Asymmetric nonlinear dynamic response and buckling of shallow spherical shells
Numerical method and computer program for computing deflection response of thin shells
Liepins, A. A.↗
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PipeSight: A High-Performance Computing Platform for Pipeline Integrity Management
The Phase I feasibility study completed as part of this project has led to a number of innovative technologies being developed and has laid the foundation for a successful Phase II effort to commercialize a platform for managing the integrity of pipelines for the damage mechanisms of the new, hybrid-energy based economy. To ground the development efforts and direction of the project, an extensive market research and customer discovery effort was undertaken early in Phase I. Through this effort, a number of pipeline owners and operators were interviewed, and the following key findings were discovered about the pipeline industry: • Small pipeline operators do not have the central engineering groups necessary to perform their own independent analysis of inspection data, but instead rely on summarized tally sheets provided to them by inspection service providers. • The time it takes to go from an inspection to a completed engineering assessment, even for small segments of pipeline, can take anywhere from 30-120 days. During this delay, critical threats can (and have been known to) cause failures. • Uncertainty is often not accounted for in the assessment of pipeline integrity. The tally sheets provided by third-party service providers are almost always deterministic in nature, identifying threats that present a concern only to the current (not the future) integrity of the pipeline. • It is uncommon to apply the latest technologies to perform advanced assessments of damaged pipelines. There is a desire to use more advanced analysis capabilities to assess threats. Many pipeline operators indicated that they would often excavate a pipeline to perform an inspection and find that the damage was not as bad as they anticipated, thus using limited resources unnecessarily. Companies are not consistent in their use of inspection data to determine corrosion rates, and those that do only calculate deterministic corrosion rates. • The industry has prominently relied on time-based inspections but has recently started to transition to risk-based inspections. However, there appears to be no uniform guidance on how to do so while properly accounting for all sources of uncertainty. • Companies are not storing inspection data in a manner that allows for the ready determination of temporal trends. • Predictive maintenance principles and practices are beginning to be used by early adopters • Some pipelines are being re-purposed to transport different process fluids than they were designed for, e.g., H 2 and CO 2 rich process streams to serve the new hybrid-energy based economy, which are presenting new integrity concerns for the existing pipeline network that crisscrosses the United States. As a result of these discoveries, we were able to target the development efforts in Phase I to best serve the needs of the industry. In Phase I, we developed a way to correlate multiple large-scale scans of the pipeline to determine a probabilistic corrosion rate that accounts for all sources of error and uncertainty in the inspection process. This probabilistic corrosion rate can be used to predict the future thickness distribution of the pipe wall. We demonstrate how this analysis may be performed in an analytical fashion and has been implemented in such a manner that it can be readily distributed using GPU computing through integration of the Kokkos programming model. We also make a very novel extension of the analytical corrosion rate model to Bayesian Networks (an explainable AI technique) that can account for non-parametric distributions of corrosion rates. With the predictions made above for the probabilistic corrosion rate and corresponding future distribution of the pipe wall thickness, we can assess the integrity of the pipeline through the use of a probabilistic engineering assessment. We developed a novel screening data analysis approach that can rapidly identify ‘hotspots’ (local thin areas) where the integrity of the pipeline is a concern. Once more, we implemented this screening approach in C++ to leverage GPU computing via the Kokkos programming model. After the critical hotspots are identified, we developed a program that can automatically generate an advanced finite element model of the damaged regions. Since the number of damaged regions that require advanced analysis can number in the thousands, we integrated an open-source container-native workflow engine for orchestrating parallel jobs on the cloud. Initially, these advanced numerical models were only designed to account for loading due to internal pressure. However, in a slight pivot from the initial Phase I proposal, we developed a complete pipe stress analysis program (called Simflex) which can simulate the complete pipeline and its response to thermal expansion, pressure, thermal bowing, weight, wind, earthquake, support displacement, support friction and external forces. This pipe stress analysis program was