Search NASA⌕ Search

SEARCH · Search NASA

Results for “variable stiffness”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Flexible body dynamic stability for high performance aircraft

Dynamic equations which include the effects of unsteady aerodynamic forces and a flexible body structure were developed for a free flying high performance fighter aircraft. The linear and angular deformations are assumed to be small in the body reference frame, allowing the equations to be linearized in the deformation variables. Equations for total body dynamics and flexible body dynamics are formulated using the hybrid coordinate method and integrated in a state space format. A detailed finite element model of a generic high performance fighter aircraft is used to generate the mass and stiffness matrices. Unsteady aerodynamics are represented by a rational function approximation of the doublet lattice matrices. The equations simplify for the case of constant angular rate of the body reference frame, allowing the effect of roll rate to be studied by computing the eigenvalues of the system. It is found that the rigid body modes of the aircraft are greatly affected by introducing a constant roll rate, while the effect on the flexible modes is minimal for this configuration.

Goforth, E. A.↗
NASA NTRS1992

A three-dimensional nonlinear Timoshenko beam based on the core-congruential formulation

A three-dimensional, geometrically nonlinear two-node Timoshenkoo beam element based on the total Larangrian description is derived. The element behavior is assumed to be linear elastic, but no restrictions are placed on magnitude of finite rotations. The resulting element has twelve degrees of freedom: six translational components and six rotational-vector components. The formulation uses the Green-Lagrange strains and second Piola-Kirchhoff stresses as energy-conjugate variables and accounts for the bending-stretching and bending-torsional coupling effects without special provisions. The core-congruential formulation (CCF) is used to derived the discrete equations in a staged manner. Core equations involving the internal force vector and tangent stiffness matrix are developed at the particle level. A sequence of matrix transformations carries these equations to beam cross-sections and finally to the element nodal degrees of freedom. The choice of finite rotation measure is made in the next-to-last transformation stage, and the choice of over-the-element interpolation in the last one. The tangent stiffness matrix is found to retain symmetry if the rotational vector is chosen to measure finite rotations. An extensive set of numerical examples is presented to test and validate the present element.

Crivelli, Luis A.↗
NASA NTRS1996

Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization

Fast methods are proposed for solving the system K(sub N)x = b resulting from the discretization of self-adjoint elliptic equations in three dimensional domains by the spectral element method. The domain is decomposed into hexahedral elements, and in each of these elements the discretization space is formed by polynomials of degree N in each variable. Gauss-Lobatto-Legendre (GLL) quadrature rules replace the integrals in the Galerkin formulation. This system is solved by the preconditioned conjugate gradients method. The conforming finite element space on the GLL mesh consisting of piecewise Q(sub 1) elements produces a stiffness matrix K(sub h) that is spectrally equivalent to the spectral element stiffness matrix K(sub N). The action of the inverse of K(sub h) is expensive for large problems, and is therefore replaced by a Schwarz preconditioner B(sub h) of this finite element stiffness matrix. The preconditioned operator then becomes B(sub h)(exp -l)K(sub N). The technical difficulties stem from the nonregularity of the mesh. Tools to estimate the convergence of a large class of new iterative substructuring and overlapping Schwarz preconditioners are developed. This technique also provides a new analysis for an iterative substructuring method proposed by Pavarino and Widlund for the spectral element discretization.

Casarin, Mario↗
NASA NTRS1982

Integrating matrix solution of the hybrid state vector equations for beam vibration

A simple, versatile, and efficient computational technique has been developed for dynamic analysis of linear elastic beam and rod type of structures. Moreover, the method provides a rather general solution approach for two-point boundary value problems that are described by a single independent spatial variable. For structural problems, the method is implemented by a mixed state vector formulation of the differential equations, combined with an integrating matrix solution procedure. Highly accurate solutions are easily achieved with this approach. Example solutions are given for beam vibration problems including discontinuous stiffness and mass parameters, elastic restraint boundary conditions, concentrated inertia loading, and rigid body modes

