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At least 217 records · Page 12

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NASA NTRS1987

DYCAST: A finite element program for the crash analysis of structures

DYCAST is a nonlinear structural dynamic finite element computer code developed for crash simulation. The element library contains stringers, beams, membrane skin triangles, plate bending triangles and spring elements. Changing stiffnesses in the structure are accounted for by plasticity and very large deflections. Material nonlinearities are accommodated by one of three options: elastic-perfectly plastic, elastic-linear hardening plastic, or elastic-nonlinear hardening plastic of the Ramberg-Osgood type. Geometric nonlinearities are handled in an updated Lagrangian formulation by reforming the structure into its deformed shape after small time increments while accumulating deformations, strains, and forces. The nonlinearities due to combined loadings are maintained, and stiffness variation due to structural failures are computed. Numerical time integrators available are fixed-step central difference, modified Adams, Newmark-beta, and Wilson-theta. The last three have a variable time step capability, which is controlled internally by a solution convergence error measure. Other features include: multiple time-load history tables to subject the structure to time dependent loading; gravity loading; initial pitch, roll, yaw, and translation of the structural model with respect to the global system; a bandwidth optimizer as a pre-processor; and deformed plots and graphics as post-processors.

Pifko, A. B.↗

NASA NTRSDate not supplied

Corrugated Rollable Tubular Booms

A promising candidate for a new class of deployable composite boom is the COrrugated ROllable TUbular Boom (COROTUB), which is to be employed on future large space structures by the National Aeronautics and Space Administration (NASA). This is due to its two corrugated thin-shells forming a closed-section,which yields high bending and torsion stiffness, allowing for high dimensional stability. The corrugation geometry that dictates the boom cross-section shape is completely defined by closed-form analytical equations given a set of key input parameters available to the designer. Parametric studies changing two geometric variables are used to evaluate which parameters most influence the cross-section’s area moment of inertia and torsional constant. The number of corrugations, flattened height of the boom, and concave and convex corrugation radii are varied to study the complete boom design space. Deeper corrugations increase the local buckling loads (crimpling) of the thin-shell boom but reduce the area moment of inertia and therefore the global Euler buckling load of the compressive member,and thus a fine balance is sought. Finite element analyses of pure bending and compression load cases for 1.22 m boom specimens were carried out to study this design trade-off in detail. Based on previous work, several thin-ply composite laminates have been selected for the different shells that form the cross-section. Feasible boom designs with a maximized stiffness and load-carrying capacity will be manufactured to study their rollability and for experimental characterization. Structural characterization tests and additional numerical analyses will provide guidelines towards future corrugated boom designs and adequate boundary conditions to maximize the boom bending strength.

Deployable Booms↗

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 NTRS1994

Analytic Sensitivities for Shape Optimization in Equivalent Plate Structural Wing Models

Equivalent plate modeling techniques based on Ritz analysis with simple polynomials prove to be efficient tools for structural modeling of wings in the preliminary design stage. Accuracy problems are encountered, however, when these models are used to obtain finite difference behavior sensitivities with respect to planform shape. The accuracy problems are associated with the poor numerical conditioning of static and eigenvalue equations. As higher-order polynomials are being used to Improve the analysis itself, the more sensitive is the finite difference derivative to the step size used. This article describes a formulation of wing equivalent plate modeling in which it is simple to obtain analytic, explicit expressions for stiffness and mass matrix elements without the need to perform numerical integration. This formulation leads naturally to analytic expressions for the derivatives of displacements, stresses, and natural frequencies with respect to shape design variables. This article examines the accuracy of finite difference derivatives compared with the analytic derivatives, and shows that In some cases it is impossible to obtain any information of value by finite differences. Analytic sensitivities, in this case, are still sufficiently accurate for design optimization.

Livne, Eli↗

NASA NTRS2002

Fidelity of the Integrated Force Method Solution

The theory of strain compatibility of the solid mechanics discipline was incomplete since St. Venant's 'strain formulation' in 1876. We have addressed the compatibility condition both in the continuum and the discrete system. This has lead to the formulation of the Integrated Force Method. A dual Integrated Force Method with displacement as the primal variable has also been formulated. A modest finite element code (IFM/Analyzers) based on the IFM theory has been developed. For a set of standard test problems the IFM results were compared with the stiffness method solutions and the MSC/Nastran code. For the problems IFM outperformed the existing methods. Superior IFM performance is attributed to simultaneous compliance of equilibrium equation and compatibility condition. MSC/Nastran organization expressed reluctance to accept the high fidelity IFM solutions. This report discusses the solutions to the examples. No inaccuracy was detected in the IFM solutions. A stiffness method code with a small programming effort can be improved to reap the many IFM benefits when implemented with the IFMD elements. Dr. Halford conducted a peer-review on the Integrated Force Method. Reviewers' response is included.

