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The general frequency response program provides the frequency response of any linear feedback control system including the open loop control system. The system characteristic matrix, obtained from the Laplace transformations of the dynamic and control equations, is input to the program. A variety of outputs are available.
Computational simulation procedures are described to evaluate the composite microfracture behavior, establish the hierarchy/sequence of fracture modes, and the influence of compliant layers and partial debonding on composite properties and microfracture initiation. These procedures are based upon three-dimensional finite element analysis and composite micromechanics equations. Typical results for the effects of compliant layers and partial debonding, microfracture initiation, and propagation and the thermomechanical cyclic loading on a SiC/Ti15 composite system are presented and discussed. The results show that interfacial debonding follows fiber or matrix fracture, and the thermomechanical cyclic loading severely degrades the composite integrity.
An analytical micromechanics based strength prediction methodology was developed to predict failure of notched metal matrix composites. The stress-strain behavior and notched strength of two metal matrix composites, boron/aluminum (B/Al) and silicon-carbide/titanium (SCS-6/Ti-15-3), were predicted. The prediction methodology combines analytical techniques ranging from a three dimensional finite element analysis of a notched specimen to a micromechanical model of a single fiber. In the B/Al laminates, a fiber failure criteria based on the axial and shear stress in the fiber accurately predicted laminate failure for a variety of layups and notch-length to specimen-width ratios with both circular holes and sharp notches when matrix plasticity was included in the analysis. For the SCS-6/Ti-15-3 laminates, a fiber failure based on the axial stress in the fiber correlated well with experimental results for static and post fatigue residual strengths when fiber matrix debonding and matrix cracking were included in the analysis. The micromechanics based strength prediction methodology offers a direct approach to strength prediction by modeling behavior and damage on a constituent level, thus, explicitly including matrix nonlinearity, fiber matrix debonding, and matrix cracking.
The surface responses due to impact load on an infinite uniaxial graphite/epoxy plate with and without delamination cracks are investigated both in time and frequency domain by using a hybrid method combining the finite element discretization of the near-field with boundary integral representation of the field outside a contour enclosing completely the crack. This combined method leads to a set of linear unsymmetric complex matrix equations which are solved to obtain the response in the frequency domain by biconjugate gradient method. The time domain response is then obtained by using an FFT. In order to capture the time-domain characteristics accurately, high order finite elements have been used. Also, both the six node singular elements and eight node transition elements are used around the crack tips to model the crack-tip singularity. It is shown that from the numerical results for surface responses both depth and length of this crack can be identified.
A computerized, analytical methodology was developed to study damage accumulation during low velocity lateral impact of layered composite plates. The impact event was modeled as perfectly plastic with complete momentum transfer to the plate structure. A transient dynamic finite element approach was selected to predict the displacement time response of the plate structure. Composite ply and interlaminar stresses were computed at selected time intervals and subsequently evaluated to predict layer and interlaminar damage. The effects of damage on elemental stiffness were then incorporated back into the analysis for subsequent time steps. Damage predicted included fiber failure, matrix ply failure and interlaminar delamination.
A finite element model that is suitable for the static analysis of shells of revolution with arbitrary local deviations is presented. The model employs three types of elements: rotational, general, and transitional shell elements. The rotational shell elements are used in the region where the shell is axisymmetric. The general shell element are used in the local region of the deviation. The transitional shell elements connect these two distinctively different types of elements and make it possible to combine them in a single analysis. The form of the global stiffness matrix resulting when different forms of nodal degrees of freedom are combined is illustrated. The coupling of harmonic degrees of freedom due to the locally nonaxisymmetric geometry was studied. The use of a substructuring technique and separate partial harmonic analysis is recommended.
A systematic finite-element model modification technique has been applied to two small problems and a model of the main wing box of a research drone aircraft. The procedure determines the sensitivity of the eigenvalues and eigenvector components to specific structural changes, calculates the required changes and modifies the finite-element model. Good results were obtained where large stiffness modifications were required to satisfy large eigenvalue changes. Sensitivity matrix conditioning problems required the development of techniques to insure existence of a solution and accelerate its convergence. A method is proposed to assist the analyst in selecting stiffness parameters for modification.
