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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Solution of Von Karman's plate equation with perturbation and series summation

A nonliner series summation technique was combined with Chien's small parameter perturbation technique to solve the problem of the finite deflection of a simply supported circular plate subjected to a uniform transverse load. Problems involving finite deflections of plates with simply supported or free edges were regarded as almost intractable. The great advantage of incorporating the summation method into the solution procedure is demonstrated.

Watson, L. G.↗
NASA NTRS2000

Double-Plate Penetration Equations

This report compares seven double-plate penetration predictor equations for accuracy and effectiveness of a shield design. Three of the seven are the Johnson Space Center original, modified, and new Cour-Palais equations. The other four are the Nysmith, Lundeberg-Stern-Bristow, Burch, and Wilkinson equations. These equations, except the Wilkinson equation, were derived from test results, with the velocities ranging up to 8 km/sec. Spreadsheet software calculated the projectile diameters for various velocities for the different equations. The results were plotted on projectile diameter versus velocity graphs for the expected orbital debris impact velocities ranging from 2 to 15 km/sec. The new Cour-Palais double-plate penetration equation was compared to the modified Cour-Palais single-plate penetration equation. Then the predictions from each of the seven double-plate penetration equations were compared to each other for a chosen shield design. Finally, these results from the equations were compared with test results performed at the NASA Marshall Space Flight Center. Because the different equations predict a wide range of projectile diameters at any given velocity, it is very difficult to choose the "right" prediction equation for shield configurations other than those exactly used in the equations' development. Although developed for various materials, the penetration equations alone cannot be relied upon to accurately predict the effectiveness of a shield without using hypervelocity impact tests to verify the design.

Hayashida, K. B.↗
NASA NTRS1993

An efficient model for coupling structural vibrations with acoustic radiation

The scattering of an incident wave by a flexible panel is studied. The panel vibration is governed by the nonlinear plate equations while the loading on the panel, which is the pressure difference across the panel, depends on the reflected and transmitted waves. Two models are used to calculate this structural-acoustic interaction problem. One solves the three dimensional nonlinear Euler equations for the flow-field coupled with the plate equations (the fully coupled model). The second uses the linear wave equation for the acoustic field and expresses the load as a double integral involving the panel oscillation (the decoupled model). The panel oscillation governed by a system of integro-differential equations is solved numerically and the acoustic field is then defined by an explicit formula. Numerical results are obtained using the two models for linear and nonlinear panel vibrations. The predictions given by these two models are in good agreement but the computational time needed for the 'fully coupled model' is 60 times longer than that for 'the decoupled model'.

Frendi, Abdelkader↗
NASA NTRS1993

On the effect of acoustic coupling on random and harmonic plate vibrations

The effect of acoustic coupling on random and harmonic plate vibrations is studied using two numerical models. In the coupled model, the plate response is obtained by integration of the nonlinear plate equation coupled with the nonlinear Euler equations for the surrounding acoustic fluid. In the uncoupled model, the nonlinear plate equation with an equivalent linear viscous damping term is integrated to obtain the response of the plate subject to the same excitation field. For a low-level, narrow-band excitation, the two models predict the same plate response spectra. As the excitation level is increased, the response power spectrum predicted by the uncoupled model becomes broader and more shifted towards the high frequencies than that obtained by the coupled model. In addition, the difference in response between the coupled and uncoupled models at high frequencies becomes larger. When a high intensity harmonic excitation is used, causing a nonlinear plate response, both models predict the same frequency content of the response. However, the level of the harmonics and subharmonics are higher for the uncoupled model. Comparisons to earlier experimental and numerical results show that acoustic coupling has a significant effect on the plate response at high excitation levels. Its absence in previous models may explain the discrepancy between predicted and measured responses.

Frendi, A.↗
NASA NTRS1993

Effect of acoustic coupling on random and harmonic plate vibrations

The effect of acoustic coupling on random and harmonic plate vibrations is studied using two numerical models. In the coupled model, the plate response is obtained by integration of the nonlinear plate equation coupled with the nonlinear Euler equations for the surrounding acoustic fluid. In the uncoupled model, the nonlinear plate equation with an equivalent linear viscous damping term is integrated to obtain the response of the plate subject to the same excitation field. For a low-level, narrow-band excitation, the two models predict the same plate response spectra. As the excitation level is increased, the response power spectrum predicted by the uncoupled model becomes broader and more shifted towards the high frequencies than that obtained by the coupled model. In addition, the difference in response between the coupled and uncoupled models at high frequencies becomes larger. When a high intensity harmonic excitation is used, causing a nonlinear plate response, both models predict the same frequency content of the response. However, the level of the harmonics and subharmonics are higher for the uncoupled model. Comparisons to earlier experimental and numerical results show that acoustic coupling has a significant effect on the plate response at high excitation levels. Its absence in previous models may explain the discrepancy between predicted and measured responses.