Lehman, L. L.↗
NASA NTRS2008

Reliability and Confidence Interval Analysis of a CMC Turbine Stator Vane

High temperature ceramic matrix composites (CMC) are being explored as viable candidate materials for hot section gas turbine components. These advanced composites can potentially lead to reduced weight, enable higher operating temperatures requiring less cooling and thus leading to increased engine efficiencies. However, these materials are brittle and show degradation with time at high operating temperatures due to creep as well as cyclic mechanical and thermal loads. In addition, these materials are heterogeneous in their make-up and various factors affect their properties in a specific design environment. Most of these advanced composites involve two- and three-dimensional fiber architectures and require a complex multi-step high temperature processing. Since there are uncertainties associated with each of these in addition to the variability in the constituent material properties, the observed behavior of composite materials exhibits scatter. Traditional material failure analyses employing a deterministic approach, where failure is assumed to occur when some allowable stress level or equivalent stress is exceeded, are not adequate for brittle material component design. Such phenomenological failure theories are reasonably successful when applied to ductile materials such as metals. Analysis of failure in structural components is governed by the observed scatter in strength, stiffness and loading conditions. In such situations, statistical design approaches must be used. Accounting for these phenomena requires a change in philosophy on the design engineer s part that leads to a reduced focus on the use of safety factors in favor of reliability analyses. The reliability approach demands that the design engineer must tolerate a finite risk of unacceptable performance. This risk of unacceptable performance is identified as a component's probability of failure (or alternatively, component reliability). The primary concern of the engineer is minimizing this risk in an economical manner. The methods to accurately determine the service life of an engine component with associated variability have become increasingly difficult. This results, in part, from the complex missions which are now routinely considered during the design process. These missions include large variations of multi-axial stresses and temperatures experienced by critical engine parts. There is a need for a convenient design tool that can accommodate various loading conditions induced by engine operating environments, and material data with their associated uncertainties to estimate the minimum predicted life of a structural component. A probabilistic composite micromechanics technique in combination with woven composite micromechanics, structural analysis and Fast Probability Integration (FPI) techniques has been used to evaluate the maximum stress and its probabilistic distribution in a CMC turbine stator vane. Furthermore, input variables causing scatter are identified and ranked based upon their sensitivity magnitude. Since the measured data for the ceramic matrix composite properties is very limited, obtaining a probabilistic distribution with their corresponding parameters is difficult. In case of limited data, confidence bounds are essential to quantify the uncertainty associated with the distribution. Usually 90 and 95% confidence intervals are computed for material properties. Failure properties are then computed with the confidence bounds. Best estimates and the confidence bounds on the best estimate of the cumulative probability function for R-S (strength - stress) are plotted. The methodologies and the results from these analyses will be discussed in the presentation.

Murthy, Pappu L. N.↗
NASA NTRS2009

Modeling and Simulation of Variable Mass, Flexible Structures

The advent of the new Ares I launch vehicle has highlighted the need for advanced dynamic analysis tools for variable mass, flexible structures. This system is composed of interconnected flexible stages or components undergoing rapid mass depletion through the consumption of solid or liquid propellant. In addition to large rigid body configuration changes, the system simultaneously experiences elastic deformations. In most applications, the elastic deformations are compatible with linear strain-displacement relationships and are typically modeled using the assumed modes technique. The deformation of the system is approximated through the linear combination of the products of spatial shape functions and generalized time coordinates. Spatial shape functions are traditionally composed of normal mode shapes of the system or even constraint modes and static deformations derived from finite element models of the system. Equations of motion for systems undergoing coupled large rigid body motion and elastic deformation have previously been derived through a number of techniques [1]. However, in these derivations, the mode shapes or spatial shape functions of the system components were considered constant. But with the Ares I vehicle, the structural characteristics of the system are changing with the mass of the system. Previous approaches to solving this problem involve periodic updates to the spatial shape functions or interpolation between shape functions based on system mass or elapsed mission time. These solutions often introduce misleading or even unstable numerical transients into the system. Plus, interpolation on a shape function is not intuitive. This paper presents an approach in which the shape functions are held constant and operate on the changing mass and stiffness matrices of the vehicle components. Each vehicle stage or component finite element model is broken into dry structure and propellant models. A library of propellant models is used to describe the distribution of mass in the fuel tank or Solid Rocket Booster (SRB) case for various propellant levels. Based on the mass consumed by the liquid engine or SRB, the appropriate propellant model is coupled with the dry structure model for the stage. Then using vehicle configuration data, the integrated vehicle model is assembled and operated on by the constant system shape functions. The system mode shapes and frequencies can then be computed from the resulting generalized mass and stiffness matrices for that mass configuration. The rigid body mass properties of the vehicle are derived from the integrated vehicle model. The coupling terms between the vehicle rigid body motion and elastic deformation are also updated from the constant system shape functions and the integrated vehicle model. This approach was first used to analyze variable mass spinning beams and then prototyped into a generic dynamics simulation engine. The resulting code was tested against Crew Launch Vehicle (CLV-)class problems worked in the TREETOPS simulation package and by Wilson [2]. The Ares I System Integration Laboratory (SIL) is currently being developed at the Marshall Space Flight Center (MSFC) to test vehicle avionics hardware and software in a hardware-in-the-loop (HWIL) environment and certify that the integrated system is prepared for flight. The Ares I SIL utilizes the Ares Real-Time Environment for Modeling, Integration, and Simulation (ARTEMIS) tool to simulate the launch vehicle and stimulate avionics hardware. Due to the presence of vehicle control system filters and the thrust oscillation suppression system, which are tuned to the structural characteristics of the vehicle, ARTEMIS must incorporate accurate structural models of the Ares I launch vehicle. The ARTEMIS core dynamics simulation models the highly coupled nature of the vehicle flexible body dynamics, propellant slosh, and vehicle nozzle inertia effects combined with mass and flexible body properties that vary significant with time during the flight. All forces that act on the vehicle during flight must be simulated, including deflected engine thrust force, spatially distributed aerodynamic forces, gravity, and reaction control jet thrust forces. These forces are used to excite an integrated flexible vehicle, slosh, and nozzle dynamics model for the vehicle stack that simulates large rigid body translations and rotations along with small elastic deformations. Highly effective matrix math operations on a distributed, threaded high-performance simulation node allow ARTEMIS to retain up to 30 modes of flex for real-time simulation. Stage elements that separate from the stack during flight are propagated as independent rigid six degrees of freedom (6DOF) bodies. This paper will present the formulation of the resulting equations of motion, solutions to example problems, and describe the resulting dynamics simulation engine within ARTEMIS.

