Diagonalized Lagrangian Robot Dynamics
A diagonal equation for robot dynamics is developed by combining recent mass matrix factorization results with classical Lagrangian mechanics.
working joint moments total joint rotational rates↗
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Progressive Fracture of Composite Structures
A new approach is described for evaluating fracture in composite structures. This approach is independent of classical fracture mechanics parameters like fracture toughness. It relies on computational simulation and is programmed in a stand-alone integrated computer code. It is multiscale, multifunctional because it includes composite mechanics for the composite behavior and finite element analysis for predicting the structural response. It contains seven modules; layered composite mechanics (micro, macro, laminate), finite element, updating scheme, local fracture, global fracture, stress based failure modes, and fracture progression. The computer code is called CODSTRAN (Composite Durability Structural ANalysis). It is used in the present paper to evaluate the global fracture of four composite shell problems and one composite built-up structure. Results show that the composite shells and the built-up composite structure global fracture are enhanced when internal pressure is combined with shear loads.
Chamis, Christos C.↗
Multiscale Multifunctional Progressive Fracture of Composite Structures
A new approach is described for evaluating fracture in composite structures. This approach is independent of classical fracture mechanics parameters like fracture toughness. It relies on computational simulation and is programmed in a stand-alone integrated computer code. It is multiscale, multifunctional because it includes composite mechanics for the composite behavior and finite element analysis for predicting the structural response. It contains seven modules; layered composite mechanics (micro, macro, laminate), finite element, updating scheme, local fracture, global fracture, stress based failure modes, and fracture progression. The computer code is called CODSTRAN (Composite Durability Structural ANalysis). It is used in the present paper to evaluate the global fracture of four composite shell problems and one composite built-up structure. Results show that the composite shells. Global fracture is enhanced when internal pressure is combined with shear loads. The old reference denotes that nothing has been added to this comprehensive report since then.
Chamis, C. C.↗
Development of Non-Optimum Factors for Launch Vehicle Propellant Tank Bulkhead Weight Estimation
Non-optimum factors are used during aerospace conceptual and preliminary design to account for the increased weights of as-built structures due to future manufacturing and design details. Use of higher-fidelity non-optimum factors in these early stages of vehicle design can result in more accurate predictions of a concept s actual weights and performance. To help achieve this objective, non-optimum factors are calculated for the aluminum-alloy gores that compose the ogive and ellipsoidal bulkheads of the Space Shuttle Super-Lightweight Tank propellant tanks. Minimum values for actual gore skin thicknesses and weld land dimensions are extracted from selected production drawings, and are used to predict reference gore weights. These actual skin thicknesses are also compared to skin thicknesses predicted using classical structural mechanics and tank proof-test pressures. Both coarse and refined weights models are developed for the gores. The coarse model is based on the proof pressure-sized skin thicknesses, and the refined model uses the actual gore skin thicknesses and design detail dimensions. To determine the gore non-optimum factors, these reference weights are then compared to flight hardware weights reported in a mass properties database. When manufacturing tolerance weight estimates are taken into account, the gore non-optimum factors computed using the coarse weights model range from 1.28 to 2.76, with an average non-optimum factor of 1.90. Application of the refined weights model yields non-optimum factors between 1.00 and 1.50, with an average non-optimum factor of 1.14. To demonstrate their use, these calculated non-optimum factors are used to predict heavier, more realistic gore weights for a proposed heavy-lift launch vehicle s propellant tank bulkheads. These results indicate that relatively simple models can be developed to better estimate the actual weights of large structures for future launch vehicles.