written generically, to handle any piping system, but contains the features needed to model long pipelines (i.e., it incorporates a model for soil mechanics and can account for the nonlinear boundary conditions necessary to simulate long underground pipelines). This pipe stress analysis program can simulate any segment of the pipeline (simple or complex) under any set of conditions and loads, to determine the supplemental loads (axial forces and bending moments) at the location of damage. This enables the most accurate state of stress to be accounted for in the pipeline, which can prove critical when evaluating the integrity of a damaged region. In the process of developing the technologies to perform the integrity assessment of the pipeline, we also extended one of the industry standard approaches for performing the assessment of local thin areas that extend more in the circumferential direction than the longitudinal direction of the pipeline. This approach was presented to the API 579-1/AS ME FFS-1 steering committee in November 2021 for consideration in the next edition of the industry standard for Fitness-For-Service (expected to be released in 2023). To help pipeline operators make decisions with the results on any integrity assessment, we developed a new approach to the life-cycle management of pipelines which uses a Bayesian Decision Network. The network is designed to help pipeline operators plan and prioritize inspection activities and ultimately make smarter, more cost-effective decisions. The Bayesian approach accounts for all sources of uncertainty and carries them through to the final optimal decisions, providing a probabilistic framework for optimizing inspection intervals. The proof-of-concept networks developed in the feasibility study are complete, verified, and are focused on a subset of the pipeline. To expand this novel approach to the scale necessary for an entire network of pipelines in Phase II, we will leverage the DOE-funded Bengi solver for industrial-scale decision making with Bayesian Networks [22]. Once implemented, we will be able to provide the pipeline industry with a much-needed tool for optimal inspection planning using truly explainable artificial intelligence (XAI). To handle all of these advanced capabilities into a cloud-based platform, the architecture of the Equity Engineering Cloud (EEC) was extended to include Argo Workflows, a framework capable of distributing and managing a massive number of jobs that consume their own resources, such that thousands of serial finite element simulations can be run in parallel. As part of this substantial undertaking, we also integrated Argo Continuous Delivery (CD) into the EEC, to aid with the rapid prototyping and iterations that will be imperative to the success of the PipeSight platform’s Agile development process in Phase II. As part of the pipe stress analysis program, we also developed a custom visualizer that leverages the DOE-funded VTK visualization library. We added custom contouring capabilities and a means for interacting visually with both the inputs and outputs of the pipe stress analysis program. We also developed routines for automating the post-processing of the finite element simulations to determine if any failure criteria are met and to visualize the deformations, stresses and strains in ParaView using the exodus II file format (a subset of netCDF).
24 POWER TRANSMISSION AND DISTRIBUTION↗
The linear and nonlinear response of infinite periodic systems to static and/or dynamic electric fields. Implementation in CRYSTAL code
An implementation of the vector potential approach (VPA) for treating the response of infinite periodic systems to static and dynamic electric fields has been initiated within the CRYSTAL code. The VPA method is based on the solution of a time-dependent Hartree-Fock or Kohn-Sham equation for the crystal orbitals wherein the usual scalar potential, that describes interaction with the field, is replaced by the vector potential. This equation may be solved either by perturbation theory or by finite field methods. With some modification all the computational procedures of molecular ab initio quantum chemistry can be adapted for periodic systems. Accessible properties include the linear and nonlinear responses of both the nuclei and the electrons. The programming of static field pure electronic (hyper)polarizabilities has been successfully tested. Dynamic electronic (hyper)polarizabilities, as well as infrared and Raman intensities, are in progress while the addition of finite fields for calculation of vibrational (hyper)polarizabilities, through nuclear relaxation procedures, will begin shortly.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Nonlinear estimation of monsoon rainfall from radar and raingage data
Estimates of climatological rainfall are made as part of the validation program for the Tropical Rainfall Measuring Mission. Radar and raingage data collected during AMEX in Darwin, Australia during 1987 and 1988 are analyzed using a nonlinear merging methodology known as disjunctive cokriging (Azimi-Zonooz et al., 1989). The methodology is outlined and the results are used to determine the most advantageous time scale for estimation.