Frendi, Abdelkader↗
NASA NTRS1992

On the coupling between a supersonic boundary layer and a flexible surface

The coupling between a two-dimensional, supersonic, laminar boundary layer and a flexible surface is studied using direct numerical computations of the Navier-Stokes equations coupled with the plate equation. The flexible surface is forced to vibrate by plane acoustic waves at normal incidence emanated by a sound source located on the side of the flexible surface opposite to the boundary layer. The effect of the source excitation frequency on the surface vibration and boundary layer stability is analyzed. We find that, for frequencies near the fifth natural frequency of the surface or lower, large disturbances are introduced in the boundary layer which may alter its stability characteristics. The interaction between a stable two-dimensional disturbance of Tollmien-Schlichting (TS) type with the vibrating surface is also studied. We find that the disturbance level is higher over the vibrating flexible surface than that obtained when the surface is rigid, which indicates a strong coupling between flow and structure. However, in the absence of the sound source the disturbance level over the rigid and flexible surfaces are identical. This result is due to the high frequency of the TS disturbance which does not couple with the flexible surface.

Frendi, Abdelkader↗
NASA NTRS1992

On the coupling between a supersonic boundary layer and a flexible surface

The coupling between a two-dimensional, supersonic, laminar boundary layer and a flexible surface is studied using direct numerical computations of the Navier-Stokes equations coupled with the plate equation. The flexible surface is forced to vibrate by plane acoustic waves at normal incidence emanated by a sound source located on the side of the flexible surface opposite to the boundary layer. The effect of the source excitation frequency on the surface vibration and boundary layer stability is analyzed. We find that, for frequencies near the fifth natural frequency of the surface or lower, large disturbances are introduced in the boundary layer which may alter its stability characteristics. The interaction between a stable two-dimensional disturbance of Tollmien-Schlichting (TS) type with the vibrating surface is also studied. We find that the disturbance level is higher over the vrating flexible surface than that obtained when the surface is rig id, which indicates a strong coupling between flow and structure. However, in the absence of the sound source the disturbance level over the rigid and flexible surfaces are identical. This result is due to the high frequency of the TS disturbance which does not couple with the flexible surface.

Frendi, Abdelkader↗
NASA NTRS1991

Single wall penetration equations

Five single plate penetration equations are compared for accuracy and effectiveness. These five equations are two well-known equations (Fish-Summers and Schmidt-Holsapple), two equations developed by the Apollo project (Rockwell and Johnson Space Center (JSC), and one recently revised from JSC (Cour-Palais). They were derived from test results, with velocities ranging up to 8 km/s. Microsoft Excel software was used to construct a spreadsheet to calculate the diameters and masses of projectiles for various velocities, varying the material properties of both projectile and target for the five single plate penetration equations. The results were plotted on diameter versus velocity graphs for ballistic and spallation limits using Cricket Graph software, for velocities ranging from 2 to 15 km/s defined for the orbital debris. First, these equations were compared to each other, then each equation was compared with various aluminum projectile densities. Finally, these equations were compared with test results performed at JSC for the Marshall Space Flight Center. These equations predict a wide variety of projectile diameters at a given velocity. Thus, it is very difficult to choose the 'right' prediction equation. The thickness of a single plate could have a large variation by choosing a different penetration equation. Even though all five equations are empirically developed with various materials, especially for aluminum alloys, one cannot be confident in the shield design with the predictions obtained by the penetration equations without verifying by tests.

Hayashida, K. B.↗
NASA NTRS1988

A cumulative damage model for continuous fiber composite laminates with matrix cracking and interply delaminations

The present cumulative damage model for the prediction of stiffness loss in graphite/epoxy laminates applies a thermomechanical constitutive theory for elastic composites with distributed damage. The model proceeds from a continuum mechanics and thermodynamics approach in which the distributed damage is characterized by a set of second-order tensor-valued internal state variables. A set of damage-dependent laminated plate equations is obtained; this is developed by modifying classical Kirchhoff plate theory.

Allen, David H.↗
NASA NTRS1995

Analysis of the Hessian for aeroelastic optimization

The symbol of the Hessian for an aeroelastic optimization model problem is analyzed. The flow is modeled by the small-disturbance full potential equation and the structure is modeled by an isotropic (von Karman) plate equation. The cost function consists of both aerodynamic and structural terms. In the new analysis the symbol of the cost function Hessian near the minimum is computed. The result indicates that under some conditions, which are likely fulfilled in most applications, the system is decoupled for the non-smooth components. The result also shows that the structure part in the Hessian is well-conditioned while the aerodynamic part is ill-conditioned. Applications of the result to optimization strategies are discussed.

