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NASA NTRS2006

Active Struts With Variable Spring Stiffness and Damping

An ultrasonic rock-abrasion tool (URAT) was developed using the same principle of ultrasonic/sonic actuation as that of the tools described in two prior NASA Tech Briefs articles: Ultrasonic/ Sonic Drill/Corers With Integrated Sensors (NPO-20856), Vol. 25, No. 1 (January 2001), page 38 and Ultrasonic/ Sonic Mechanisms for Drilling and Coring (NPO-30291), Vol. 27, No. 9 (September 2003), page 65. Hence, like those tools, the URAT offers the same advantages of low power demand, mechanical simplicity, compactness, and ability to function with very small axial loading (very small contact force between tool and rock). Like a tool described in the second of the cited previous articles, a URAT includes (1) a drive mechanism that comprises a piezoelectric ultrasonic actuator, an amplification horn, and a mass that is free to move axially over a limited range and (2) an abrasion tool bit. A URAT tool bit is a disk that has been machined or otherwise formed to have a large number of teeth and an overall shape chosen to impart the desired shape (which could be flat or curved) to the rock surface to be abraded. In operation, the disk and thus the teeth are vibrated in contact with the rock surface. The concentrated stresses at the tips of the impinging teeth repeatedly induce microfractures and thereby abrade the rock. The motion of the tool induces an ultrasonic transport effect that displaces the cuttings from the abraded area. The figure shows a prototype URAT. A piezoelectric-stack/horn actuator is housed in a cylindrical container. The movement of the actuator and bit with respect to the housing is aided by use of mechanical sliders. A set of springs accommodates the motion of the actuator and bit into or out of the housing through an axial range between 5 and 7 mm. The springs impose an approximately constant force of contact between the tool bit and the rock to be abraded. A dust shield surrounds the bit, serving as a barrier to reduce the migration of rock debris to sensitive instrumentation or mechanisms in the vicinity. A bushing at the tool-bit end of the housing reduces the flow of dust into the actuator and retains the bit when no axial load is applied.

Farley, Gary L.↗

NASA NTRS2015

Design and Testing of a Dynamically-Tuned Magnetostrictive Spring with Electrically-Controlled Stiffness

This paper details the development of an electrically-controlled, variable-stiffness spring based on magnetostrictive materials. The device, termed a magnetostrictive Varispring, can be applied as a semi-active vibration isolator or switched stiffness vibration controller for reducing transmitted vibrations. The Varispring is designed using 1D linear models that consider the coupled electrical response, mechanically-induced magnetic diffusion, and the effect of internal mass on dynamic stiffness. Modeling results illustrate that a Terfenol-D-based Varispring has a rise time almost an order of magnitude smaller and a magnetic diffusion cut-off frequency over two orders of magnitude greater than a Galfenol-based Varispring. The results motivate the use of laminated Terfenol-D rods for a greater stiffness tuning range and increased bandwidth. The behavior of a prototype Varispring is examined under vibratory excitation up to 6 MPa and 25 Hz using a dynamic load frame. For this prototype, stiffness is indirectly varied by controlling the excitation current. Preliminary measurements of continuous stiffness tuning via sinusoidal currents up to 1 kHz are presented. The measurements demonstrate that the Young's modulus of the Terfenol-D rod inside the Varispring can be continuously varied by up to 21.9 GPa. The observed stiffness tuning range is relatively constant up to 500 Hz, but significantly decreases thereafter. The stiffness tuning range can be greatly increased by improving the current and force control such that a more consistent current can be applied and the Varispring can be accurately tested at a more optimal bias stress.

Vibration control↗

NASA NTRS1991

Advanced development of the boundary element method for elastic and inelastic thermal stress analysis

The focus of this dissertation is on advanced development of the boundary element method for elastic and inelastic thermal stress analysis. New formulations for the treatment of body forces and nonlinear effects are derived. These formulations, which are based on particular integral theory, eliminate the need for volume integrals or extra surface integrals to account for these effects. The formulations are presented for axisymmetric, two and three dimensional analysis. Also in this dissertation, two dimensional and axisymmetric formulations for elastic and inelastic, inhomogeneous stress analysis are introduced. The derivatives account for inhomogeneities due to spatially dependent material parameters, and thermally induced inhomogeneities. The nonlinear formulation of the present work are based on an incremental initial stress approach. Two inelastic solutions algorithms are implemented: an iterative; and a variable stiffness type approach. The Von Mises yield criterion with variable hardening and the associated flow rules are adopted in these algorithms. All formulations are implemented in a general purpose, multi-region computer code with the capability of local definition of boundary conditions. Quadratic, isoparametric shape functions are used to model the geometry and field variables of the boundary (and domain) of the problem. The multi-region implementation permits a body to be modeled in substructured parts, thus dramatically reducing the cost of analysis. Furthermore, it allows a body consisting of regions of different (homogeneous) material to be studied. To test the program, results obtained for simple test cases are checked against their analytic solutions. Thereafter, a range of problems of practical interest are analyzed. In addition to displacement and traction loads, problems with body forces due to self-weight, centrifugal, and thermal loads are considered.