Krajewski, Witold F.↗
Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems
The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods.
Murthy, V. R.↗
Program for the solution of multipoint boundary value problems of quasilinear differential equations
Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.
Source record↗
The relationship between phytoplankton concentration and light attenuation in ocean waters
The accuracy of chlorophyll estimates by ocean color algorithms is affected by the variability of particulate attenuation; the presence of dissolved organic matter; and the nonlinear inverse relationship between the attenuation coefficient, K, and chlorophyll. Data collected during the Warm Core Rings Program were used to model the downwelling light field and determine the impact of these errors. A possible mechanism for the nonlinearity of K and chlorophyll is suggested; namely, that changing substrate from nitrate-nitrogen to ammonium causes enhanced blue absorption by photosynthetic phytoplankton in oligotrophic surface waters.
Phinney, David A.↗
Occupant Responses in a Full-Scale Crash Test of the Sikorsky ACAP Helicopter
A full-scale crash test of the Sikorsky Advanced Composite Airframe Program (ACAP) helicopter was performed in 1999 to generate experimental data for correlation with a crash simulation developed using an explicit nonlinear, transient dynamic finite element code. The airframe was the residual flight test hardware from the ACAP program. For the test, the aircraft was outfitted with two crew and two troop seats, and four anthropomorphic test dummies. While the results of the impact test and crash simulation have been documented fairly extensively in the literature, the focus of this paper is to present the detailed occupant response data obtained from the crash test and to correlate the results with injury prediction models. These injury models include the Dynamic Response Index (DRI), the Head Injury Criteria (HIC), the spinal load requirement defined in FAR Part 27.562(c), and a comparison of the duration and magnitude of the occupant vertical acceleration responses with the Eiband whole-body acceleration tolerance curve.
Jackson, Karen E.↗
Occupant Responses in a Full-Scale Crash Test of the Sikorsky ACAP Helicopter
A full-scale crash test of the Sikorsky Advanced Composite Airframe Program (ACAP) helicopter was performed in 1999 to generate experimental data for correlation with a crash simulation developed using an explicit nonlinear, transient dynamic finite element code. The airframe was the residual flight test hardware from the ACAP program. For the test, the aircraft was outfitted with two crew and two troop seats, and four anthropomorphic test dummies. While the results of the impact test and crash simulation have been documented fairly extensively in the literature, the focus of this paper is to present the detailed occupant response data obtained from the crash test and to correlate the results with injury prediction models. These injury models include the Dynamic Response Index (DRI), the Head Injury Criteria (HIC), the spinal load requirement defined in FAR Part 27.562(c), and a comparison of the duration and magnitude of the occupant vertical acceleration responses with the Eiband whole-body acceleration tolerance curve.
Jackson, Karen E.↗
Acoustic fatigue life prediction for nonlinear structures with multiple resonant modes
This report documents an effort to develop practical and accurate methods for estimating the fatigue lives of complex aerospace structures subjected to intense random excitations. The emphasis of the current program is to construct analytical schemes for performing fatigue life estimates for structures that exhibit nonlinear vibration behavior and that have numerous resonant modes contributing to the response.