Tobbe, Patrick A.↗
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 NTRS2019

Inducing Bistability in Collapsible Tubular Masts Booms with Thin-Ply Composite Shells

Bistable rollable booms are favorable when a low strain energy requirement for the coiled state is imposed and have more controllable deployment when compared to monostable booms. An inextensional analytical model describing the bending deformation mechanics of Collapsible Tubular Mast (CTM) booms was used to determine how design variables induce bistability, or the existence of two strain energy wells in the rolled-up and unrolled states. The effects of varying lamina material, laminate layup, and shell arc geometries between different inner and outer shell segments on the second strain energy well and stiffness properties were determined for boom cross-sections formed by circular segments. The full design space for two-walled composite CTM booms was explored to evaluate the validity of the developed analytical model. Optimized CTM boom designs were experimentally characterized for comparisons against model results. The model under-predicted the stable coiled diameter of the co-cured two-walled booms by up to 8.9% and 23.4% for the individual thin shells wrapped alone.

Andrew J Lee↗
NASA NTRS1981

Fatigue mechanisms in metal matrix composite laminates

Certain aspects of the damage process are described. The shakedown phenomenon in laminates is first explained. This is followed by a presentation of matrix test data used in evaluating the shakedown limits of the laminates used in the subsequent experiments. Test results suggesting that there is no loss of elastic stiffness in laminates loaded at constant amplitudes within their shakedown limits are presented. Damage accumulation and the development of the saturation damage state are illustrated by experimental results on specimens loaded outside the shakedown range. Attention is also given to the behavior of laminates subjected to variable cyclic loading.

Dvorak, G. J.↗
NASA NTRSDate not supplied

Aeroelastic Analysis of an Urban Air Mobility Rotor in Forward Edgewise Flight

Urban Air Mobility vehicle concepts represent a new type of vertical lift machine. From the use of multirotor configurations to the use of variable RPM for thrust control of rigid, propeller-style rotors, many of the UAM concepts observed in industry have departed significantly from traditional VTOL designs. While such novel vehicle types may provide beneficial mission capability and efficiency, they have not been as thoroughly studied as more traditional configurations, and new aeromechanics analysis must be conducted. Operating states such as low-tip-speed rotors in edgewise flight may prove to yield unusual aeroelastic behavior and must be investigated. In the present work, a rotorcraft comprehensive analysis is used to analyze the aeroelastic characteristics of a fixed-pitch, variable RPM rotor in edgewise flight. The rotor model, a three-bladed, fixed pitch propeller, was developed in a previous work. Floquet theory analysis is used to capture the periodic nature of the dynamics. Parameters such as rotor rotational speed, forward flight speed, and blade torsion stiffness are varied and their impact on performance and stability are assessed. A value of torsion stiffness is identified to yield stable flight from 0-100 kts with a wide range of RPM values. The results may be used to provide insight into the aeroelastic characteristics of certain UAM-type rotors.

