Short-time stability of forced linear time- varying systems.
Sufficient conditions for short time stability of forced linear time varying systems in terms of coefficient matrix and forcing function.
H D'Angelo↗
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An efficient algorithm using matrix methods to solve wind tunnel force-balance equations
An iterative procedure applying matrix methods to accomplish an efficient algorithm for automatic computer reduction of wind-tunnel force-balance data has been developed. Balance equations are expressed in a matrix form that is convenient for storing balance sensitivities and interaction coefficient values for online or offline batch data reduction. The convergence of the iterative values to a unique solution of this system of equations is investigated, and it is shown that for balances which satisfy the criteria discussed, this type of solution does occur. Methods for making sensitivity adjustments and initial load effect considerations in wind-tunnel applications are also discussed, and the logic for determining the convergence accuracy limits for the iterative solution is given. This more efficient data reduction program is compared with the technique presently in use at the NASA Langley Research Center, and computational times on the order of one-third or less are demonstrated by use of this new program.
Smith, D. L.↗
Development of a model of space station solar array
Space structures, such as the space station solar arrays, must be extremely lightweight, flexible structures. Accurate prediction of the natural frequencies and mode shapes is essential for determining the structural adequacy of components, and designing a control system. The tension preload in the blanket of photovoltaic solar collectors, and the free/free boundary conditions of a structure in space, causes serious reservations on the use of standard finite element techniques of solution. In particular, a phenomena known as grounding, or false stiffening, of the stiffness matrix occurs during rigid body rotation. The grounding phenomena is examined in detail. Numerous stiffness matrices developed by others are examined for rigid body rotation capability, and found lacking. Various techniques are used for developing new stiffness matrices from the rigorous solutions of the differential equations, including the solution of the directed force problem. A new directed force stiffness matrix developed by the author provides all the rigid body capabilities for the beam in space.
Bosela, Paul A.↗
Evaluation of the thin deformable active optics mirror concept
The active optics concept using a thin deformable mirror has been successfully demonstrated using a 30 in. diameter, 1/2 in. thick mirror and a 61 point matrix of forces for alignment. Many of the problems associated with the design, fabrication, and launch of large aperture diffraction-limited astronomical telescopes have been resolved and experimental data created that can provide accurate predictions of performance in orbit.
Robertson, H. J.↗
IECON '87: Industrial applications of control and simulation; Proceedings of the 1987 International Conference on Industrial Electronics, Control, and Instrumentation, Cambridge, MA, Nov. 3, 4, 1987
Recent advances in control-system design and simulation are discussed in reviews and reports. Among the topics considered are fast algorithms for generating near-optimal binary decision programs, trajectory control of robot manipulators with compensation of load effects via a six-axis force sensor, matrix integrators for real-time simulation, a high-level control language for an autonomous land vehicle, and a practical engineering design method for stable model-reference adaptive systems. Also addressed are the identification and control of flexible-limb robots with unknown loads, adaptive control and robust adaptive control for manipulators with feedforward compensation, adaptive pole-placement controllers with predictive action, variable-structure strategies for motion control, and digital signal-processor-based variable-structure controls.