Arian, Eyal↗
DOE OSTI2020

Onset dynamics of air-water menisci on rock fracture surfaces

Information on menisci dynamics and equilibrium contact angles, θ e , is needed for modeling multiphase flow of fluids in geologic formations. The wettability of fracture faces is relevant to applications such as waterflooding in enhanced oil recovery and evaluation of caprock integrity for geologic carbon sequestration. We investigated the vertical capillary rise of air-water menisci on exposed fracture faces for a sandstone, a shale, and three granites. The experimental design approximated that employed in the Wilhelmy plate method. Replicate fracture faces were prepared by fracturing cylindrical rock cores using the Brazilian method and splitting the fractured cores apart along their fracture planes. Meniscus onset was imaged from a cross-sectional perspective using dynamic neutron radiography, and quantified with change point analysis. An existing model for meniscus onset fitted the experimental data very well (median R 2 = 0.96). Capillary rise was typified by t 2/3 scaling (where t is time), followed by a constant equilibrium height, z e . The average time taken for the menisci to reach z e was 0.39 s, with no differences between rock types. The menisci achieved a greater vertical extent on the fracture faces of the sedimentary rocks as compared to those of the granites. Apparent θ e values were calculated from the best fit estimates of z e using the Wilhelmy plate equation for a smooth and planar vertical surface. Despite the fractal roughness of some of the fracture faces, there was a significant linear relationship (R 2 = 0.80) between the apparent θ e values and intrinsic θ e values measured on polished surfaces of the same rocks using the sessile drop method. The regression equation indicated the apparent θ e values were consistently greater than the intrinsic values. This overestimation may be due to averaging of pixels at the air-water-solid interface, a required step in the image analysis. Further exploration of the range of applicability and measurement accuracy of this proposed new technique would be valuable.

58 GEOSCIENCES↗
NASA NTRS1978

A solution procedure for behavior of thick plates on a nonlinear foundation and postbuckling behavior of long plates

Approximate solutions for three nonlinear orthotropic plate problems are presented: (1) a thick plate attached to a pad having nonlinear material properties which, in turn, is attached to a substructure which is then deformed; (2) a long plate loaded in inplane longitudinal compression beyond its buckling load; and (3) a long plate loaded in inplane shear beyond its buckling load. For all three problems, the two dimensional plate equations are reduced to one dimensional equations in the y-direction by using a one dimensional trigonometric approximation in the x-direction. Each problem uses different trigonometric terms. Solutions are obtained using an existing algorithm for simultaneous, first order, nonlinear, ordinary differential equations subject to two point boundary conditions. Ordinary differential equations are derived to determine the variable coefficients of the trigonometric terms.

Stein, M.↗
NASA NTRS1989

Modal interaction in postbuckled plates. Theory

Plates can have more than one buckled solution for a fixed set of boundary conditions. The theory for the identification and the computation of multiple solutions in buckled plates is examined. The theory predicts modal interaction (which is also called change in buckle pattern or secondary buckling) in experiments on certain plates with multiple theoretical solutions. A set of coordinate functions is defined for Galerkin's method so that the von Karman plate equations are reduced to a coupled set of cubic equations in generalized coordinates that are uncoupled in the linear terms. An iterative procedure for solving modal interaction problems is suggested based on this cubic form.

Thurston, Gaylen A.↗
NASA NTRS1994

Finite dimensional approximation of a class of constrained nonlinear optimal control problems

An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

Gunzburger, Max D.↗
NASA NTRS1996

Computation of Static Shapes and Voltages for Micromachined Deformable Mirrors with Nonlinear Electrostatic Actuators

In modeling micromachined deformable mirrors with electrostatic actuators whose gap spacings are of the same order of magnitude as those of the surface deformations, it is necessary to use nonlinear models for the actuators. In this paper, we consider micromachined deformable mirrors modeled by a membrane or plate equation with nonlinear electrostatic actuator characteristics. Numerical methods for computing the mirror deformation due to given actuator voltages and the actuator voltages required for producing the desired deformations at the actuator locations are presented. The application of the proposed methods to circular deformable mirrors whose surfaces are modeled by elastic membranes is discussed in detail. Numerical results are obtained for a typical circular micromachined mirror with electrostatic actuators.

Wang, P. K. C.↗
NASA NTRS2002

Use of High Fidelity Methods in Multidisciplinary Optimization-A Preliminary Survey

Multidisciplinary optimization is a key element of design process. To date multidiscipline optimization methods that use low fidelity methods are well advanced. Optimization methods based on simple linear aerodynamic equations and plate structural equations have been applied to complex aerospace configurations. However, use of high fidelity methods such as the Euler/ Navier-Stokes for fluids and 3-D (three dimensional) finite elements for structures has begun recently. As an activity of Multidiscipline Design Optimization Technical Committee (MDO TC) of AIAA (American Institute of Aeronautics and Astronautics), an effort was initiated to assess the status of the use of high fidelity methods in multidisciplinary optimization. Contributions were solicited through the members MDO TC committee. This paper provides a summary of that survey.

Guruswamy, Guru P.↗