which the entire simulation is performed. These generalized coordinates and the associated oscillatory aerodynamic force coefficient matrices are used to construct an efficient time-domain, state-space model for basic aeroelastic case. The time simulation can then be performed by simply changing the mass, stiffness and damping coupling terms when structural changes occur. It is shown that the size of the aeroelastic model required for time simulation with large structural changes at a few a priori known locations is similar to that required for direct analysis of a single structural case. The method is applied to the simulation of an aeroelastic wind-tunnel model. The diverging oscillations are followed by the activation of a tip-ballast decoupling mechanism that stabilizes the system but may cause significant transient overshoots.

Karpel, M.↗

NASA NTRS1992

Stiffness and thermoelastic coefficients for composite laminates

Simple analytic expressions are presented for the stiffness and thermoelastic coefficients of composite laminates in terms of the material properties of the individual layers. Expressions for the derivatives of the various coefficients with respect to each of the material properties and fiber orientation angles are also included. For typical high-performance composites, numerical values are given showing the effects of the stacking sequence and the fiber orientation angle of quasi-isotropic and angle-ply laminates on the values of the various coefficients and their sensitivity derivatives. The expressions for the thermoelastic coefficients and the sensitivity derivatives are given herein for the first time.

Noor, Ahmed K.↗

NASA NTRS1993

Transverse cracking and stiffness reduction in composite laminates

A study of transverse cracking mechanism in composite laminates is presented using a singular hybrid finite element model. The model provides the global structural response as well as the precise local crack-tip stress fields. An elasticity basis for the problem is established by employing Lekhnitskii's complex variable potentials and method of eigenfunction expansion. Stress singularities associated with the transverse crack are obtained by decomposing the deformation into the symmetric and antisymmetric modes and proper boundary conditions. A singular hybrid element is thereby formulated based on the variational principle of a modified hybrid functional to incorporate local crack singularities. Axial stiffness reduction due to transverse cracking is studied. The results are shown to be in very good agreement with the existing experimental data. Comparison with simple shear lag analysis is also given. The effects of stress intensity factors and strain energy density on the increase of crack density are analyzed. The results reveal that the parameters approach definite limits when crack densities are saturated, an evidence of the existence of characteristic damage state.

Yuan, F. G.↗

NASA NTRS1934

The torsional stiffness of thin duralumin shells subjected to large torques

This report gives a simple method of estimating the torsional stiffness of thin shells, such as box beams or stressed-skin wings under large torque loads. A general efficiency chart for shells in torsion is established, based on the assumption that the efficiency of the web sheet in resisting deformation decreases linearly with the average stress. The chart is used to calculate the torsional deflections of eight box beams, a test wing panel, and a complete wing; the results of the calculations are shown in comparison with the test results. The agreement is probably as good as might be expected considering the empirical nature of the method and the well-known dispersion between results of tests on thin sheet-metal structures.

Kuhn, Paul↗

NASA NTRS1938

Tables of stiffness and carry-over factor for structural members under axial load

Tables of stiffness and carry-over factor are presented for members in which the cross section and axial load do not vary along the length of the member. These tables are of use in solving problems in the stability of structural members under axial load as well as in application of the Cross method of moment distribution when the effects of axial load in the members are considered. The interval between successive values of the argument is small enough to make interpolation unnecessary in engineering calculations.

Lundquist, Eugene E↗

NASA NTRS1929

Cantilever Wings for Modern Aircraft: Some Aspects of Cantilever Wing Construction with Special Reference to Weight and Torsional Stiffness

In the foregoing remarks I have made an attempt to touch on some of the structural problems met with in cantilever wings, and dealt rather fully with a certain type of single-spar construction. The experimental test wing was a first attempt to demonstrate the principles of this departure from orthodox methods. The result was a wing both torsionally stiff and of light weight - lighter than a corresponding biplane construction.

WINGS - STRUCTURE↗