Hopkins, Dale↗

NASA NTRS1995

Global Dynamic Modeling of Space-Geodetic Data

The proposal had outlined a year for program conversion, a year for testing and debugging, and two years for numerical experiments. We kept to that schedule. In first (partial) year, author designed a finite element for isostatic thin-shell deformation on a sphere, derived all of its algebraic and stiffness properties, and embedded it in a new finite element code which derives its basic solution strategy (and some critical subroutines) from earlier flat-Earth codes. Also designed and programmed a new fault element to represent faults along plate boundaries. Wrote a preliminary version of a spherical graphics program for the display of output. Tested this new code for accuracy on individual model plates. Made estimates of the computer-time/cost efficiency of the code for whole-earth grids, which were reasonable. Finally, converted an interactive graphical grid-designer program from Cartesian to spherical geometry to permit the beginning of serious modeling. For reasons of cost efficiency, models are isostatic, and do not consider the local effects of unsupported loads or bending stresses. The requirements are: (1) ability to represent rigid rotation on a sphere; (2) ability to represent a spatially uniform strain-rate tensor in the limit of small elements; and (3) continuity of velocity across all element boundaries. Author designed a 3-node triangle shell element which has two different sets of basis functions to represent (vector) velocity and all other (scalar) variables. Such elements can be shown to converge to the formulas for plane triangles in the limit of small size, but can also applied to cover any area smaller than a hemisphere. The difficult volume integrals involved in computing the stiffness of such elements are performed numerically using 7 Gauss integration points on the surface of the sphere, beneath each of which a vertical integral is performed using about 100 points.

Bird, Peter↗

NASA NTRS1983

Nonlinear structural dynamics analysis using a modified modal method

The procedure for predicting the nonlinear dynamic response of structural components subjected to a step loading is presented. The procedure is a modified modal method that involves a change of dependent variables from the unknown nodal degrees of freedom of the finite element model of the structure to a smaller set of generalized coordinates. This change of dependent variables uses a combination of the nonlinear static solution and some selected vibration mode shapes. The vibration mode shapes correspond to the eigenvectors obtained by solving a standard free vibration eigenvalue problem wherein the stiffness matrix is expanded about the nonlinear static solution. A strategy is also presented for determining which and how many vibration mode shapes to include in the transformation. The effect of inaccurate representation of the spatial distribution of the applied load on the nonlinear dynamic response is discussed for two classes of structural behavior. Application of the procedure to structures which exhibit a stiffening behavior and to those with a softening behavior is presented.

Knight, N. F., Jr.↗

NASA NTRS1996

Implicit Extrapolation Methods for Variable Coefficient Problems

Implicit extrapolation methods for the solution of partial differential equations are based on applying the extrapolation principle indirectly. Multigrid tau-extrapolation is a special case of this idea. In the context of multilevel finite element methods, an algorithm of this type can be used to raise the approximation order, even when the meshes are nonuniform or locally refined. Here previous results are generalized to the variable coefficient case and thus become applicable for nonlinear problems. The implicit extrapolation multigrid algorithm converges to the solution of a higher order finite element system. This is obtained without explicitly constructing higher order stiffness matrices but by applying extrapolation in a natural form within the algorithm. The algorithm requires only a small change of a basic low order multigrid method.

Jung, M.↗

NASA NTRS1976

Random vibration of compliant wall

The paper is concerned with the realistic case of two-dimensional random motion of a membrane with bending stiffness supported on a viscoelastic spring substrate and on an elastic base plate under both subsonic and supersonic boundary layer turbulence. The cross-power spectral density of surface displacements is solved in terms of design variables of the compliant wall - such as the dimensions and material properties of the membrane (Mylar), substrate (PVC foam), and panel (aluminum) - so that a sensitivity analysis can be made to examine the influence of each design variable on the surface response statistics. Three numerical examples typical of compliant wall design are worked out and their response statistics in relation to wave drag and roughness drag are assessed. The results can serve as a guideline for experimental investigation of the drag reduction concept through the use of a compliant wall.

