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At least 559 records · Page 31

Studies in tilt rotor VTOL aircraft aeroelasticity, volume 2

Two methods for natural mode vibration analysis are discussed. The first consists of a direct approach based on a finite element representation of the complete structure as an entity. The mass and stiffness matrices for the complete structure are assembled by properly combining the mass and stiffness matrices of the individual elements into which the structure has been divided. The second approach is that of component mode synthesis. This method is based on the concept of synthesizing the natural modes of the complete structure from modes of conveniently difined substructures, or components, into which the structure has been partitioned. In this way the expedient of reducing the system degrees of freedom, and thus the size of the eigenvalue problem, can be introduced by partial modal synthesis.

Kvaternik, R. G.↗

Flow-induced vibrations of the SSME LOX inlet tee vanes

This paper describes the results of a program initiated to identify the cause and the mechanism of 4-kHz vibrations of the Space Shuttle main engine's (SSME's) LOX inlet tee, which were revealed in 17 percent of the SSMEs during ground tests. The results of the engines' inspection, structural analyses, computational fluid dynamics studies, literature reviews, expert consultations, and laboratory testings identified the probable cause of the 4-kHz vibrations being related to the fact that the walls of some tees were thinner than in the mojority of tees, resulting in less stiff structures. The mechanism of the vibrations was identified as vortex shedding in combination with a structural coupling with the thrust cone, which increased the vane mobility, which, in turn, aggravated the fluid coupling with the thrust cone. As a result, the vane mobility was increased, aggravating the fluid coupling with the vanes. An internal modification was developed and was successfully demonstrated on an engine that had previously exhibited a 4-kHz problem.

O'Connor, G. M.↗

A non‐intrusive domain‐decomposition model reduction method for linear steady‐state partial differential equations with random coefficients

Abstract Domain decomposition methods have been proved to be an effective strategy to reduce the dimension of parametric partial differential equations (PDEs). However, existing domain decomposition methods for parametric PDEs are usually intrusive, which means domain decomposition based solvers need to be implemented from scratch for each target parametric PDE. To address this issue, we develop a new non‐intrusive domain‐decomposition model reduction method for linear steady‐state PDEs with random‐field coefficients. As a variant of our previous work by Mu and Zhang, the new method only needs access to the final linear system, that is, the global stiffness matrix and the right hand side, of a deterministic PDE solver, in order to build a domain‐decomposition‐based reduced model without intrusive implementation from scratch. The key idea is to remove the interface condition between sub‐domains and rely on the correlation between columns of the linear system to couple the sub‐domains. The non‐intrusive feature enables the applicability of the proposed method to a broader class of uncertainty quantification problems, where many legacy codes/solvers can be fully reused by our method. Two numerical examples including diffusion equations with random diffusivity and convection‐dominated transport with random velocity, are provided to demonstrate the effectiveness and efficiency of our method.

Zhang, Guannan↗

A numerical method for interface problems in elastodynamics

The numerical implementation of a formulation for a class of interface problems in elastodynamics is discussed. This formulation combines the use of the finite element and boundary integral methods to represent the interior and the exteriro regions, respectively. In particular, the response of a semicylindrical alluvial valley in a homogeneous halfspace to incident antiplane SH waves is considered to determine the accuracy and convergence of the numerical procedure. Numerical results are obtained from several combinations of the incidence angle, frequency of excitation, and relative stiffness between the inclusion and the surrounding halfspace. The results tend to confirm the theoretical estimates that the convergence is of the order H(2) for the piecewise linear elements used. It was also observed that the accuracy descreases as the frequency of excitation increases or as the relative stiffness of the inclusion decreases.

Mcghee, D. S.↗

Overcoming Geometry-Induced Stiffness with IMplicit-Explicit (IMEX) Runge-Kutta Algorithms on Unstructured Grids with Applications to CEM, CFD, and CAA

My goal is to develop and implement efficient, accurate, and robust Implicit-Explicit Runge-Kutta (IMEX RK) methods [9] for overcoming geometry-induced stiffness with applications to computational electromagnetics (CEM), computational fluid dynamics (CFD) and computational aeroacoustics (CAA). IMEX algorithms solve the non-stiff portions of the domain using explicit methods, and isolate and solve the more expensive stiff portions using implicit methods. Current algorithms in CEM can only simulate purely harmonic (up to lOGHz plane wave) EM scattering by fighter aircraft, which are assumed to be pure metallic shells, and cannot handle the inclusion of coatings, penetration into and radiation out of the aircraft. Efficient MEX RK methods could potentially increase current CEM capabilities by 1-2 orders of magnitude, allowing scientists and engineers to attack more challenging and realistic problems.