Hartley, Tom T.↗
Constant Applied Force Stimulates Osteoblast Proliferation Via Matrix-Integrin-Signaling Pathways
Reduced weight-bearing caused by immobilization, bed-rest or microgravity leads to atrophy in mechanosensitive tissue such as muscle and bone. We hypothesize that bone tissue requires earth s gravity (1-g) for the maintenance of extracellular matrix, integrin, and kinase-mediated cell growth and survival pathways. We investigate the role of matrix-integrin signaling in bone cells using cell culture centrifugation to provide different levels of hypergravity mechanostimulation. The 10-50-g range we use also mimics physiological intermedullary pressure (1.2 - 5 kPa). 24 hours at 50-g increased primary rat osteoblast proliferation on collagen Type I and fibronectin, but not laminin or uncoated plastic. BrdU incorporation in primary osteoblasts over 24 h showed hypergravity increased the number of cells actively synthesizing DNA from about 60% at 1-g to over 90% at 25-g. Primary rat fibroblasts grown at 50-g (24 h) showed no proliferation increase, suggesting this is a tissue-specific phenomenon. These results suggest that the betal and alpha4 integrins may be involved. To further test this, we used osteocytic-like MLO-Y4 cells that showed increased proliferation at 1-g with stable expression of a betal integrin cytoplasmic tail and transmembrane domain construct. At 50-g, MLO-Y4/betal cells showed greater MAPK activation than MLO-Y4 vector controls, suggesting that betal integrin is involved in transducing mitogenic signals in response to hypergravity. Preliminary results also show that interfering with the alpha4 integrin in primary osteoblasts grown on fibronectin blocked the proliferation response. These results indicate that cells from mechanosensitive bone tissue can respond to gravity-generated forces, and this response involves specific matrix and integrin-dependent signaling pathways.
Vercoutere, W.↗
Force Reconstruction Using the Inverse of the Mode-Shape Matrix [Book Chapter]
A new technique for force reconstruction is developed. To estimate the externally applied force, this technique sums the weight-scaled acceleration signals, and is referred to as the Sum of Weighted Accelerations Technique (SWAT). To obtain the scalar weights the inverse of the mode shape matrix is used. Application of this technique is illustrated with both numerical calculations using a mass-spring model and experimental data from a structure impacting a rigid barrier.
055001 -- Nuclear Fuels-- Safeguards, Inspection, ↗
Program Determines Minimum-State Approximations To Unsteady Aerodynamic Forces
MIST implements minimum-state method for determining rational approximations of matrix of aerodynamic force coefficients. Accepts complex tabular data representing generalized unsteady aerodynamic forces over set of reduced frequencies. Determines approximations to tabular data in Laplace domain by use of rational functions. Provides capability to select coefficients of denominator in rational approximations, to constrain approximation selectably without increasing size of problem, and determines and emphasizes criticial frequency ranges in determining approximations. Written in ANSI FORTRAN 77.
Karpel, Mordechay↗
Ex Vivo Growth of Bioengineered Ligaments and Other Tissues
A method of growing bioengineered tissues for use in surgical replacement of damaged anterior cruciate ligaments has been invented. An anterior cruciate ligament is one of two ligaments (the other being the posterior cruciate ligament) that cross in the middle of a knee joint and act to prevent the bones in the knee from sliding forward and backward relative to each other. Anterior cruciate ligaments are frequently torn in sports injuries and traffic accidents, resulting in pain and severe limitations on mobility. By making it possible to grow replacement anterior cruciate ligaments that structurally and functionally resemble natural ones more closely than do totally synthetic replacements, the method could create new opportunities for full or nearly full restoration of functionality in injured knees. The method is also adaptable to the growth of bioengineered replacements for other ligaments (e.g., other knee ligaments as well as those in the hands, wrists, and elbows) and to the production of tissues other than ligaments, including cartilage, bones, muscles, and blood vessels. The method is based on the finding that the histomorphological properties of a bioengineered tissue grown in vitro from pluripotent cells within a matrix are affected by the direct application of mechanical force to the matrix during growth generation. This finding provides important new insights into the relationships among mechanical stress, biochemical and cell-immobilization methods, and cell differentiation, and is applicable to the production of the variety of tissues mentioned above. Moreover, this finding can be generalized to nonmechanical (e.g., chemical and electromagnetic) stimuli that are experienced in vivo by tissues of interest and, hence, the method can be modified to incorporate such stimuli in the ex vivo growth of replacements for the various tissues mentioned above. In this method, a three-dimensional matrix made of a suitable material is seeded with pluripotent stem cells. The patient s bone-marrow stromal cells are preferably used as the pluripotent cells in this method. Suitable matrix materials are materials to which cells can adhere for example, collagen type I. The seeded matrix is attached to anchors at opposite ends and then the cells in the matrix are cultured under conditions appropriate for the growth and regeneration of cells. Suitable anchor materials are materials to which the matrix can attach; examples include demineralized bone and Goinopra coral that has been treated to convert its calcium carbonate to calcium phosphate.