Henry, Donald P., Jr.↗

NASA NTRS1989

Advanced applications of BEM to inelastic analysis of solids

Newly evolved boundary element solution algorithms are utilized for solving a range of elastoplastic and thermoplastic problems. The first algorithm is the typical iterative procedure in which the unknown boundary solution and the initial stress (or strain) rates are found together in an incremental iterative fashion. The second one is a variable stiffness type approach in which the incremental boundary solution is obtained in a direct (noniterative) manner. The third procedure differs from the two prior algorithms in that volume integration is not needed to incorporate the nonlinear effects in the analysis. Instead, initial stress rates are introduced in the boundary element system by way of particular integrals. The methodology is used in a general purpose, multiregion system that employs quadratic isoparametric shape functions to model the geometry and field variables of the body and can admit up to 15 substructured areas of different material properties.

Banerjee, P. K.↗

NASA NTRS1981

Tile densification with TEOS

Densification process uses brushed or sprayed coating of tetraethyl orthosilicate. Liquid is applied and cured in three steps; tile weight increase averages 0.15 g per square centimeter. TEOS liquid is prepared by mixing TEOS with hydrochloric acid and adding marking dye. TEOS application provides variable stiffness, strength, and penetration. Surface of tile shows no buidup and is more durable for additional coatings.

Ecord, G. M.↗

NASA NTRS1986

Spline-based distributed system identification with application to large space antennas

A parameter and state estimation technique for distributed models is demonstrated through the solution of a problem generic to large space antenna system identification. Assuming the position of the reflective surface of the maypole (hoop/column) antenna to be approximated by the static two-dimensional, stretched-membrane partial differential equation with variable-stiffness coefficient functions, a spline-based approximation procedure is described that estimates the shape and stiffness functions from data set observations. For given stiffness functions, the Galerkin projection with linear spline-based functions is applied to project the distributed problem onto a finite-dimensional subspace wherein algebraic equations exist for determining a static shape (state) prediction. The stiffness functions are then parameterized by cubic splines and the parameters estimated by an output error technique. Numerical results are presented for data descriptive of a 100-m-diameter maypole antenna.

Banks, H. T.↗

NASA NTRS1992

Eigenvalue error analysis of viscously damped structures using a Ritz reduction method

The efficient solution of the eigenvalue problem that results from inserting passive dampers with variable stiffness and damping coefficients into a structure is addressed. Eigenanalysis of reduced models obtained by retaining a number of normal modes augmented with Ritz vectors corresponding to the static solutions resulting from the load patterns introduced by the dampers has been empirically shown to yield excellent approximations to the full eigenvalue problem. An analysis of this technique in the case of a single damper is presented. A priori and a posteriori error estimates are generated and tested on numerical examples. Comparison theorems with modally truncated models and a Markov parameter matching reduced-order model are derived. These theorems corroborate the heuristic that residual flexibility methods improve low-frequency approximation of the system. The analysis leads to other techniques for eigenvalue approximation. Approximate closed-form solutions are derived that include a refinement to eigenvalue derivative methods for approximation. An efficient Newton scheme is also developed. A numerical example is presented demonstrating the effectiveness of each of these methods.

Chu, Cheng-Chih↗

NASA NTRS1993

Probabilistic simulation of stress concentration in composite laminates

A computational methodology is described to probabilistically simulate the stress concentration factors in composite laminates. This new approach consists of coupling probabilistic composite mechanics with probabilistic finite element structural analysis. The probabilistic composite mechanics is used to probabilistically describe all the uncertainties inherent in composite material properties while probabilistic finite element is used to probabilistically describe the uncertainties associated with methods to experimentally evaluate stress concentration factors such as loads, geometry, and supports. The effectiveness of the methodology is demonstrated by using it to simulate the stress concentration factors in composite laminates made from three different composite systems. Simulated results match experimental data for probability density and for cumulative distribution functions. The sensitivity factors indicate that the stress concentration factors are influenced by local stiffness variables, by load eccentricities and by initial stress fields.

Chamis, C. C.↗

NASA NTRS1994

Probabilistic Simulation of Stress Concentration in Composite Laminates

A computational methodology is described to probabilistically simulate the stress concentration factors (SCF's) in composite laminates. This new approach consists of coupling probabilistic composite mechanics with probabilistic finite element structural analysis. The composite mechanics is used to probabilistically describe all the uncertainties inherent in composite material properties, whereas the finite element is used to probabilistically describe the uncertainties associated with methods to experimentally evaluate SCF's, such as loads, geometry, and supports. The effectiveness of the methodology is demonstrated by using is to simulate the SCF's in three different composite laminates. Simulated results match experimental data for probability density and for cumulative distribution functions. The sensitivity factors indicate that the SCF's are influenced by local stiffness variables, by load eccentricities, and by initial stress fields.