Kanevsky, Alex↗

Stability analysis of position and force control problems for robot arms

Stability issues involving the control of a robot arm under the influence of external forces are discussed. Several different scenarios are considered: position control with the external force as an unmodeled disturbance, compliant control for a bounded external force in some subspace, and compliant control for a force due to the interaction with an environment whose dynamical behavior can be modeled. In each of these cases, a stability analysis using the Lyapunov method is presented. An explanation of instability is put forth for the case in which the environment has flexibility and the gains are inappropriately chosen. When the environment is stiff in the force control subspace, robust stability can be achieved with the integral force feedback.

Wen, John T.↗

A pressurized cylindrical shell with a fixed end which contains an axial part-through or through crack

In this paper a cylindrical shell having a very stiff end plate or a flange is considered. It is assumed that near the end the cylinder contains an axial flow which may be modeled as a part-through surface crack or through crack. The primary objective is to study the effect of the end constraining on the stress intensity factor which is the main fracture mechanics parameter. The applied loads acting on the cylinder are assumed to be axisymmetric. Thus the crack problem under consideration is symmetric with respect to the plane of the crack and consequently only the mode I stress intensity factors are nonzero. With this limitation, the general perturbation problem for a cylinder with a built-in end containing an axial crack is considered. Reissner's shell theory is used to formulate the problem. The part-through crack problem is treated by using a line-spring model. In the case of a crack tip terminating at the fixed end it is shown that the integral equation of the shell problem has the same generalized Cauchy kernel as the corresponding plane stress elasticity problem. Even though the problem is formulated for a general surface crack profile and arbitrary crack surface tractions, the numerical results are obtained only for a semielliptic part-through axial crack located at the inside or outside surface of the cylinder and for internal pressure acting on the cylinder. The stress intensity factors are calculated and presented for a relatively wide range of dimensionless length parameters of the problem.

Yahsi, O. S.↗

Investigation of supersonic chemically reacting and radiating channel flow

The 2-D time-dependent Navier-Stokes equations are used to investigate supersonic flows undergoing finite rate chemical reaction and radiation interaction for a hydrogen-air system. The explicit multistage finite volume technique of Jameson is used to advance the governing equations in time until convergence is achieved. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The multidimensional radiative transfer equations for a nongray model are provided for a general configuration and then reduced for a planar geometry. Both pseudo-gray and nongray models are used to represent the absorption-emission characteristics of the participating species. The supersonic inviscid and viscous, nonreacting flows are solved by employing the finite volume technique of Jameson and the unsplit finite difference scheme of MacCormack. The specified problem considered is of the flow in a channel with a 10 deg compression-expansion ramp. The calculated results are compared with those of an upwind scheme. The problem of chemically reacting and radiating flows are solved for the flow of premixed hydrogen-air through a channel with parallel boundaries, and a channel with a compression corner. Results obtained for specific conditions indicate that the radiative interaction can have a significant influence on the entire flow field.

Mani, Mortaza↗

Time Frequency Analysis of Spacecraft Propellant Tank Spinning Slosh

Many spacecraft are designed to spin about an axis along the flight path as a means of stabilizing the attitude of the spacecraft via gyroscopic stiffness. Because of the assembly requirements of the spacecraft and the launch vehicle, these spacecraft often spin about an axis corresponding to a minor moment of inertia. In such a case, any perturbation of the spin axis will cause sloshing motions in the liquid propellant tanks that will eventually dissipate enough kinetic energy to cause the spin axis nutation (wobble) to grow further. This spinning slosh and resultant nutation growth is a primary design problem of spinning spacecraft and one that is not easily solved by analysis or simulation only. Testing remains the surest way to address spacecraft nutation growth. This paper describes a test method and data analysis technique that reveal the resonant frequency and damping behavior of liquid motions in a spinning tank. Slosh resonant frequency and damping characteristics are necessary inputs to any accurate numerical dynamic simulation of the spacecraft.

