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At least 199 records · Page 11

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NASA NTRS1978

Computerized symbolic manipulation in structural mechanics Progress and potential

Status and recent applications of computerized symbolic manipulation to structural mechanics problems are summarized. The applications discussed include; (1) generation of characteristic arrays of finite elements; (2) evaluation of effective stiffness and mass coefficients of continuum models for repetitive lattice structures; and (3) application of Rayleigh-Ritz technique to free vibration analysis of laminated composite elliptic plates. The major advantages of using computerized symbolic manipulation in each of these applications are outlined. A number of problem areas which limit the realization of the full potential of computerized symbolic manipulation in structural mechanics are examined and some of the means of alleviating them are discussed.

Noor, A. K.↗

NASA NTRS1990

Dynamic substructuring by the boundary flexibility vector method of component mode synthesis

Component mode synthesis (CMS) is a method of dynamic analysis, for structures having a large number of degrees of freedom (DOF). These structures often required lengthy computer CPU time and large computer memory resources, if solved directly by the finite-element method (FEM). In CMS, the structure is divided into independent components in which the DOF are defined by a set of generalized coordinates defined by displacement shapes. The number of the generalized coordinates are much less than the original number of physical DOF, in the component. The displacement shapes are used to transform the component property matrices and any applied external loads, to a reduced system of coordinates. Reduced system property matrices are assembled, and any type of dynamic analysis is carried out in the reduced coordinate system. Any obtained results are back transformed to the original component coordinate systems. In all conventional methods of CMS, the mode shapes used for components are dynamic mode shapes, supplemented by static deflected shapes. Historically, all the dynamic mode shapes used in conventional CMS are the natural modes (eigenvectors) of components. A new method of CMS, namely the boundary flexibility vector method of CMS, is presented. The method provides for the incorporation of a set of static Ritz vectors, referred to as boundary flexibility vectors, as a replacement and/or supplement to conventional eigenvectors, as displacement shapes for components. The generation of these vectors does not require the solution of a costly eigenvalue problem, as in the case of natural modes in conventional CMS, and hence a substantial saving in CPU time can be achieved. The boundary flexibility vectors are generated from flexibility (or stiffness) properties of components. The formulation presented is for both free and fixed-interface components, and for both the free and forced vibration problems. Free and forced vibration numerical examples are presented to verify the accuracy of the method and the saving in CPU time. Compared to conventional methods of CMS, the results indicate that by using the new method, more accurate results can be obtained with a substantial saving in CPU time.

Abdallah, Ayman Ahmed↗

NASA NTRS1991

A locally refined rectangular grid finite element method - Application to computational fluid dynamics and computational physics

The present FEM technique addresses both linear and nonlinear boundary value problems encountered in computational physics by handling general three-dimensional regions, boundary conditions, and material properties. The box finite elements used are defined by a Cartesian grid independent of the boundary definition, and local refinements proceed by dividing a given box element into eight subelements. Discretization employs trilinear approximations on the box elements; special element stiffness matrices are included for boxes cut by any boundary surface. Illustrative results are presented for representative aerodynamics problems involving up to 400,000 elements.

Young, David P.↗

NASA NTRS1987

Exact finite element method analysis of viscoelastic tapered structures to transient loads

A general method is presented for determining the dynamic torsional/axial response of linear structures composed of either tapered bars or shafts to transient excitations. The method consists of formulating and solving the dynamic problem in the Laplace transform domain by the finite element method and obtaining the response by a numerical inversion of the transformed solution. The derivation of the torsional and axial stiffness matrices is based on the exact solution of the transformed governing equation of motion, and it consequently leads to the exact solution of the problem. The solution permits treatment of the most practical cases of linear tapered bars and shafts, and employs modeling of structures with only one element per member which reduces the number of degrees of freedom involved. The effects of external viscous or internal viscoelastic damping are also taken into account.

Spyrakos, Constantine Chris↗

NASA NTRS1975

A triangular thin shell finite element: Nonlinear analysis

Aspects of the formulation of a triangular thin shell finite element which pertain to geometrically nonlinear (small strain, finite displacement) behavior are described. The procedure for solution of the resulting nonlinear algebraic equations combines a one-step incremental (tangent stiffness) approach with one iteration in the Newton-Raphson mode. A method is presented which permits a rational estimation of step size in this procedure. Limit points are calculated by means of a superposition scheme coupled to the incremental side of the solution procedure while bifurcation points are calculated through a process of interpolation of the determinants of the tangent-stiffness matrix. Numerical results are obtained for a flat plate and two curved shell problems and are compared with alternative solutions.

Thomas, G. R.↗

NASA NTRS1981

Abrasive drill for resilient materials

Resilient materials normally present problem in obtaining accurate and uniform hole size and position. Tool is fabricated from stiff metal rod such as tungsten or carbon steel that has diameter slightly smaller than required hole. Piercing/centering point is ground on one end of rod. Rod is then plasma-sprayed (flame-sprayed) with suitable hard abrasive coating. High-speed, slow-feed operation of tool is necessary for accurate holes, and this can be done with drill press, hard drill, or similar machines.