Aeroelastic Analysis↗
NASA NTRS2015

Analysis of Human-Spacesuit Interaction

Astronauts sustain injuries of various natures such as finger delamination, joint pain, and redness due to their interaction with the space suit. The role of the Anthropometry and Biomechanics Facility is to understand the biomechanics, environmental variables, and ergonomics of the suit. This knowledge is then used to make suggestions for improvement in future iterations of the space suit assembly to prevent injuries while allowing astronauts maneuverability, comfort, and tactility. The projects I was involved in were the Extravehicular Mobility Unit (EMU) space suit stiffness study and the glove feasibility study. The EMU project looked at the forces exerted on the shoulder, arm, and wrist when subjects performed kinematic tasks with and without a pressurized suit. The glove study consisted of testing three conditions - the Series 4000 glove, the Phase VI glove, and the no glove condition. With more than forty channels of sensor data total, it was critical to develop programs that could analyze data with basic descriptive statistics and generate relevant graphs to help understand what happens within the space suit and glove. In my project I created a Graphical User Interface (GUI) in MATLAB that would help me visualize what each sensor was doing within a task. The GUI is capable of displaying overlain plots and can be synchronized with video. This was helpful during the stiffness testing to visualize how the forces on the arm acted while the subject performed tasks such as shoulder adduction/abduction and bicep curls. The main project of focus, however, was the glove comparison study. I wrote MATLAB programs which generated movies of the strain vectors during specific tasks. I also generated graphs that summarized the differences between each glove for the strain, shear and FSR sensors. Preliminary results indicate that the Phase VI glove places less strain and shear on the hand. Future work includes continued data analysis of surveys and sensor data. In the end, the ideal glove is one that provides more tactility for the astronauts but lessens injuries. Often times, a more tactile glove transmits forces better to the hand; thus, achieving a balance of both a tactile and safe glove is the main challenge present.

Thomas, Neha↗
NASA NTRS1993

Synthesis and analysis of a new class of six-degree-of-freedom parallel minimanipulators

A new class of six-degree-of-freedom parallel minimanipulators capable of providing high resolution and high-stiffness for fine position and force control in a hybrid serial-parallel manipulator system is presented. Positional resolution and stiffness of minimanipulators are improved using two-degree-of-freedom planar linkages as drivers. The minimanipulators are based on only three inextensible limbs, as opposed to most of the six-limbed parallel manipulators, which makes it possible to reduce its direct kinematics to solving a polynomial in a single variable and to diminish possibility of mechanical interference between limbs. The base-mounted minimanipulator actuators are characterized by high payload capacity, small actuator size, and low power dissipitation.

Tsai, Lung-Wen↗
NASA NTRS1978

An algorithm for optimal structural design with frequency constraints

The paper presents a finite element method for minimum weight design of structures with lower-bound constraints on the natural frequencies, and upper and lower bounds on the design variables. The design algorithm is essentially an iterative solution of the Kuhn-Tucker optimality criterion. The three most important features of the algorithm are: (1) a small number of design iterations are needed to reach optimal or near-optimal design, (2) structural elements with a wide variety of size-stiffness may be used, the only significant restriction being the exclusion of curved beam and shell elements, and (3) the algorithm will work for multiple as well as single frequency constraints. The design procedure is illustrated with three simple problems.

Kiusalaas, J.↗
NASA NTRS1993

IPACS (Integrated Probabilistic Assessment of Composite Structures): Code development and applications

A methodology and attendant computer code have been developed and are described to computationally simulate the uncertain behavior of composite structures. The uncertain behavior includes buckling loads, stress concentration factors, displacements, stress/strain etc., which are the consequences of the inherent uncertainties (scatter) in the primitive (independent random) variables (constituent, ply, laminate and structural) that describe the composite structures. The computer code, IPACS (Integrated Probabilistic Assessment of Composite Structures), can handle both composite mechanics and composite structures. Application to probabilistic composite mechanics is illustrated by its uses to evaluate the uncertainties in the major Poisson's ratio and in laminate stiffness and strength. IPACS application to probabilistic structural analysis is illustrated by its use to evaluate the uncertainties in the buckling of a composite plate, in the stress concentration factor in a composite panel and in the vertical displacement and ply stress in a composite aircraft wing segment.