Yang, J.-N.↗

NASA NTRS1976

A computer program for anisotropic shallow-shell finite elements using symbolic integration

A FORTRAN computer program for anisotropic shallow-shell finite elements with variable curvature is described. A listing of the program is presented together with printed output for a sample case. Computation times and central memory requirements are given for several different elements. The program is based on a stiffness (displacement) finite-element model in which the fundamental unknowns consist of both the displacement and the rotation components of the reference surface of the shell. Two triangular and four quadrilateral elements are implemented in the program. The triangular elements have 6 or 10 nodes, and the quadrilateral elements have 4 or 8 nodes. Two of the quadrilateral elements have internal degrees of freedom associated with displacement modes which vanish along the edges of the elements (bubble modes). The triangular elements and the remaining two quadrilateral elements do not have bubble modes. The output from the program consists of arrays corresponding to the stiffness, the geometric stiffness, the consistent mass, and the consistent load matrices for individual elements. The integrals required for the generation of these arrays are evaluated by using symbolic (or analytic) integration in conjunction with certain group-theoretic techniques. The analytic expressions for the integrals are exact and were developed using the symbolic and algebraic manipulation language.

Andersen, C. M.↗

NASA NTRS2012

Probabilistic Sensitivity Analysis for Launch Vehicles with Varying Payloads and Adapters for Structural Dynamics and Loads

This paper examines Probabilistic Sensitivity Analysis (PSA) methods and tools in an effort to understand their utility in vehicle loads and dynamic analysis. Specifically, this study addresses how these methods may be used to establish limits on payload mass and cg location and requirements on adaptor stiffnesses while maintaining vehicle loads and frequencies within established bounds. To this end, PSA methods and tools are applied to a realistic, but manageable, integrated launch vehicle analysis where payload and payload adaptor parameters are modeled as random variables. This analysis is used to study both Regional Response PSA (RRPSA) and Global Response PSA (GRPSA) methods, with a primary focus on sampling based techniques. For contrast, some MPP based approaches are also examined.

McGhee, David S.↗

NASA NTRS1988

Minimum weight design of rotorcraft blades with multiple frequency and stress constraints

A method is developed for the minimum weight design of helicopter rotor blades having multiple coupled flap-lag natural frequency constraints, in addition to a constraint on the minimum blade autorotation value that will ensure sufficient rotary inertia for autorotation in the event of engine failure. Design variables encompass blade taper ratio, box beam dimensions, and the magnitudes of the nonstructural weights. Optimum designs have been obtained for both rectangular and tapered blades; attention is given to the optimum blade weight effect and the blade mass and stiffness distribution effects of adding constraints on higher frequencies and stresses.

Chattopadhyay, Aditi↗

NASA NTRS1981

Substructure program for analysis of helicopter vibrations

A substructure vibration analysis which was developed as a design tool for predicting helicopter vibrations is described. The substructure assembly method and the composition of the transformation matrix are analyzed. The procedure for obtaining solutions to the equations of motion is illustrated for the steady-state forced response solution mode, and rotor hub load excitation and impedance are analyzed. Calculation of the mass, damping, and stiffness matrices, as well as the forcing function vectors of physical components resident in the base program code, are discussed in detail. Refinement of the model is achieved by exercising modules which interface with the external program to represent rotor induced variable inflow and fuselage induced variable inflow at the rotor. The calculation of various flow fields is discussed, and base program applications are detailed.

Sopher, R.↗

NASA NTRS1991

Stacking-sequence optimization for buckling of laminated plates by integer programming

Integer-programming formulations for the design of symmetric and balanced laminated plates under biaxial compression are presented. Both maximization of buckling load for a given total thickness and the minimization of total thickness subject to a buckling constraint are formulated. The design variables that define the stacking sequence of the laminate are zero-one integers. It is shown that the formulation results in a linear optimization problem that can be solved on readily available software. This is in contrast to the continuous case, where the design variables are the thicknesses of layers with specified ply orientations, and the optimization problem is nonlinear. Constraints on the stacking sequence such as a limit on the number of contiguous plies of the same orientation and limits on in-plane stiffnesses are easily accommodated. Examples are presented for graphite-epoxy plates under uniaxial and biaxial compression using a commercial software package based on the branch-and-bound algorithm.

Haftka, Raphael T.↗

NASA NTRS2011

High-Temperature Smart Structures for Engine Noise Reduction and Performance Enhancement