Wu, K. Chauncey↗
Lightweight Bulldozer Attachment for Construction and Excavation on the Lunar Surface
A lightweight bulldozer blade prototype has been designed and built to be used as an excavation implement in conjunction with the NASA Chariot lunar mobility platform prototype. The combined system was then used in a variety of field tests in order to characterize structural loads, excavation performance and learn about the operational behavior of lunar excavation in geotechnical lunar simulants. The purpose of this effort was to evaluate the feasibility of lunar excavation for site preparation at a planned NASA lunar outpost. Once the feasibility has been determined then the technology will become available as a candidate element in the NASA Lunar Surface Systems Architecture. In addition to NASA experimental testing of the LANCE blade, NASA engineers completed analytical work on the expected draft forces using classical soil mechanics methods. The Colorado School of Mines (CSM) team utilized finite element analysis (FEA) to study the interaction between the cutting edge of the LANCE blade and the surface of soil. FEA was also used to examine various load cases and their effect on the lightweight structure of the LANCE blade. Overall it has been determined that a lunar bulldozer blade is a viable technology for lunar outpost site preparation, but further work is required to characterize the behavior in 1/6th G and actual lunar regolith in a vacuum lunar environment.
Mueller, Robert↗
TPSAS-NF1676L-13579-DND
During aerospace vehicle conceptual and preliminary design, empirical non-optimum factors are typically applied to predicted structural component weights to account for undefined manufacturing and design details. Non-optimum factors are developed here for 32 aluminum-lithium 2195 orthogrid panels comprising the liquid hydrogen tank barrel of the Space Shuttle External Tank using measured panel weights and manufacturing drawings. Minimum values for skin thickness, axial and circumferential blade stiffener thickness and spacing, and overall panel thickness are used to estimate individual panel weights. Panel non-optimum factors computed using a coarse weights model range from 1.21 to 1.77, and a refined weights model (including weld lands and skin and stiffener transition details) yields non-optimum factors of between 1.02 and 1.54. Acreage panels have an average 1.24 non-optimum factor using the coarse model, and 1.03 with the refined version. Non-optimum factors are also calculated for the aluminum-alloy gores that compose the ogive and ellipsoidal bulkheads of the Space Shuttle Super-Lightweight Tank propellant tanks. Minimum values for actual gore skin thicknesses and weld land dimensions are extracted from component production drawings, and are used to predict reference gore weights. These actual skin thicknesses are also compared to skin thicknesses predicted using classical structural mechanics and tank proof-test pressures. Both coarse and refined weights models are developed for the gores. The coarse model is based on the proof-test skin thicknesses, and the refined model uses the actual skin thicknesses and weld land details. Both models include manufacturing tolerance weight estimates. To determine the gore non-optimum factors, these reference weights are then compared to flight hardware weights reported in a mass properties database. The gore non-optimum factors computed using the coarse weights model range from 1.18 to 2.36, with an average non-optimum factor of 1.68. Application of the refined weights model yields non-optimum factors between 1.00 and 1.45, with an average non-optimum factor of 1.13. To demonstrate their utility, these calculated non-optimum factors are then used to predict more realistic (i.e., heavier) gore weights for a proposed heavy-lift launch vehicle's propellant tank bulkheads.
K Chauncey Wu↗
STS-1 Forward RCS Oxidizer Tank Subsystem Failure Assessment
The launch of the Space Shuttle Columbia on STS-1 in April 1981 marked the beginning of a new era in American spaceflight. It was the only crewed first flight of a launch vehicle, and was also among the first vehicles to use large solid rockets as primary propulsion. A potential disaster was narrowly averted at liftoff when ignition overpressure waves pulse swept up the Shuttle stack. The frequency of this transient shock wave exceeded pre-launch predictions, and resulted in high, alternating normal accelerations along the length of the vehicle. Among the results of this unexpected loading was failure of an oxidizer tank support strut in the orbiter’s forward reaction control system module, which could have led to loss of the mission, crew and vehicle. This particular incident is investigated in more detail using classical structural mechanics, and the results are discussed to provide additional insight.