This report investigates the identifiability of modal parameters of flexible structures. Expressions are derived for Cramer-Rao lower bounds for the modal parameters, that is, frequencies, damping ratios and mode shapes or slopes. The optimal initial state, which maximizes the trace of the Fisher information matrix in the absence of persistent input, is obtained. The concepts discussed are applied to a finite-element model of the 122 meter hoop/column antenna. The numerical results show that the identifiability of the structural frequencies is excellent, followed by that of the damping ratios and the mode-slopes.
The governing equations for the analysis of open branch-chain mechanical systems are developed in a form suitable for implementation in a general purpose finite element computer program. Lagrange's form of d'Alembert's principle is used to derive the system mass matrix and force vector. The generalized coordinates are selected as the unconstrained relative degrees of freedom giving the position and orientation of each slave link with respect to their master link. Each slave link may have from zero to six degrees of freedom relative to the reference frames of its master link. A strategy for automatic generation of the system mass matrix and force vector is described.
The problem of choosing an optimum scheme for the electrooptical analyzer of polarization and related control principles are discussed. An electrooptical deflector, which is advantageously used to employ a single photodetector and to remove systematic errors inherent in magnetographs with two photodetectors in the wings of the line is discussed, as well as adjustment errors of optical elements of the polarization analyzer and errors of control voltages. A method for measuring the telescope's polarization matrix, reduction of magnetographic measurements for instrumental polarization and calibration of magnetograph channels are examined. Questions of evaluating scattered light and of reducing magnetic field measurements are also considered as a computational procedure for the magnetic field vector parameters is briefly outlined. Computer control of the solar magnetograph and of the processing and control system software is discussed.
High strength at elevated temperatures, low density, resistance to wear, and abundance of nonstrategic raw materials make structural ceramics attractive for advanced heat engine applications. Unfortunately, ceramics have a low fracture toughness and fail catastrophically because of overload, impact, and contact stresses. Ceramic matrix composites provide the means to achieve improved fracture toughness while retaining desirable characteristics, such as high strength and low density. Materials scientists and engineers are trying to develop the ideal fibers and matrices to achieve the optimum ceramic matrix composite properties. A need exists for the development of failure models for the design of ceramic matrix composite heat engine components. Phenomenological failure models are currently the most frequently used in industry, but they are deterministic and do not adequately describe ceramic matrix composite behavior. Semi-empirical models were proposed, which relate the failure of notched composite laminates to the stress a characteristic distance away from the notch. Shear lag models describe composite failure modes at the micromechanics level. The enhanced matrix cracking stress occurs at the same applied stress level predicted by the two models of steady state cracking. Finally, statistical models take into consideration the distribution in composite failure strength. The intent is to develop these models into computer algorithms for the failure analysis of ceramic matrix composites under monotonically increasing loads. The algorithms will be included in a postprocessor to general purpose finite element programs.
Using the Newtonian method, the equations of motion are developed for the coupled bending-torsion steady-state response of beams rotating at constant angular velocity in a fixed plane. The resulting equations are valid to first order strain-displacement relationships for a long beam with all other nonlinear terms retained. In addition, the equations are valid for beams with the mass centroidal axis offset (eccentric) from the elastic axis, nonuniform mass and section properties, and variable twist. The solution of these coupled, nonlinear, nonhomogeneous, differential equations is obtained by modifying a Hunter linear second-order transfer-matrix solution procedure to solve the nonlinear differential equations and programming the solution for a desk-top personal computer. The modified transfer-matrix method was verified by comparing the solution for a rotating beam with a geometric, nonlinear, finite-element computer code solution; and for a simple rotating beam problem, the modified method demonstrated a significant advantage over the finite-element solution in accuracy, ease of solution, and actual computer processing time required to effect a solution.
A methodology to improve the stability robustness of feedback control systems designed using direct eigenspace assignment techniques is presented. The method consists of considering the sensitivity of the minimum singular value of the return difference transfer matrix at the plant input to small changes in the desired closed-loop eigenvalues and the specified elements of the desired closed-loop eigenvectors. Closed-form expressions for the gradient of the minimum return difference singular value with respect to desired closed-loop eigenvalue and eigenvector parameters are derived. Closed-form expressions for the gradients of the control feedback gains with respect to the specified eigenspace parameters are obtained as an intermediate step. The use of the gradient information to improve the guaranteed gain and phase margins in eigenspace assignment based designs is demonstrated by application to an advanced fighter aircraft.
