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NASA NTRS1977

A multilevel approach for minimum weight structural design including local and system buckling constraints

A rational multilevel approach for minimum weight structural design of truss and wing structures including local and system buckling constraints is presented. Overall proportioning of the structure is achieved at the system level subject to strength, displacement and system buckling constraints, while the detailed component designs are carried out separately at the component level satisfying local buckling constraints. Total structural weight is taken to be the objective function at the system level while employing the change in the equivalent system stiffness of the component as the component level objective function. Finite element analysis is used to predict static response while system buckling behavior is handled by incorporating a geometric stiffness matrix capability. Buckling load factors and the corresponding mode shapes are obtained by solving the eigenvalue problem associated with the assembled elastic stiffness and geometric stiffness matrices for the structural system. At the component level various local buckling failure modes are guarded against using semi-empirical formulas. Mathematical programming techniques are employed at both the system and component level.

Schmit, L. A., Jr.↗

NASA NTRS1976

Stiffness coupling application to modal synthesis program, users guide

A FORTRAN IV computer program used to perform modal synthesis of structures by stiffness coupling, using the dynamic transformation method is described. The program was named SCAMP (Stiffness Coupling Approach Modal-Synthesis Program). The program begins with the entry of a substructure's physical mode shapes and eigenvalues or a substructure's mass and stiffness matrix. If the mass and stiffness matrices are entered, the eigen problem for the individual substructure is solved. Provisions are included for a maximum of 20 substructures which are coupled by stiffness matrix springs. Each substructure has a number degrees of freedom (DOF), except that for DOF greater than 100; vector sets having maximum row and column size of 100 were generated prior to entering SCAMP. The substructures are then coupled together via coupling springs, and the dynamic transformation is used to reduce the size of the eigen problem.

Kuhar, E. J.↗

NASA NTRS1991

Simplified computational methods for elastic and elastic-plastic fracture problems

This paper presents an overview of some of the recent (1984-1991) developments in computational/analytical methods in the mechanics of fracture: (i) analytical solutions for elliptical or circular cracks embedded in isotropic or transversely isotropic solids (the crack-plane being at an arbitrary angle to the axis of transverse isotropy), with crack-faces being subjected to arbitrary tractions; (ii) finite-element or boundary-element alternating methods for two- and three-dimensional crack problems; (iii) a "direct-stiffness" method for stiffened panels with flexible fasteners and with multiple cracks, using the alternating method; (iv) multiplesite-damage near a row of fastener holes; (v) analysis of cracks with bonded repair patches; (vi) methods for generation of weight-functions for 2- and 3-D crack problems, and (vii) domain-integral methods for elastic-plastic or inelastic crack mechanics.

Aging Aircraft↗

NASA NTRS1993

Optimization of blade arrangement in a randomly mistuned cascade using simulated annealing

This paper presents preliminary results of an investigation on mistuning of bladed-disk assemblies aimed at capturing the benefits of mistuning on stability, while at the same time, minimizing the adverse effects on response by solving the following problem: given a set of N turbine blades, each being a small random perturbation of the same nominal blade, determine the best arrangement of the N blades in a mistuned cascade with regard to aeroelastic response. In the studies reported here, mistuning of the blades is restricted to small differences in torsional stiffness. The large combinatorial optimization problem of seeking the best arrangement by blade exchanges is solved using a simulated annealing algorithm.

Thompson, Edward A.↗

NASA NTRS1983

Integrated technology rotor/flight research rotor concept definition study

As part of the Integrated Technology Rotor/Flight Research Rotor (ITR/FRR) Program a number of advanced rotor system designs were conceived and investigated. From these, several were chosen that best meet the started ITR goals with emphasis on stability, reduced weight and hub drag, simplicity, low head moment stiffness, and adequate strength and fatigue life. It was concluded that obtaining low hub moment stiffness was difficult when only the blade flexibility of bearingless rotor blades is considered, unacceptably low fatigue life being the primary problem. Achieving a moderate hub moment stiffness somewhat higher than state of the art articulated rotors in production today is possible within the fatigue life constraint. Alternatively, low stiffness is possible when additional rotor elements, besides the blades themselves, provide part of the rotor flexibility. Two primary designs evolved as best meeting the general ITR requirements that presently exist. An I shaped flexbeam with an external torque tube can satisfy the general goals but would have either higher stiffness or reduced fatigue life. The elastic gimbal rotor can achieve a better combination of low stiffness and high fatigue life but would be a somewhat heavier design and possibly exhibit a higher risk of aeromechanical instability.