One of key NASA goals is to develop and integrate noise reduction technology to enable unrestricted air transportation service to all communities. One of the technical priorities of this activity has been to account for and reduce noise via propulsion/airframe interactions, identifying advanced concepts to be integrated with the airframe to mitigate these noise-producing mechanisms. An adaptive geometry chevron using embedded smart structures technology offers the possibility of maximizing engine performance while retaining and possibly enhancing the favorable noise characteristics of current designs. New high-temperature shape memory alloy (HTSMA) materials technology enables the devices to operate in both low-temperature (fan) and high-temperature (core) exhaust flows. Chevron-equipped engines have demonstrated reduced noise in testing and operational use. It is desirable to have the noise benefits of chevrons in takeoff/landing conditions, but have them deployed into a minimum drag position for cruise flight. The central feature of the innovation was building on rapidly maturing HTSMA technology to implement a next-generation aircraft noise mitigation system centered on adaptive chevron flow control surfaces. In general, SMA-actuated devices have the potential to enhance the demonstrated noise reduction effectiveness of chevron systems while eliminating the associated performance penalty. The use of structurally integrated smart devices will minimize the mechanical and subsystem complexity of this implementation. The central innovations of the effort entail the modification of prior chevron designs to include a small cut that relaxes structural stiffness without compromising the desired flow characteristics over the surface; the reorientation of SMA actuation devices to apply forces to deflect the chevron tip, exploiting this relaxed stiffness; and the use of high-temperature SMA (HTSMA) materials to enable operation in the demanding core chevron environment. The overall conclusion of these design studies was that the cut chevron concept is a critical enabling step in bringing the variable geometry core chevron within reach. The presence of the cut may be aerodynamically undesirable in some respects, but it is present only when the chevron is not immersed in the core jet exhaust. When deployed, the gap closes as the chevron tip enters the high-speed, high-temperature core stream. Aeroacoustic testing and flow visualization support the contention that this cut is inconsequential to chevron performance.

Quackenbush, Todd R.↗

NASA NTRS2005

Energy Finite Element Analysis for Computing the High Frequency Vibration of the Aluminum Testbed Cylinder and Correlating the Results to Test Data

The Energy Finite Element Analysis (EFEA) is a finite element based computational method for high frequency vibration and acoustic analysis. The EFEA solves with finite elements governing differential equations for energy variables. These equations are developed from wave equations. Recently, an EFEA method for computing high frequency vibration of structures either in vacuum or in contact with a dense fluid has been presented. The presence of fluid loading has been considered through added mass and radiation damping. The EFEA developments were validated by comparing EFEA results to solutions obtained by very dense conventional finite element models and solutions from classical techniques such as statistical energy analysis (SEA) and the modal decomposition method for bodies of revolution. EFEA results have also been compared favorably with test data for the vibration and the radiated noise generated by a large scale submersible vehicle. The primary variable in EFEA is defined as the time averaged over a period and space averaged over a wavelength energy density. A joint matrix computed from the power transmission coefficients is utilized for coupling the energy density variables across any discontinuities, such as change of plate thickness, plate/stiffener junctions etc. When considering the high frequency vibration of a periodically stiffened plate or cylinder, the flexural wavelength is smaller than the interval length between two periodic stiffeners, therefore the stiffener stiffness can not be smeared by computing an equivalent rigidity for the plate or cylinder. The periodic stiffeners must be regarded as coupling components between periodic units. In this paper, Periodic Structure (PS) theory is utilized for computing the coupling joint matrix and for accounting for the periodicity characteristics.

Vlahopoulos, Nickolas↗

NASA NTRS1986

Variable-Force Eddy-Current Damper

Variable damping achieved without problems of containing viscous fluids. Eddy-current damping obtained by moving copper or aluminum conductors through magnetic fields. Position of magnet carrier determines amount of field engagement and, therefore, amount of damping. Three advantages of concept: Magnitudes of stiffness and damping continously varied from maximum to zero without bringing rotor or shaft to stop; used in rotating machines not having viscous fluids available such as lubricating oils; produces sizable damping forces in machines that pump liquid hydrogen at - 246 degrees C and liquid oxygen at - 183 degrees C and are compact in size.

Cunningham, R. E.↗

NASA NTRS1987

The effects of pin elasticity, clearance, and friction on the stresses in a pin-loaded orthotropic plate

The effects of pin elasticity, clearance, and friction on the stresses in a pin loaded orthotropic plate are studied. The effects are studied by posing the problem as a planar contact elasticity problem, the pin and the plate being two elastic bodies which interact through contact. Coulomb friction is assumed, the pin loads the plate in one of its principal material directions, and the plate is infinite in extent. A collocation scheme and interaction, in conjunction with a complex variable series solution, are used to obtain numerical results. The contact region between the plate and pin is unknown and must be solved for as part of the solution. The same is true of the region of friction induced no slip. Two pin stiffnesses, two clearance levels, two friction levels and two laminates, a (0/+ or - 45/90)s and a (02/+ or - 45)s, are studied. The effects of pin elasticity, clearance, and friction on the load capacity of the plate are assessed by comparing the load capacity of the plate with the capacity when the pin is rigid, perfectly fitting, and frictionless.

Hyer, M. W.↗