Space Shuttle↗
STS-1 Forward RCS Oxidizer Tank Subsystem Failure Assessment
The launch of the Space Shuttle Columbia on STS-1 marked the beginning of a new era in American spaceflight. It was the only crewed first flight of a launch vehicle to date, and was also the first crewed system to use large solid rockets as primary propulsion. A potential disaster was narrowly averted at liftoff when an ignition overpressure pulse swept up the Shuttle stack. The frequency of this transient shock wave exceeded pre-launch predictions, and resulted in high, alternating normal accelerations along the length of the vehicle. Among the results of this unexpected loading was failure of an oxidizer tank support strut in the orbiter’s forward reaction control system module, which could have led to loss of the mission, crew, and vehicle. This particular incident is investigated in more detail using classical structural mechanics, and the results are discussed to provide additional insight.
Space Shuttle↗
STS-1 Forward RCS Oxidizer Tank Subsystem Preliminary Failure Assessment
The launch of the Space Shuttle Columbia on STS-1 marked the beginning of a new era in American spaceflight. It was the only crewed first flight of a launch vehicle to date, and was also the first crewed system to use large solid rockets as primary propulsion. A potential disaster was narrowly averted at liftoff when an ignition overpressure pulse swept up the Shuttle stack. The frequency of this transient shock wave exceeded pre-launch predictions, and resulted in high, alternating normal accelerations along the length of the vehicle. Among the results of this unexpected loading was failure of an oxidizer tank support strut in the orbiter’s forward reaction control system module, which could have led to loss of the mission, crew, and vehicle. This particular incident is investigated in more detail using classical structural mechanics, and the results are discussed to provide additional insight.
Space Shuttle↗
Nonlinear Dynamic Analyses of STS-1 Forward RCS Oxidizer Tank Structural Failure
At liftoff of the first Space Shuttle mission, a strong ignition overpressure pulse excited the stack. The frequency of the experienced pressure wave exceeded pre-launch predictions, and resulted in high, alternating normal accelerations along the length of the vehicle. As result of this unexpected loading, an oxidizer tank support strut in the orbiter’s forward reaction control system module failed in buckling under axial compression, which could have led to loss of the mission, crew, and vehicle. This incident is investigated in more detail using linear and nonlinear finite element analyses, complementing previous analyses with classical structural mechanics. The results of these analyses are examined to provide additional insight into the accident and to better inform future design decisions for modern space vehicle systems and structures.
Space Shuttle↗
Nonlinear Dynamic Analyses of STS-1 Forward RCS Oxidizer Tank Structural Failure
At liftoff of the first Space Shuttle mission, a strong ignition overpressure pulse excited the stack. The frequency of the experienced pressure wave exceeded pre-launch predictions, and resulted in high, alternating normal accelerations along the length of the vehicle. As result of this unexpected loading, an oxidizer tank support strut in the orbiter’s forward reaction control system module failed in buckling under axial compression, which could have led to loss of the mission, crew, and vehicle. This incident is investigated in more detail using linear and nonlinear finite element analyses, complementing previous analyses with classical structural mechanics. The results of these analyses are examined to provide additional insight into the accident and to better inform future design decisions for modern space vehicle systems and structures.
Space Shuttle↗
STS-1 Forward RCS Oxidizer Tank Subsystem Structural Failure Assessment
The launch of the Space Shuttle Columbia on STS-1 marked the beginning of a new era in American spaceflight. It was the only crewed first flight of a launch vehicle to date, and was also the first crewed system to use large solid rockets as primary propulsion. A potential disaster was narrowly averted at liftoff when an ignition overpressure pulse swept up the Shuttle stack. The frequency of this transient shock wave exceeded pre-launch predictions, and resulted in high, alternating normal accelerations along the length of the vehicle. Among the results of this unexpected loading was failure of an oxidizer tank support strut in the orbiter’s forward reaction control system module, which could have led to loss of the mission, crew, and vehicle. This particular incident is investigated in more detail using classical structural mechanics and finite element analyses, and the results are discussed to provide additional insight.