Chamis, C. C.↗

NASA NTRS2003

Automated Finite Element Analysis of Elastically-Tailored Plates

A procedure for analyzing and designing elastically tailored composite laminates using the STAGS finite element solver has been presented. The methodology used to produce the elastic tailoring, namely computer-controlled steering of unidirectionally reinforced composite material tows, has been reduced to a handful of design parameters along with a selection of construction methods. The generality of the tow-steered ply definition provides the user a wide variety of options for laminate design, which can be automatically incorporated with any finite element model that is composed of STAGS shell elements. Furthermore, the variable stiffness parameterization is formulated so that manufacturability can be assessed during the design process, plus new ideas using tow steering concepts can be easily integrated within the general framework of the elastic tailoring definitions. Details for the necessary implementation of the tow-steering definitions within the STAGS hierarchy is provided, and the format of the ply definitions is discussed in detail to provide easy access to the elastic tailoring choices. Integration of the automated STAGS solver with laminate design software has been demonstrated, so that the large design space generated by the tow-steering options can be traversed effectively. Several design problems are presented which confirm the usefulness of the design tool as well as further establish the potential of tow-steered plies for laminate design.

Jegley, Dawn C.↗

NASA NTRS2007

Evaluation of a Highly Anticlastic Panel with Tow Overlaps

A rectangular, variable-stiffness panel with tow overlaps was manufactured using an advanced tow placement machine. The cured panel had large anticlastic imperfections, with measured amplitudes of over two times the average panel thickness. These imperfections were not due to the overall steered-fiber layup or the tow overlaps, but instead resulted from local asymmetries in the laminate that were caused by a manufacturing oversight. In the nominal panel layup, fiber angles vary linearly from 60 degrees on the panel axial centerline to 30 degrees on the parallel edges. A geometrically nonlinear analysis was performed with a -280 degree Fahrenheit thermal load to simulate the postcure cooldown to room temperature. The predicted geometric imperfections correlated well with the measured panel shape. Unique structural test fixtures were then developed which greatly reduced these imperfections, but they also caused prestresses in the panel. Surface imperfections measured after the panel was installed in the test fixtures were used with nonlinear finite element analyses to predict these fixturing-induced prestresses. These prestresses were also included in structural analyses of panel end compression to failure, and the analytical results compared well with test data when both geometric and material nonlinearities were included.

Wu, K. Chauncey↗

NASA NTRS2012

TPSAS-NF1676L-13539-DND

The performance of variable stiffness composite panels is characterized using experiments and structural analyses. Fabricated using a fiber placement system, the fiber angle in these panels varies continuously within each ply. Measured panel shapes and thermal responses are correlated with finite element analyses. Large geometric imperfections require unique fixtures to both straighten the panel edges and provide structural test boundary conditions. Panels show linear prebuckling and nonlinear postbuckling under applied end shortening, which occur at higher loads than a baseline panel. Panel responses to in-plane loading are computed using geometric and materially nonlinear analyses that include mechanical prestresses and measured imperfections. Analytical strains and displacements also correlate well with measured results.

Chauncey Wu↗

NASA NTRSDate not supplied

RESIDUAL DEFORMATION ANALYSIS IN COMPOSITE SHELL STRUCTURES MANUFACTURED USING AUTOMATED FIBER PLACEMENT

The manufacturing of composites typically produces residual stresses that can significantly affect the final shape of the structure. The process of automated fiber placement (AFP) has become a prominent manufacturing technique in developing layups with tailored, variable stiffness morphology. The steered patterns of fiber tows with and without overlaps produce residual deformations that are distinctive from traditional layups. Digital image correlation was used to measure the AFP lamina coefficients of thermal expansion, which were incorporated into finite element analyses (FEA) to model the cooling phase of the cure cycle. The effects of nonlinear analysis and temperature-dependent lamina properties calculated using self-consistent field micromechanics, on the resulting residual deformation of shells, were also modeled. The predicted residual deformation was analyzed by considering out-of-roundness in cylindrical shells and compared to the experimental results. The shell FEA results were well-correlated with the overall deformed shape of the AFP cylinder with overlaps, while the shell FEA model of the AFP cylinder without overlaps did not show as good of qualitative match of the deformation pattern. Analytical correlation with measured results were insensitive to material softening at elevated temperatures, geometric nonlinearities, and variations in measured lamina thermal properties. To improve the accuracy of the residual deformation analysis, these results suggest that the thermo-chemical shrinkages preceding the cooldown should be considered, as well as possible variations in ply level microstructure due to the presence of the embedded fiber tow gaps and overlaps.