A methodology to improve the stability robustness of feedback control systems designed using direct eigenspace assignment techniques is presented. The method consists of considering the sensitivity of the minimum singular value of the return difference transfer matrix at the plant input to small changes in the desired closed-loop eigenvalues and the specified elements of the desired closed-loop eigenvectors. Closed-form expressions for the gradient of the minimum return difference singular value with respect to desired closed-loop eigenvalue and eigenvector parameters are derived. Closed-form expressions for the gradients of the control feedback gains with respect to the specified eigenspace parameters are obtained as an intermediate step. The use of the gradient information to improve the guaranteed gain and phase margins in eigenspace assignment based designs is demonstrated by application to an advanced fighter aircraft.
Evaluations performed during a Phase B study directed towards defining an optimal design for the Earth Observing Scanning Polarimeter (EOSP) instrument is summarized. An overview of the experiment approach is included which provides a summary of the scientific objectives, the background of the measurement approach, and the measurement method. In the instrumentation section, details of the design are discussed starting with the key instrument features required to accomplish the scientific objectives and a system characterization in terms of the Stokes vector/Mueller matrix formalism. This is followed by a detailing of the instrument design concept, the design of the individual elements of the system, the predicted performance, and a summary of appropriate instrument testing and calibration. The selected design makes use of key features of predecessor polarimeters and is fully compatible with the Earth Observing System spacecraft requirements.
Cost effective composite structure has motivated the investigation of several new approaches to develop composite structure from innovative material forms. Among the promising new approaches is the conversion of planar sheet to components of complex curvature through sheet forming or stretch forming. In both cases, the potential for material stretch in the fiber direction appears to offer a clear advantage in formability over continuous fiber systems. In the present study, the authors have established a framework which allows the simulation of the anisotropic mechanisms of deformation of long discontinuous fiber laminates wherein the matrix phase is a viscous fluid. The initial study focuses upon the establishment of micromechanics models for prediction of the effective anisotropic viscosities of the oriented fiber assembly in a viscous matrix. Next, the developed constitutive relation is employed through an analogy with incompressible elasticity to exercise the finite element technique for determination of local fiber orientation and laminate thickness after forming. Results are presented for the stretch bending of a curved beam from an arbitrary composite laminate and the bulging of a clamped sheet. Structural analyses are conducted to determine the effect of microstructure on the performance of curved beams manufactured from long discontinuous fiber composites. For the purposes of this study, several curved beams with ideal and non-ideal microstructures are compared for response under pure bending. Material parameters are determined from a separate microstructural analysis.
The talk will discuss current work in developing and applying the INS2D and INS3D flow solvers to problems in high-lift aerodynamics, primarily multi-element airfoils. These flow solvers solve the incompressible Navier-Stokes equations using the method of artificial compressibility. High-lift system flowfields are perhaps the most challenging aeronautical configurations for CFD. Difficulties with convergence for multi-element configurations using fine-grid overset meshes has led to research in using Krylov-space iterative matrix solvers. In particular, a Generalized Minimum Residual (GMRES) solver has found to be a dramatic improvement over a previously used Gauss-Seidal line-relaxation solver.
This report discusses the design implications for spacecraft radiators made possible by the successful fabrication and proof-of-concept testing of a graphite-fiber-carbon-matrix composite (i.e., carbon-carbon (C-C)) heat pipe. The prototype heat pipe, or space radiator element, consists of a C-C composite shell with integrally woven fins. It has a thin-walled furnace-brazed metallic (Nb-1%Zr) liner with end caps for containment of the potassium working fluid. A short extension of this liner, at increased wall thickness beyond the C-C shell, forms the heat pipe evaporator section which is in thermal contact with the radiator fluid that needs to be cooled. From geometric and thermal transport properties of the C-C composite heat pipe tested, a specific radiator mass of 1.45 kg/sq m can be derived. This is less than one-fourth the specific mass of present day satellite radiators. The report also discusses the advantage of segmented space radiator designs utilizing heat pipe elements, or segments, in their survivability to micrometeoroid damage. This survivability is further raised by the use of condenser sections with attached fins, which also improve the radiation heat transfer rate. Since the problem of heat radiation from a fin does not lend itself to a closed analytical solution, a derivation of the governing differential equation and boundary conditions is given in appendix A, along with solutions for rectangular and parabolic fin profile geometries obtained by use of a finite difference computer code written by the author.