space shuttle↗
Evanescent radiation, quantum mechanics and the Casimir effect
An attempt to bridge the gap between classical and quantum mechanics and to explain the Casimir effect is presented. The general nature of chaotic motion is discussed from two points of view: the first uses catastrophe theory and strange attractors to describe the deterministic view of this motion; the underlying framework for chaos in these classical dynamic systems is their extreme sensitivity to initial conditions. The second interpretation refers to randomness associated with probabilistic dynamics, as for Brownian motion. The present approach to understanding evanescent radiation and its relation to the Casimir effect corresponds to the first interpretation, whereas stochastic electrodynamics corresponds to the second viewpoint. The nonlinear behavior of the electromagnetic field is also studied. This well-understood behavior is utilized to examine the motions of two orbiting charges and shows a closeness between the classical behavior and the quantum uncertainty principle. The evanescent radiation is used to help explain the Casimir effect.
Schatten, Kenneth H.↗
The absence of ray-effects in the discrete ordinate solution to the transport equation in spherical coordinates in multi-dimensions
The streaming operator of the transport equation is derived for spherical coordinates by starting from Newton’s second law for a free particle expressed in spherical coordinates. We shall show that the partial derivatives with respect to the velocity variables of the particle, which are absent in the Cartesian coordinate formulation of the transport equation, arise in the spherical coordinate formulation of the transport equation in response to the centrifugal force which prevents a free particle from ‘falling into the origin’ of the coordinate system.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Quantum mechanical closure of partial differential equations with symmetries
We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a quantum mechanical representation, we use the space of quantum density operators to model the unresolved degrees of freedom of the original dynamics in a statistical sense, and the framework of quantum measurement to predict their contributions to the resolved dynamics. The embedded dynamics is discretized by a positivity preserving process, leading to a compressed representation that is invariant under the dynamical symmetries of the resolved dynamics. We present a data based formulation of the closure scheme and apply it to a closure problem for the shallow water equations. The numerical results demonstrate that our closure model can accurately predict the main features of the true dynamics, including for out of sample initial conditions.
Delay embedding↗
Free-energy estimates from nonequilibrium trajectories under varying-temperature protocols
The Jarzynski equality allows the calculation of free-energy differences using values of work measured from nonequilibrium trajectories. The number of trajectories required to accurately estimate free-energy differences in this way grows sharply with the size of work fluctuations, motivating the search for protocols that perform desired transformations with minimum work. However, protocols of this nature can involve varying temperature, to which the Jarzynski equality does not apply. Here, we derive a variant of the Jarzynski equality that applies to varying-temperature protocols, and show that it can have better convergence properties than the standard version of the equality. We derive this modified equality and the associated fluctuation relation within the framework of Markovian stochastic dynamics, complementing related derivations done within the framework of Hamiltonian dynamics.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
On a finite element CFD algorithm for compressible, viscous and turbulent aerodynamic flows
This paper develops and analyses individual construction aspects of an efficient and accurate finite element algorithm for prediction of viscous and turbulent flow fields of impact in aerodynamics. The theoretical construction employs a Taylor weak statement (TWS) for coincident embedding of stability mechanisms within a classic Galerkin finite element formulation of semidiscrete approximation error orthogonalization. A wide variety of the stabilizing mechanisms of independently derived CFD algorithms are contained within the TWS theory. An implicit construction that meets the requirement of efficient convergence to steady state is developed. The theoretical asymptotic error estimates of the TWS finite element algorithm for supersonic and viscous boundary layer flows are verified. Application to a three-dimensional turbulent flow is cited.
Baker, A. J.↗
Flow lasers
The present work reviews the fluid-mechanical aspects of high-power continuous-wave (CW) lasers. The flow characteristics of these devices appear as classical fluid-mechanical phenomena recast in a complicated interactive environment. The fundamentals of high-power lasers are reviewed, followed by a discussion of the N2-CO2 gas dynamic laser. Next, the HF/DF supersonic diffusion laser is described, and finally the CO electrical-discharge laser is discussed.
Christiansen, W. H.↗