Green, Steven T.↗

The effects of aeroelastic deformation on the unaugmented stopped-rotor dynamics of an X-Wing aircraft

A new design concept in the development of VTOL aircraft with high forward flight speed capability is that of the X-Wing, a stiff, bearingless helicopter rotor system which can be stopped in flight and the blades used as two forward-swept and two aft-swept wings. Because of the usual configuration in the fixed-wing mode, there is a high potential for aeroelastic divergence or flutter and coupling of blade vibration modes with rigid-body modes. An aeroelastic stability analysis of an X-Wing configuration aircraft was undertaken to determine if these problems could exist. This paper reports on the results of dynamic stability analyses in the lateral and longitudinal directions including the vehicle rigid-body and flexible modes. A static aeroelastic analysis using the normal vibration mode equations of motion was performed to determine the cause of a loss of longitudinal static margin with increasing airspeed. This loss of static margin was found to be due to aeroelastic washin of the forward-swept blades and washout of the aft-swept blades moving the aircraft aerodynamic center forward of the center of gravity. This phenomenon is likely to be generic to X-Wing aircraft.

Gilbert, Michael G.↗

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.↗

The response of cylindrical panels fabricated from symmetrically and unsymmetrically laminated composite materials

Equations are developed which govern the deflection response of long cylindrical panels subjected to a line load. The line load is directed toward the center of curvature of the panel, is located at an arbitrary point along the arc length of the panel, and is included at an arbitrary angle relative to the radial direction. Only the geometrically linear problem is considered and the spatial dependence in the problem is reduced to one independent variable, specifically, the arc length along the panel. The problem is thus solvable in closed form. Both symmetrically laminated and the less common unsymmetrically laminated simply supported panels are studied. The unsymmetrically laminated case was considered because the natural shape of an unsymmetric laminate is cylindrical. Results are presented which show the influence of the location and inclination of the line load on panel deflection. Shallow and deep panels are considered. Both the symmetric and unsymmetric panels exhibit similar behavior, the unsymmetric configurations being less stiff. Limited experimental results are presented.

Carper, D. M.↗

The effects of aeroelastic deformation on the unaugmented stopped-rotor dynamics of an X-Wing aircraft

A new design concept in the development of vertical takeoff and landing aircraft with high forward flight speed capability is that of the X-Wing. The X-Wing is a stiff, bearingless helicopter rotor system which can be stopped in flight and the blades used as two forward-swept wings and two aft-swept wings. Because of the unusual configuration in the fixed-wing mode, there is a high potential for aeroelastic divergence or flutter and coupling of blade vibration modes with rigid-body modes. An aeroelastic stability analysis of an X-Wing configuration aircraft was undertaken to determine if these problems could exist. This paper reports on the results of dynamic stability analyses in the lateral and longitudinal directions including the vehicle rigid-body and flexible modes. A static aeroelastic analysis using the normal vibration mode equations of motion was performed to determine the cause of a loss of longitudinal static margin with increasing airspeed. This loss of static margin was found to be due to aeroelastic 'washin' of the forward-swept blades and 'washout' of the aft-swept blades moving the aircraft aerodynamic center forward of the center of gravity. This phenomenon is likely to be generic to X-Wing aircraft.

Gilbert, Michael G.↗

Modeling of composite beams and plates for static and dynamic analysis

The main purpose of this research was to develop a rigorous theory and corresponding computational algorithms for through-the-thickness analysis of composite plates. This type of analysis is needed in order to find the elastic stiffness constants for a plate and to post-process the resulting plate solution in order to find approximate three-dimensional displacement, strain, and stress distributions throughout the plate. This also requires the development of finite deformation plate equations which are compatible with the through-the-thickness analyses. After about one year's work, we settled on the variational-asymptotical method (VAM) as a suitable framework in which to solve these types of problems. VAM was applied to laminated plates with constant thickness in the work of Atilgan and Hodges. The corresponding geometrically nonlinear global deformation analysis of plates was developed by Hodges, Atilgan, and Danielson. A different application of VAM, along with numerical results, was obtained by Hodges, Lee, and Atilgan. An expanded version of this last paper was submitted for publication in the AIAA Journal.