Composites↗

NASA NTRSDate not supplied

A Design Framework for Thick and Thin Tow-Steered Composites Using Mechanics of Structure Genome

The design of tow-steered composites is one of the most popular and promising topics under the class of variable stiffness structures. In this work, the authors propose a new design framework and tool for the optimization of tow-steered composites. Mechanics of structure genome (MSG) provides accurate computation of plate/shell section properties including thick and highly curved structures. The computed section properties can be directly used in commercial computer-aided engineering tools. Tow-steered composites are modeled through a design framework wherein tow paths are parameterized in a general way and projected onto a finite element mesh, and MSG calculates the local shell/plate properties. The result is a complete workflow from design parameter input to structural performance evaluation. An open-source optimization software package is used to enable constrained optimization of structural stiffness for the broad tow-steered composite design space. Numerical examples are provided to demonstrate the capabilities of this tool and the promise and potential of tow-steered designs that optimize structural performance while satisfying manufacturing constraints.

Su Tian↗

NASA NTRSDate not supplied

A Design Framework for Thick and Thin Tow-Steered Composites Using Mechanics of Structure Genome

Su Tian↗

NASA NTRS1998

Gel stretch method: a new method to measure constitutive properties of cardiac muscle cells

Diastolic dysfunction is an important cause of congestive heart failure; however, the basic mechanisms causing diastolic congestive heart failure are not fully understood, especially the role of the cardiac muscle cell, or cardiocyte, in this process. Before the role of the cardiocyte in this pathophysiology can be defined, methods for measuring cardiocyte constitutive properties must be developed and validated. Thus this study was designed to evaluate a new method to characterize cardiocyte constitutive properties, the gel stretch method. Cardiocytes were isolated enzymatically from normal feline hearts and embedded in a 2% agarose gel containing HEPES-Krebs buffer and laminin. This gel was cast in a shape that allowed it to be placed in a stretching device. The ends of the gel were held between a movable roller and fixed plates that acted as mandibles. Distance between the right and left mandibles was increased using a stepper motor system. The force applied to the gel was measured by a force transducer. The resultant cardiocyte strain was determined by imaging the cells with a microscope, capturing the images with a CCD camera, and measuring cardiocyte and sarcomere length changes. Cardiocyte stress was characterized with a finite-element method. These measurements of cardiocyte stress and strain were used to determine cardiocyte stiffness. Two variables affecting cardiocyte stiffness were measured, the passive elastic spring and viscous damping. The passive spring was assessed by increasing the force on the gel at 1 g/min, modeling the resultant stress vs. strain relationship as an exponential [sigma = A/k(ekepsilon - 1)]. In normal cardiocytes, A = 23.0 kN/m2 and k = 16. Viscous damping was assessed by examining the loop area between the stress vs. strain relationship during 1 g/min increases and decreases in force. Normal cardiocytes had a finite loop area = 1.39 kN/m2, indicating the presence of viscous damping. Thus the gel stretch method provided accurate measurements of cardiocyte constitutive properties. These measurements have allowed the first quantitative assessment of passive elastic spring properties and viscous damping in normal mammalian cardiocytes.

Non-NASA Center↗

NASA NTRS1989

Internal state variable approach for predicting stiffness reductions in fibrous laminated composites with matrix cracks

A mathematical model utilizing the internal state variable concept is proposed for predicting the upper bound of the reduced axial stiffnesses in cross-ply laminates with matrix cracks. The axial crack opening displacement is explicitly expressed in terms of the observable axial strain and the undamaged material properties. A crack parameter representing the effect of matrix cracks on the observable axial Young's modulus is calculated for glass/epoxy and graphite/epoxy material systems. The results show that the matrix crack opening displacement and the effective Young's modulus depend not on the crack length, but on its ratio to the crack spacing.

Lee, Jong-Won↗

NASA NTRS1976

Derivatives of a statically reduced stiffness matrix with respect to sizing variables

An expression is obtained for the first derivatives with respect to the sizing variables of a statically reduced stiffness matrix that is a nonlinear function of the sizing variables, where the unreduced stiffness matrix is a linear function of the sizing variables. An accepted procedure to reduce the number of degrees of freedom is to eliminate a number of nodal displacements from the degrees of freedom such that the accuracy of the flutter analysis is not significantly affected. In a typical optimization procedure with flutter constraints, the derivative of the stiffness matrix may be used in a form that contains the characteristic vector of the flutter matrix equation and the transpose of the characteristic vector of the adjoint flutter matrix equation corresponding to a particular solution of the flutter equation.

Oconnell, R. F.↗