Altman, Gregory↗
Crack Driving Forces in a Multilayered Coating System for Ceramic Matrix Composite Substrates
The effects of the top coating thickness, modulus and shrinkage strains on the crack driving forces for a baseline multilayer Yttria-Stabilized-Zirconia/Mullite/Si thermal and environment barrier coating (TEBC) system for SiC/SiC ceramic matrix composite substrates are determined for gas turbine applications. The crack driving forces increase with increasing modulus, and a low modulus thermal barrier coating material (below 10 GPa) will have no cracking issues under the thermal gradient condition analyzed. Since top coating sintering increases the crack driving forces with time, highly sintering resistant coatings are desirable to maintain a low tensile modulus and maintain a low crack driving force with time. Finite element results demonstrated that an advanced TEBC system, such as ZrO2/HfO2, which possesses improved sintering resistance and high temperature stability, exhibited excellent durability. A multi-vertical cracked structure with fine columnar spacing is an ideal strain tolerant coating capable of reducing the crack driving forces to an acceptable level even with a high modulus of 50 GPa.
Ghosn, Louis J.↗
Reinforcement induced microcracking during the conversion of polymer-derived ceramics
This study investigates the role of discontinuous reinforcement on the microcracking of a preceramic polymer matrix during polymer to ceramic conversion. The material system comprised a carbosilane-based, preceramic polymer reinforced with mullite particles. The preceramic resin slurry was formulated for photopolymerization on a digital light projection 3D printer. Micro X-ray computed tomography, using a synchrotron light source, monitored a printed composite part during pyrolysis. The conversion of the carbosilane matrix into Si(O)C generated microcracks in the matrix that radially extended from particles. The likelihood of microcrack formation positively correlated with particle size. The largest particles (>10 4 µm 3 volume or >60 µm side length) always abutted microcracks, while the matrix surrounding smaller particles (<5 µm) was free of microcracks. Numerical calculations showed the particles resist the shrinking matrix during its conversion. This created tensile stresses within the matrix. The driving force for microcrack growth was also analyzed with regard to the influence of matrix material parameters, particle form-factor and crack length. These results reveal the need to consider the form factor of discontinuous reinforcements, with regard to the material properties of the polymer-derived ceramic, in order to reduce or eliminate defects in the final part.
36 MATERIALS SCIENCE↗
Time-Dependent Stress Rupture Strength Degradation of Hi-Nicalon Fiber-Reinforced Silicon Carbide Composites at Intermediate Temperatures
The stress rupture strength of silicon carbide fiber-reinforced silicon carbide composites with a boron nitride fiber coating decreases with time within the intermediate temperature range of 700 to 950 degree Celsius. Various theories have been proposed to explain the cause of the time-dependent stress rupture strength. The objective of this paper is to investigate the relative significance of the various theories for the time-dependent strength of silicon carbide fiber-reinforced silicon carbide composites. This is achieved through the development of a numerically based progressive failure analysis routine and through the application of the routine to simulate the composite stress rupture tests. The progressive failure routine is a time-marching routine with an iterative loop between a probability of fiber survival equation and a force equilibrium equation within each time step. Failure of the composite is assumed to initiate near a matrix crack and the progression of fiber failures occurs by global load sharing. The probability of survival equation is derived from consideration of the strength of ceramic fibers with randomly occurring and slow growing flaws as well as the mechanical interaction between the fibers and matrix near a matrix crack. The force equilibrium equation follows from the global load sharing presumption. The results of progressive failure analyses of the composite tests suggest that the relationship between time and stress-rupture strength is attributed almost entirely to the slow flaw growth within the fibers. Although other mechanisms may be present, they appear to have only a minor influence on the observed time-dependent behavior.