Chamis, C. C.↗
NASA NTRS1985

A survey of unified constitutive theories

The state of the art of time temperature dependent elastic viscoplastic constitutive theories which are based on the unified approach werre assessed. This class of constitutive theories is characterized by the use of kinetic equations and internal variables with appropriate evolutionary equations for treating all aspects of inelastic deformation including plasticity, creep, and stress relaxation. More than 10 such unified theories which are shown to satisfy the uniqueness and stability criteria imposed by Drucker's postulate and Ponter's inequalities are identified. The theories are compared for the types of flow law, kinetic equation, evolutionary equation of the internal variables, and treatment of temperature dependence. The similarities and differences of these theories are outlined in terms of mathematical formulations and illustrated by comparisons of theoretical calculations with experimental results which include monotonic stress-strain curves, cyclic hysteresis loops, creep and stress relaxation rates, and thermomechanical loops. Numerical methods used for integrating these stiff time temperature dependent constitutive equations are reviewed.

Chan, K. S.↗
NASA NTRS1993

Probabilistic assessment of composite structures

A methodology and attendant computer code were developed and are used to computationally simulate the uncertain behavior of composite structures. The uncertain behavior includes buckling loads, stress concentration factors, displacements, stress/strain, etc., which are the consequences of the inherent uncertainties (scatter) in the primitive (independent random) variables (constituent, ply, laminate, and structural) that describe the composite structures. The computer code is IPACS (Integrated Probabilistic Assessment of Composite Structures). IPACS can simulate both composite mechanics and composite structural behavior. Application to probabilistic composite mechanics is illustrated by its use to evaluate the uncertainties in the major Poisson's ratio and in laminate stiffness and strength. IPACS' application to probabilistic structural analysis is illustrated by its used to evaluate the uncertainties in the buckling of a composite plate, the stress concentration factor in a composite panel, and the vertical displacement and ply stress in a composite aircraft wing segment. IPACS' application to probabilistic design is illustrated by its use to assess the thin composite shell (pipe).

Chamis, C. C.↗
NASA NTRS1993

Preconditioning for the Navier-Stokes equations with finite-rate chemistry

The extension of Van Leer's preconditioning procedure to generalized finite-rate chemistry is discussed. Application to viscous flow is begun with the proper preconditioning matrix for the one-dimensional Navier-Stokes equations. Eigenvalue stiffness is resolved and convergence-rate acceleration is demonstrated over the entire Mach-number range from nearly stagnant flow to hypersonic. Specific benefits are realized at the low and transonic flow speeds typical of complete propulsion-system simulations. The extended preconditioning matrix necessarily accounts for both thermal and chemical nonequilibrium. Numerical analysis reveals the possible theoretical improvements from using a preconditioner for all Mach number regimes. Numerical results confirm the expectations from the numerical analysis. Representative test cases include flows with previously troublesome embedded high-condition-number areas. Van Leer, Lee, and Roe recently developed an optimal, analytic preconditioning technique to reduce eigenvalue stiffness over the full Mach-number range. By multiplying the flux-balance residual with the preconditioning matrix, the acoustic wave speeds are scaled so that all waves propagate at the same rate, an essential property to eliminate inherent eigenvalue stiffness. This session discusses a synthesis of the thermochemical nonequilibrium flux-splitting developed by Grossman and Cinnella and the characteristic wave preconditioning of Van Leer into a powerful tool for implicitly solving two and three-dimensional flows with generalized finite-rate chemistry. For finite-rate chemistry, the state vector of unknowns is variable in length. Therefore, the preconditioning matrix extended to generalized finite-rate chemistry must accommodate a flexible system of moving waves. Fortunately, no new kind of wave appears in the system. The only existing waves are entropy and vorticity waves, which move with the fluid, and acoustic waves, which propagate in Mach number dependent directions. The nonequilibrium vibrational energies and species densities in the unknown state vector act strictly as convective waves. The essential concept for extending the preconditioning to generalized chemistry models is determining the differential variables which symmetrize the flux Jacobians. The extension is then straight-forward. This algorithm research effort will be released in a future version of the production level computational code coined the General Aerodynamic Simulation Program (GASP), developed by Walters, Slack, and McGrory.

Godfrey, Andrew G.↗
NASA NTRS2004

Turbine Engine Stability/Instability With Rub Forces Axisymmetric Rotor-Support Stiffness

The stability/instability condition of a turbine rotor with axisymmetric supports is determined in the presence of gyroscopic loads and rub-induced destabilizing forces. A modal representation of the turbine engine is used, with one mode in each of the vertical and horizontal planes. The use of non-spinning rotor modes permits an explicit treatment of gyroscopic effects. The two linearized modal equations of motion of a rotor with axisymmetric supports are reduced to a single equation in a complex variable. The resulting eigenvalues yield explicit expressions at the stability boundary, for the whirl frequency as well as the required damping for stability in the presence of the available rub-induced destabilization. Conversely, the allowable destabilization in the presence of the available damping is also given.

Gallardo, Vicente↗