Carlson, R. G.↗

NASA NTRS1995

Reliability enhancement of Navier-Stokes codes through convergence acceleration

Methods for enhancing the reliability of Navier-Stokes computer codes through improving convergence characteristics are presented. The improving of these characteristics decreases the likelihood of code unreliability and user interventions in a design environment. The problem referred to as a 'stiffness' in the governing equations for propulsion-related flowfields is investigated, particularly in regard to common sources of equation stiffness that lead to convergence degradation of CFD algorithms. Von Neumann stability theory is employed as a tool to study the convergence difficulties involved. Based on the stability results, improved algorithms are devised to ensure efficient convergence in different situations. A number of test cases are considered to confirm a correlation between stability theory and numerical convergence. The examples of turbulent and reacting flow are presented, and a generalized form of the preconditioning matrix is derived to handle these problems, i.e., the problems involving additional differential equations for describing the transport of turbulent kinetic energy, dissipation rate and chemical species. Algorithms for unsteady computations are considered. The extension of the preconditioning techniques and algorithms derived for Navier-Stokes computations to three-dimensional flow problems is discussed. New methods to accelerate the convergence of iterative schemes for the numerical integration of systems of partial differential equtions are developed, with a special emphasis on the acceleration of convergence on highly clustered grids.

Merkle, Charles L.↗

NASA NTRS1977

Complex eigenvalue extraction in NASTRAN by the tridiagonal reduction (FEER) method

An extension of the Tridiagonal Reduction (FEER) method to complex eigenvalue analysis in NASTRAN is described. As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum are extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order is much lower than that of the full size problem. The reduction process is effected automatically, and thus avoids the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admits mass, damping and stiffness matrices which are unrestricted in character, i.e., they may be real, complex, symmetric or unsymmetric, singular or non-singular.

Newman, M.↗

NASA NTRS1978

Extension of the tridiagonal reduction (FEER) method for complex eigenvalue problems in NASTRAN

As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum were extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order was much lower than that of the full size problem. The reduction process was effected automatically, and thus avoided the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admitted mass, damping, and stiffness matrices which were unrestricted in character, i.e., they might be real, symmetric or nonsymmetric, singular or nonsingular.

Newman, M.↗

NASA NTRS1982

Space station preliminary design report

The results of a 3 month preliminary design and analysis effort is presented. The configuration that emerged consists of a very stiff deployable truss structure with an overall triangular cross section having universal modules attached at the apexes. Sufficient analysis was performed to show feasibility of the configuration. An evaluation of the structure shows that desirable attributes of the configuration are: (1) the solar cells, radiators, and antennas will be mounted to stiff structure to minimize control problems during orbit maintenance and correction, docking, and attitude control; (2) large flat areas are available for mounting and servicing of equipment; (3) Large mass items can be mounted near the center of gravity of the system to minimize gravity gradient torques; (4) the trusses are lightweight structures and can be transported into orbit in one Shuttle flight; (5) the trusses are expandable and will require a minimum of EVA; and (6) the modules are anticipated to be structurally identical except for internal equipment to minimize cost.

Source record↗

NASA NTRS1987

Modeling and control of beam-like structures

The most popular finite element codes are based upon appealing theories of convergence of modal frequencies. For example, the popularity of cubic elements for beam-like structures is due to the rapid convergence of modal frequencies and stiffness properties. However, for those problems in which the primary consideration is the accuracy of response of the structure at specified locations it is more important to obtain accuracy in the modal costs than in the modal frequencies. The modal cost represents the contribution of a mode in the norm of the response vector. This paper provides a complete modal cost analysis for beam-like continua. Upper bounds are developed for mode truncation errors in the model reduction process and modal cost analysis dictates which modes to retain in order to reduce the model for control design purposes.