Progressive Failure Analysis↗
A Numerical Solution Routine for Investigating Oxidation-Induced Strength Degradation Mechanisms in SiC/SiC Composites
The stress rupture strength of silicon carbide fiber-reinforced silicon carbide (SiCSiC) composites with a boron nitride (BN) fiber coating decreases with time within the intermediate temperature range of 700-950 C. Various theories have been proposed to explain the cause of the time dependent stress rupture strength. Some previous authors have suggested that the observed composite strength behavior is due to the inherent time dependent strength of the fibers, which is caused by the slow growth of flaws within the fibers. Flaw growth is supposedly enabled by oxidation of free carbon at the grain boundaries. The objective of this paper is to investigate the relative significance of the various theories for the time-dependent strength of SiCSiC composites. This is achieved through the development of a numerically-based progressive failure analysis routine and through the application of the routine to simulate the composite stress rupture tests. The progressive failure routine is a time marching routine with an iterative loop between a probability of fiber survival equation and a force equilibrium equation within each time step. Failure of the composite is assumed to initiate near a matrix crack and the progression of fiber failures occurs by global load sharing. The probability of survival equation is derived from consideration of the strength of ceramic fibers with randomly occurring and slow growing flaws as well as the mechanical interaction between the fibers and matrix near a matrix crack. The force equilibrium equation follows from the global load sharing presumption. The results of progressive failure analyses of the composite tests suggest that the relationship between time and stress-rupture strength is attributed almost entirely to the slow flaw growth within the fibers. Although other mechanisms may be present, they appear to have only a minor influence on the observed time dependent behavior.
degradation↗
A Low-Rank QTT-based Finite Element Method for Elasticity Problems
We present an efficient and robust numerical algorithm for solving the linear elasticity problem that combines the Quantized Tensor Train format and a domain partitioning strategy. This approach makes it possible to solve the linear elasticity problem on a computational domain that is more general than a square. By integrating Z-ordering and subdomain concatenation, our method substantially decreases memory usage and achieves a notable reduction in rank compared to established Finite Element implementations like the FEniCS platform. This efficiency is maintained while still guaranteeing exponential convergence with respect to the number of degrees of freedom. This performance gain, however, requires a fundamental rethinking of how core finite element operations are implemented. This includes changes to mesh discretization, node and degree of freedom ordering, stiffness matrix and internal nodal force assembly, and the execution of algebraic matrix-vector operations. In this work, we discuss all these aspects in detail and assess the method’s performance in the numerical approximation of three representative test cases.
97 MATHEMATICS AND COMPUTING↗
RMS massless arm dynamics capability in the SVDS
The equations of motion for the remote manipulator system, assuming that the masses and inertias of the arm can be neglected, are developed for implementation into the space vehicle dynamics simulation (SVDS) program for the Orbiter payload system. The arm flexibility is incorporated into the equations by the computation of flexibility terms for use in the joint servo model. The approach developed in this report is based on using the Jacobian transformation matrix to transform force and velocity terms between the configuration space and the task space to simplify the form of the equations.
Flanders, H. A.↗
A numerical algorithm for endochronic plasticity and comparison with experiment
A numerical algorithm based on the finite element method of analysis of the boundary value problem in a continuum is presented, in the case where the plastic response of the material is given in the context of endochronic plasticity. The relevant constitutive equation is expressed in incremental form and plastic effects are accounted for by the method of an induced pseudo-force in the matrix equations. The results of the analysis are compared with observed values in the case of a plate with two symmetric notches and loaded longitudinally in its own plane. The agreement between theory and experiment is excellent.