Hodges, Dewey H.↗

Interlaminar stress analysis of dropped-ply laminated plates and shells by a mixed method

A mixed method of approximation based on Reissner's variational principle is developed for the linear analysis of interlaminar stresses in laminated composites, with special interest in laminates that contain terminated internal plies (dropped-ply laminates). Two models are derived, one for problems of generalized plane deformation and the other for the axisymmetric response of shells of revolution. A layerwise approach is taken in which the stress field is assumed with an explicit dependence on the thickness coordinate in each layer. The dependence of the stress field on the thickness coordinate is determined such that the three-dimensional equilibrium equations are satisfied by the approximation. The solution domain is reduced to one dimension by integration through the thickness. Continuity of tractions and displacements between layers is imposed. The governing two-point boundary value problem is composed of a system of both differential and algebraic equations (DAE's) and their associated boundary conditions. Careful evaluation of the system of DAE's was required to arrive at a form that allowed application of a one-step finite difference approximation. A two-stage Gauss implicit Runge-Kutta finite difference scheme was used for the solution because of its relatively high degree of accuracy. Patch tests of the two models revealed problems with solution accuracy for the axisymmetric model of a cylindrical shell loaded by internal pressure. Parametric studies of dropped-ply laminate characteristics and their influence on the interlaminar stresses were performed using the generalized plane deformation model. Eccentricity of the middle surface of the laminate through the ply drop-off was found to have a minimal effect on the interlaminar stresses under longitudinal compression, transverse tension, and in-plane shear. A second study found the stiffness change across the ply termination to have a much greater influence on the interlaminar stresses.

Harrison, Peter N.↗

One-sweep moment-based semi-implicit-explicit integration for gray thermal radiation transport

Thermal radiation transport (TRT) is a time dependent, high dimensional partial integro-differential equation. In practical applications such as inertial confinement fusion, TRT is coupled to other physics such as hydrodynamics, plasmas, etc., and the timescales one is interested in capturing are often much slower than the radiation timescale. As a result, TRT is treated implicitly, and due to its stiffness and high dimensionality, is often a dominant computational cost in multiphysics simulations. Here we develop a new approach for implicit-explicit (IMEX) integration of gray TRT in the deterministic SN setting, which requires only one sweep per stage, with the simplest first-order method requiring only one sweep per time step. The partitioning of equations is done via a moment-based high-order low-order formulation of TRT, where the streaming operator and first two moments are used to capture the asymptotic stiff regimes of the streaming limit and diffusion limit. Absorption-reemission is treated explicitly, and although stiff, is sufficiently damped by the implicit solve that we achieve stable accurate time integration without incorporating the coupling of the high order and low order equations implicitly. Due to nonlinear coupling of the high-order and low-order equations through temperature-dependent opacities, to facilitate IMEX partitioning and higher-order methods, we use a semi-implicit integration approach amenable to nonlinear partitions. In conclusion, results are demonstrated on thick Marshak and crooked pipe benchmark problems, demonstrating orders of magnitude improvement in accuracy and wallclock compared with the standard first-order implicit integration typically used.

97 MATHEMATICS AND COMPUTING↗

Thermomechanically induced pre- and postbuckling of general structure

An algorithmic solution strategy which enables handling the positive/indefinite stiffness characteristics associated with the pre and postbuckling of structures subject to complex thermomechanical loading fields was developed. The flexibility of the procedure is such that it can be applied to both finite difference and element type simulations. Due to the generality of the algorithmic approach developed, both kinematic and thermal/mechanical type material nonlinearity including inelastic effects can be treated. This includes the possibility of handling completely general thermomechanical boundary conditions. To demonstrate the scheme, the results of several benchmark problems are presented.

Padovan, J.↗

Structural concepts for large solar concentrators

The Sunflower large solar concentrator, developed in the early 1970's, is a salient example of a high-efficiency concentrator. The newly emphasized needs for solar dynamic power on the Space Station and for large, lightweight thermal sources are outlined. Existing concepts for high efficiency reflector surfaces are examined with attention to accuracy needs for concentration rates of 1000 to 3000. Concepts using stiff reflector panels are deemed most likely to exhibit the long-term consistent accuracy necessary for low-orbit operation, particularly for the higher concentration ratios. Quantitative results are shown of the effects of surface errors for various concentration and focal-length diameter ratios. Cost effectiveness is discussed. Principal sources of high cost include the need for various dished panels for paraboloidal reflectors and the expense of ground testing and adjustment. A new configuration is presented addressing both problems, i.e., a deployable Pactruss backup structure with identical panels installed on the structure after deployment in space. Analytical results show that with reasonable pointing errors, this new concept is capable of concentration ratios greater than 2000.

Hedgepeth, John M.↗