Hu, A.↗

NASA NTRS1988

Modal cost analysis for simple continua

The most popular finite element codes are based upon appealing theories of convergence of modal frequencies. For example, the popularity of cubic elements for beam-like structures is due to the rapid convergence of modal frequencies and stiffness properties. However, for those problems in which the primary consideration is the accuracy of response of the structure at specified locations, it is more important to obtain accuracy in the modal costs than in the modal frequencies. The modal cost represents the contribution of a mode in the norm of the response vector. This paper provides a complete modal cost analysis for simple continua such as beam-like structures. Upper bounds are developed for mode truncation errors in the model reduction process and modal cost analysis dictates which modes to retain in order to reduce the model for control design purposes.

Hu, A.↗

NASA NTRS1991

A prototype power assist EVA glove

The most recent generation of space suit EVA gloves has addressed the problem of loose fit and stiffness in the fingers, but it remains difficult to build a glove assembly with low metacarpophalangeal joint stiffness. Fatigue due to constantly displacing the glove from a neutral position has been reported as the limiting factor in some EVA activities. This paper outlines an actuation system that uses gas filled bladders attached to the back of the EVA glove to provide the necessary force to bend the glove at the metacarpal joint, thus providing greater endurance during finger grasping tasks. A simple on-off controller senses hand movement through small pressure sensors between the finger and the glove restraint. The controller then fills or exhausts the bladders on the back of the glove to effectively move the neutral position of the glove as the hand inside moves.

Main, John A.↗

NASA NTRS1993

Modelling of thick composites using a layerwise laminate theory

The layerwise laminate theory of Reddy (1987) is used to develop a layerwise, two-dimensional, displacement-based, finite element model of laminated composite plates that assumes a piecewise continuous distribution of the tranverse strains through the laminate thickness. The resulting layerwise finite element model is capable of computing interlaminar stresses and other localized effects with the same level of accuracy as a conventional 3D finite element model. Although the total number of degrees of freedom are comparable in both models, the layerwise model maintains a 2D-type data structure that provides several advantages over a conventional 3D finite element model, e.g. simplified input data, ease of mesh alteration, and faster element stiffness matrix formulation. Two sample problems are provided to illustrate the accuracy of the present model in computing interlaminar stresses for laminates in bending and extension.

Robbins, D. H., Jr.↗

NASA NTRS1990

Shape optimization for maximum stability and dynamic stiffness

Any optimization of structures for maximum stability or for maximum dynamic stiffness deals with an eigenvalue problem. The goal of this optimization is to raise the lowest eigenvalue (or eigenvalues) of the problem to its highest (optimal) level at a constant volume of the structure. Likely the lowest eigenvalue may be either inherently multi-modal or it can become multi-modal as a result of the optimization process. The multimodeness introduces some ambiguity to the eigenvalue problem and make the optimization difficult to handle. Thus far, only the simplest cases of multi-modal structures have been effectively optimized using rather elaborate analytical methods. Numerous publications report design of a minimum volume structure with different eigenvalues constraints, in which, however, the modality of the problem is assumed a priori. The method presented here utilizes a multi-modal optimality criteria and allows for inclusion of an arbitrary number of buckling or vibrations modes which might influence the optimization process. The real multi-modality of the problem, that is the number of modes participating in the final optimal design is determined iteratively. Because of a natural use of the FEM technique the method is easy to program and might be helpful in design of large flexible space structures.