Valanis, K. C.↗
Accuracy of the Generalized Self-Consistent Method in Modelling the Elastic Behaviour of Periodic Composites
Local stress and strain fields in the unit cell of an infinite, two-dimensional, periodic fibrous lattice have been determined by an integral equation approach. The effect of the fibres is assimilated to an infinite two-dimensional array of fictitious body forces in the matrix constituent phase of the unit cell. By subtracting a volume averaged strain polarization term from the integral equation we effectively embed a finite number of unit cells in a homogenized medium in which the overall stress and strain correspond to the volume averaged stress and strain of the constrained unit cell. This paper demonstrates that the zeroth term in the governing integral equation expansion, which embeds one unit cell in the homogenized medium, corresponds to the generalized self-consistent approximation. By comparing the zeroth term approximation with higher order approximations to the integral equation summation, both the accuracy of the generalized self-consistent composite model and the rate of convergence of the integral summation can be assessed. Two example composites are studied. For a tungsten/copper elastic fibrous composite the generalized self-consistent model is shown to provide accurate, effective, elastic moduli and local field representations. The local elastic transverse stress field within the representative volume element of the generalized self-consistent method is shown to be in error by much larger amounts for a composite with periodically distributed voids, but homogenization leads to a cancelling of errors, and the effective transverse Young's modulus of the voided composite is shown to be in error by only 23% at a void volume fraction of 75%.
Walker, Kevin P.↗
Elastic Model Transitions: A Hybrid Approach Utilizing Quadratic Inequality Constrained Least Squares (LSQI) and Direct Shape Mapping (DSM)
A method for transitioning linear time invariant (LTI) models in time varying simulation is proposed that utilizes a hybrid approach for determining physical displacements by augmenting the original quadratically constrained least squares (LSQI) algorithm with Direct Shape Mapping (DSM) and modifying the energy constraints. The approach presented is applicable to simulation of the elastic behavior of launch vehicles and other structures that utilize discrete LTI finite element model (FEM) derived mode sets (eigenvalues and eigenvectors) that are propagated throughout time. The time invariant nature of the elastic data presents a problem of how to properly transition elastic states from the prior to the new model while preserving motion across the transition and ensuring there is no truncation or excitation of the system. A previous approach utilizes a LSQI algorithm with an energy constraint to effect smooth transitions between eigenvector sets with no requirement that the models be of similar dimension or have any correlation. This approach assumes energy is conserved across the transition, which results in significant non-physical transients due to changing quasi-steady state energy between mode sets, a phenomenon seen when utilizing a truncated mode set. The computational burden of simulating a full mode set is significant so a subset of modes is often selected to reduce run time. As a result of this truncation, energy between mode sets may not be constant and solutions across transitions could produce non-physical transients. In an effort to abate these transients an improved methodology was developed based on the aforementioned approach, but this new approach can handle significant changes in energy across mode set transitions. It is proposed that physical velocities due to elastic behavior be solved for using the LSQI algorithm, but solve for displacements using a two-step process that independently addresses the quasi-steady-state and non-steady-state contributions to the elastic displacement. For structures subject to large external forces, such as thrust or atmospheric drag, it is imperative to capture these forces when solving for elastic displacement. To simplify the mathematical formulation, assumptions are made regarding mass matrix normalization, constant external forcing, and constant viscous damping. These simplifications allow for direct solutions to the quasi-steady-state displacements through a process titled Direct Shape Mapping. DSM solves for the displacements using the eigenvalues of the elastic modes and the external forcing and returns a set of elastic displacements dictated by the eigenvectors of the post-transition mode set. For the non-steady-state contributions to displacement we formulate a LSQI problem that is constrained by energy of the non-steady state terms. The contributions from the quasi-steady-state and non-steady state solutions are then combined to obtain the physical displacements associated with the new set of eigenvectors. Results for the LSQI-DSM approach show significant reduction/complete removal of transients across mode set transitions while maintaining elastic motion from the prior state. For time propagation applications employing discrete elastic models that need to be transitioned in time and where running with full a full mode set is not feasible, the method developed offers a practical solution to simulating vehicle elasticity.
Hannan, Mike R.↗