Miles, R. N.↗
Alfvén wave collisions, the fundamental building block of plasma turbulence. I. Asymptotic solution
The nonlinear interaction between counterpropagating Alfvén waves is the physical mechanism underlying the cascade of energy to small scales in astrophysical plasma turbulence. Beginning with the equations for incompressible MHD, an asymptotic analytical solution for the nonlinear evolution of these Alfvén wave collisions is derived in the weakly nonlinear limit. The resulting qualitative picture of nonlinear energy transfer due to this mechanism involves two steps: first, the primary counterpropagating Alfvén waves interact to generate an inherently nonlinear, purely magnetic secondary fluctuation with no parallel variation; second, the two primary waves each interact with this secondary fluctuation to transfer energy secularly to two tertiary Alfvén waves. These tertiary modes are linear Alfvén waves with the same parallel wavenumber as the primary waves, indicating the lack of a parallel cascade. The amplitude of these tertiary modes increases linearly with time due to the coherent nature of the resonant four-wave interaction responsible for the nonlinear energy transfer. The implications of this analytical solution for turbulence in astrophysical plasmas are discussed. The solution presented here provides valuable intuition about the nonlinear interactions underlying magnetized plasma turbulence, in support of an experimental program to verify in the laboratory the nature of this fundamental building block of astrophysical plasma turbulence.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
H–J–B Equations of Optimal Consumption-Investment and Verification Theorems
We consider a consumption-investment problem on infinite time horizon maximizing discounted expected HARA utility for a general incomplete market model. Based on dynamic programming approach we derive the relevant H–J–B equation and study the existence and uniqueness of the solution to the nonlinear partial differential equation. By using the smooth solution we construct the optimal consumption rate and portfolio strategy and then prove the verification theorems under certain general settings.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Modeling and Simulation of Rotary Sloshing in Launch Vehicles
The nonlinear dynamics of propellant sloshing during orbital ascent are usually neglected in the flight control analysis of large boost vehicles under the assumption that the viscous damping of the fluid is sufficient to suppress nonlinear phenomena and confine the fluid to small, planar free surface displacements. In this case, the sloshing dynamics can be modeled using a spring-mass-damper or linearized pendulum mechanical analog. However, large, smooth-wall tanks without significant internal hardware or ring baffles are still susceptible to nonlinear effects. In particular, rotary sloshing can present a risk to flight control as it involves the formation of a stable limit cycle which can lead to undesirable roll coupling. The underlying phenomena of jump resonance does not manifest in linear models, but can be reproduced using a nonlinear spherical pendulum or the Bauer paraboloid model developed during the Apollo/Saturn program. In this paper, a detailed analysis of the rotary sloshing dynamics of these mechanical analogs is presented, and discussed in the context of flight control stability. High-fidelity simulations of a representative boost vehicle are used to verify the semi-analytical predictions of the nonlinear dynamic response.
Modeling↗
Nonlinear viscoelastic characterization of thin polyethylene film
In order to understand the state of stress and strain in a typical balloon fabricated from thin polyethylene film, experiment data in the literature reviewed. It was determined that the film behaves as a nonlinear viscoelasticity material and should be characterized accordingly. A simple uniaxial, nonlinear viscoelastic model was developed for predicting stress given a certain strain history. The simple model showed good qualitative agreement with results of constant rate, uniaxial accurately predicting stresses for cyclic strain histories typical of balloon flights. A program was outlined which will result in the development of a more complex nonlinear viscoelastic model.
Wilbeck, J. S.↗
Combustion instability with partial length acoustic liners
The development is discussed of analytical techniques and numerical methods for the prediction of the stability behavior of liquid propellant rocket combustors with partial length acoustic liners, injector face baffles, and nonlinear combustion responses. Three primary objectives included: (1) extension of the Green's Function integral-iteration technique previously developed so that nonlinear three dimensional wave propagation effects could be included in stability predictions; (2) development of an analytical technique and a computer program for the prediction of the damping effects caused by injector face baffles; and (3) inclusion of a nonlinear, wave distortation dependent, combustion response model in the global stability analysis and determination of its effect on combustor stability.