Koch, A. J.↗

NASA NTRS1983

Noise transmission through sidewall treatments applicable to twin-engine turboprop aircraft

The noise transmission loss characteristics of the sidewall treatment in the propeller plane of a twin-engine turboprop aircraft are experimentally investigated in the NASA Langley Research Center Transmission Loss Facility. The sound attenuation properties of the individual elements of this treatment are evaluated showing least noise transmission loss in the low frequencies (below 500 Hz) where the excitation levels at the propeller blade passage frequency and the first few harmonics are highest. It is shown that single and double wall resonances play an important role in the noise transmission loss values of the treatment at these low frequencies suggesting that a limp mass with a very low resonance frequency serves better as a trim panel than a trim panel having a high structural stiffness. It is indicated that the window structures might be a potential noise control problem.

Grosveld, F. W.↗

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 NTRS1983

Application of the method of lines for solutions of the Navier-Stokes equations using a nonuniform grid distribution

The feasibility of the method of lines for solutions of physical problems requiring nonuniform grid distributions is investigated. To attain this, it is also necessary to investigate the stiffness characteristics of the pertinent equations. For specific applications, the governing equations considered are those for viscous, incompressible, two dimensional and axisymmetric flows. These equations are transformed from the physical domain having a variable mesh to a computational domain with a uniform mesh. The two governing partial differential equations are the vorticity and stream function equations. The method of lines is used to solve the vorticity equation and the successive over relaxation technique is used to solve the stream function equation. The method is applied to three laminar flow problems: the flow in ducts, curved-wall diffusers, and a driven cavity. Results obtained for different flow conditions are in good agreement with available analytical and numerical solutions. The viability and validity of the method of lines are demonstrated by its application to Navier-Stokes equations in the physical domain having a variable mesh.

Abolhassani, J. S.↗

NASA NTRS1991

Resolved rate and torque control schemes for large scale space based kinematically redundant manipulators

Resolved rate control of kinematically redundant ground based manipulators is a challenging problem. The structural, actuator, and control loop frequency characteristics of industrial grade robots generally allow operation with resolved rate control; a rate command is achievable with good accuracy. However, space based manipulators are different, typically have less structural stiffness, more motor and joint friction, and lower control loop cycle frequencies. These undesirable characteristics present a considerable Point of Resolution (POR) control problem for space based, kinematically redundant manipulators for the following reason: a kinematically redundant manipulator requires an arbitrary constraint to solve for the joint rate commands. A space manipulator will not respond to joint rate commands because of these characteristics. A space based manipulator simulation, including free end rigid body dynamics, motor dynamics, motor striction/friction, gearbox backlash, joint striction/friction, and Space Station Remote Manipulator System type configuration parameters, is used to evaluate the performance of a documented resolved rate control law. Alternate schemes which include torque control are also evaluated.

Robert W Bailey↗

NASA NTRS1962

SOME SHELL STABILITY PROBLEMS IN MISSILE AND SPACE VEHICLE ANALYSIS

A brief discussion is presented of three structural shell stability studies in progress at Lockheed Missiles & Space Company: the stabilizing influence of solid propellants, the effect of cushion stiffness on buckling under cushion loading, and the snap-through buckling of axially loaded cylinders. Recent analytical results are compared with test data. Also included is a brief description of a few shell stability problems of present interest to LMSC for which satisfactory methods of analysis are not available.

MISSILE↗

NASA NTRS1986

Physical and numerical sources of computational inefficiency in integration of chemical kinetic rate equations: Etiology, treatment and prognosis

The design of a very fast, automatic black-box code for homogeneous, gas-phase chemical kinetics problems requires an understanding of the physical and numerical sources of computational inefficiency. Some major sources reviewed in this report are stiffness of the governing ordinary differential equations (ODE's) and its detection, choice of appropriate method (i.e., integration algorithm plus step-size control strategy), nonphysical initial conditions, and too frequent evaluation of thermochemical and kinetic properties. Specific techniques are recommended (and some advised against) for improving or overcoming the identified problem areas. It is argued that, because reactive species increase exponentially with time during induction, and all species exhibit asymptotic, exponential decay with time during equilibration, exponential-fitted integration algorithms are inherently more accurate for kinetics modeling than classical, polynomial-interpolant methods for the same computational work. But current codes using the exponential-fitted method lack the sophisticated stepsize-control logic of existing black-box ODE solver codes, such as EPISODE and LSODE. The ultimate chemical kinetics code does not exist yet, but the general characteristics of such a code are becoming apparent.

Pratt, D. T.↗

NASA NTRS1989

Parallel linear equation solvers for finite element computations

The overall objective of this research is to develop efficient methods for the solution of linear and nonlinear systems of equations on parallel and supercomputers, and to apply these methods to the solution of problems in structural analysis. Attention has been given so far only to linear equations. The methods considered for the solution of the stiffness equation Kx=f have been Choleski factorization and the conjugate gradient iteration with SSOR and Incomplete Choleski preconditioning. More detail on these methods will be given on subsequent slides. These methods have been used to solve for the static displacements for the mast and panel focus problems in conjunction with the CSM testbed system based on NICE/SPAR.