Szyszkowski, W.↗

NASA NTRS1993

Computational techniques for high-speed flows with viscous and chemical effects

Algorithms for solving the Euler and the Navier-Stokes equations in conjunction with chemical kinetic equations are presented. The convective flux is estimated from a quasi one dimensional interpolation procedure. Shock, contact, and expansion waves and thermochemical nonequilibrium phenomena are captured by the Lax-Friedrichs technique. Relaxation techniques were developed to enhance their effectiveness in dealing with spatial and temporal stiffness associated with the physical problems. Both explicit and implicit smoothers were implemented into the standard multigrid time stepping method. Unsteady and steady scalar problems are discussed. A perfect gas and equilibrium air shock tube problem is investigated. Numerical schemes and techniques are compared for the problems of shock and boundary layer interaction and three dimensional viscous, nonequilibrium flow encompassing an aerobrake. The results are comparable in accuracy against other high order non-oscillatory techniques. The multigrid methods are assessed using a Mach 8 flow over a complete planar body, a sphere, and a blunt delta wing at 20 deg incidence. Applying an implicit multigrid method on a nested grid of 128 by 64 nodes the reduction factor is 0.25. The central processing unit reduction factor is 2.2 after both the single and multigrid Runge-Kutta solutions converged to machine zero on a grid of 37 by 41 by 73 nodes.

Li, C. P.↗

NASA NTRS2006

Low-Velocity Impact Response of Sandwich Beams with Functionally Graded Core

The problem of low-speed impact of a one-dimensional sandwich panel by a rigid cylindrical projectile is considered. The core of the sandwich panel is functionally graded such that the density, and hence its stiffness, vary through the thickness. The problem is a combination of static contact problem and dynamic response of the sandwich panel obtained via a simple nonlinear spring-mass model (quasi-static approximation). The variation of core Young's modulus is represented by a polynomial in the thickness coordinate, but the Poisson's ratio is kept constant. The two-dimensional elasticity equations for the plane sandwich structure are solved using a combination of Fourier series and Galerkin method. The contact problem is solved using the assumed contact stress distribution method. For the impact problem we used a simple dynamic model based on quasi-static behavior of the panel - the sandwich beam was modeled as a combination of two springs, a linear spring to account for the global deflection and a nonlinear spring to represent the local indentation effects. Results indicate that the contact stiffness of thc beam with graded core Increases causing the contact stresses and other stress components in the vicinity of contact to increase. However, the values of maximum strains corresponding to the maximum impact load arc reduced considerably due to grading of thc core properties. For a better comparison, the thickness of the functionally graded cores was chosen such that the flexural stiffness was equal to that of a beam with homogeneous core. The results indicate that functionally graded cores can be used effectively to mitigate or completely prevent impact damage in sandwich composites.

Apetre, N. A.↗

NASA NTRS1995

Analysis and Development of Finite Element Methods for the Study of Nonlinear Thermomechanical Behavior of Structural Components

Underintegrated methods are investigated with respect to their stability and convergence properties. The focus was on identifying regions where they work and regions where techniques such as hourglass viscosity and hourglass control can be used. Results obtained show that underintegrated methods typically lead to finite element stiffness with spurious modes in the solution. However, problems exist (scalar elliptic boundary value problems) where underintegrated with hourglass control yield convergent solutions. Also, stress averaging in underintegrated stiffness calculations does not necessarily lead to stable or convergent stress states.

Oden, J. Tinsley↗

NASA NTRS1996

Preconditioned Mixed Spectral Element Methods for Elasticity and Stokes Problems

Preconditioned iterative methods for the indefinite systems obtained by discretizing the linear elasticity and Stokes problems with mixed spectral elements in three dimensions are introduced and analyzed. The resulting stiffness matrices have the structure of saddle point problems with a penalty term, which is associated with the Poisson ratio for elasticity problems or with stabilization techniques for Stokes problems. The main results of this paper show that the convergence rate of the resulting algorithms is independent of the penalty parameter, the number of spectral elements Nu and mildly dependent on the spectral degree eta via the inf-sup constant. The preconditioners proposed for the whole indefinite system are block-diagonal and block-triangular. Numerical experiments presented in the final section show that these algorithms are a practical and efficient strategy for the iterative solution of the indefinite problems arising from mixed spectral element discretizations of elliptic systems.

Pavarino, Luca F.↗