Mitchell, C. E.↗
Blade loss transient dynamics analysis, volume 1. Task 2: TETRA 2 theoretical development
The theoretical development of the forced steady state analysis of the structural dynamic response of a turbine engine having nonlinear connecting elements is discussed. Based on modal synthesis, and the principle of harmonic balance, the governing relations are the compatibility of displacements at the nonlinear connecting elements. There are four displacement compatibility equations at each nonlinear connection, which are solved by iteration for the principle harmonic of the excitation frequency. The resulting computer program, TETRA 2, combines the original TETRA transient analysis (with flexible bladed disk) with the steady state capability. A more versatile nonlinear rub or bearing element which contains a hardening (or softening) spring, with or without deadband, is also incorporated.
Gallardo, Vincente C.↗
Linearized Aeroelastic Solver Applied to the Flutter Prediction of Real Configurations
A fast-running unsteady aerodynamics code, LINFLUX, was previously developed for predicting turbomachinery flutter. This linearized code, based on a frequency domain method, models the effects of steady blade loading through a nonlinear steady flow field. The LINFLUX code, which is 6 to 7 times faster than the corresponding nonlinear time domain code, is suitable for use in the initial design phase. Earlier, this code was verified through application to a research fan, and it was shown that the predictions of work per cycle and flutter compared well with those from a nonlinear time-marching aeroelastic code, TURBO-AE. Now, the LINFLUX code has been applied to real configurations: fans developed under the Energy Efficient Engine (E-cubed) Program and the Quiet Aircraft Technology (QAT) project. The LINFLUX code starts with a steady nonlinear aerodynamic flow field and solves the unsteady linearized Euler equations to calculate the unsteady aerodynamic forces on the turbomachinery blades. First, a steady aerodynamic solution is computed for given operating conditions using the nonlinear unsteady aerodynamic code TURBO-AE. A blade vibration analysis is done to determine the frequencies and mode shapes of the vibrating blades, and an interface code is used to convert the steady aerodynamic solution to a form required by LINFLUX. A preprocessor is used to interpolate the mode shapes from the structural dynamics mesh onto the computational fluid dynamics mesh. Then, LINFLUX is used to calculate the unsteady aerodynamic pressure distribution for a given vibration mode, frequency, and interblade phase angle. Finally, a post-processor uses the unsteady pressures to calculate the generalized aerodynamic forces, eigenvalues, an esponse amplitudes. The eigenvalues determine the flutter frequency and damping. Results of flutter calculations from the LINFLUX code are presented for (1) the E-cubed fan developed under the E-cubed program and (2) the Quiet High Speed Fan (QHSF) developed under the Quiet Aircraft Technology project. The results are compared with those obtained from the TURBO-AE code. A graph of the work done per vibration cycle for the first vibration mode of the E-cubed fan is shown. It can be seen that the LINFLUX results show a very good comparison with TURBO-AE results over the entire range of interblade phase angle. The work done per vibration cycle for the first vibration mode of the QHSF fan is shown. Once again, the LINFLUX results compare very well with the results from the TURBOAE code.
Reddy, Tondapu S.↗
The role of computerized symbolic manipulation in rotorcraft dynamics analysis
The potential role of symbolic manipulation programs in development and solution of the governing equations for rotorcraft dynamics problems is discussed and illustrated. Nonlinear equations of motion for a helicopter rotor blade represented by a rotating beam are developed making use of the computerized symbolic manipulation program MACSYMA. The use of computerized symbolic manipulation allows the analyst to concentrate on more meaningful tasks, such as establishment of physical assumptions, without being sidetracked by the tedious and trivial details of the algebraic manipulations. Furthermore, the resulting equations can be produced, if necessary, in a format suitable for numerical solution. A perturbation-type solution for the resulting dynamical equations is shown to be possible with a combination of symbolic manipulation and standard numerical techniques. This should ultimately lead to a greater physical understanding of the behavior of the solution than is possible with purely numerical techniques. The perturbation analysis of the flapping motion of a rigid rotor blade in forward flight is presented, for illustrative purposes, via computerized symbolic manipulation with a method that bypasses Floquet theory.
Crespo Da Silva, Marcelo R. M.↗