Ortega, James M.↗

NASA NTRS1972

Nonapplicability of linear finite element programs to the stress analysis of tires

A static finite element stress analysis of an inflated radial car tire was carried out. The deformed shape of the sidewall presents outward bulging. The analysis of a homogeneous isotropic toroidal shell shows that the problem is common to all solids of this type. The study suggests that the geometric stiffness due to the inflation pressure has to be taken into account. Also, the resulting large displacements make it necessary for the geometry to be updated at each load step.

Durand, M.↗

NASA NTRSDate not supplied

Error Localization Examples: Looking for a Needle in a Hay-stack

Finite element models (FEM) are routinely developed and used during fabrication of high dollar-value hardware. NASA as part of the pre-flight certification of launch vehicles routinely conducts vibration and static tests to calibrate models used for flight-risk assessments. As part of the calibration process, certain areas in the model are modified, using engineering judgment and sensitivity analysis, to match the test results. Unfortunately, tools to identify problem areas in the FEM using test data directly are scarce. Over the years, Error Localization Algorithms (ELA) have been proposed with very limited success. Recently, the Analytical Dynamics Model Improvement (ADMI) algorithm, which computes closed-form mass and stiffness corrections to match the test data exactly, have been shown to be effective for error localization. The paper will present several FEM example problems where ELA is used with simulated test data to determine FEM problem areas. For each example, the correct answer is shown along with ELA results. It is shown that the ELA process is able to identify general problem areas in the FEM, which are consistent with known model perturbations. However, in most cases the ELA identified area of improvement is larger than the true answer. Nonetheless, with proper optimization tools, calibration results using the ELA identified areas provide excellent results.

error localization↗

NASA NTRS1993

The effect of nonsymmetric pressure stiffness on the dynamic characteristics of Solid Rocket Motors

This paper discusses the effect of pressure on the dynamics of pre-stiffened structures such as the Advanced Solid Rocket Motor (ASRM). Previous work in which the stiffness terms resulting from constant pressure were derived has been extended to enable modeling of nonconstant pressure applied over nonenclosed volumes. These conditions will result in nonsymmetric terms in the global stiffness matrix which will not cancel out. Three new pressure stiffness elements incorporating these nonsymmetric terms have been implemented as dummy elements in COSMIC NASTRAN and have been tested on various simple examples as well as an existing ASRM NASTRAN finite element model. The results indicate that for all load cases of practical interest to the ASRM program, the nonsymmetric terms have very little effect on the dynamic characteristics. In addition, the pressure stiffness elements developed in the previous work which assumed constant pressure gave virtually the same results as the new elements even for problems in which the pressures are not constant. The original elements appear to work well as long as the pressure gradient across any individual element is no larger than about 0.75 psi/inch. The new elements are therefore most useful for determining the conditions under which the original pressure stiffness elements can be used.

Christensen, Eric R.↗

NASA NTRS1983

On a finite-difference method for solving transient viscous flow problems

A method has been developed to solve the unsteady, compressible Navier-Stokes equation with the property of consistency and the ability of minimizing the equation stiffness. It relies on innovative extensions of the state-of-the-art finite-difference techniques and is composed of: (1) the upwind scheme for split-flux and the central scheme for conventional flux terms in the inviscid and viscous regions, respectively; (2) the characteristic treatment of both inviscid and viscous boundaries; (3) an ADI procedure compatible with interior and boundary points; and (4) a scalar matrix coefficient including viscous terms. The performance of this method is assessed with four sample problems; namely, a standing shock in the Laval duct, a shock reflected from the wall, the shock-induced boundary-layer separation, and a transient internal nozzle flow. The results from the present method, an existing hybrid block method, and a well-known two-step explicit method are compared and discussed. It is concluded that this method has an optimal trade-off between the solution accuracy and computational economy, and other desirable properties for analyzing transient viscous flow problems.

Li, C. P.↗

NASA NTRS1988

Extension and validation of a method for locating damaged members in large space trusses

The damage location approach employs the control system capabilities for the structure to test the structure and measure the dynamic response. The measurements are then used in a system identification algorithm to produce a model of the damaged structure. The model is compared to one for the undamaged structure to find regions of reduced stiffness which indicate the location of damage. Kabe's 3,4 stiffness matrix adjustment method was the central identification algorithm. The strength of his method is that, with minimal data, it preserves the representation of the physical connectivity of the structure in the resulting model of the damaged truss. However, extensive storage and computational effort were required as a result. Extension of the damage location method to overcome these problems is the first part of the current work. The central system identification algorithm is replaced with the MSMT method of stiffness matrix adjustment which was previously derived by generalizing an optimal-update secant method form quasi-Newton approaches for nonlinear optimization. Validation of the extended damage location method is the second goal.

Smith, Suzanne Weaver↗