Analytical Methods in Vibrations.
Book on analytical methods in vibrations covering general mathematical formulations of common features of various vibrating systems
STATISTICAL ANALYSIS↗
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Results for “Mathematical analysis”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Advances in 3-D Inelastic Analysis Methods for hot section components
3-D Inelastic Analysis Methods are described. These methods consist of a series of new computer codes embodying a progression of mathematical models (mechanics of materials, specialty finite element, boundary element) for streamlined analysis of: (1) combustor liners, (2) turbine blades, and (3) turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain) and global (dynamics, buckling) structural behavior of the three selected components. Three computer codes, referred to as MOMM (Mechanics of Materials Model), MHOST (MARC-Hot Section Technology), and BEST (Boundary Element Stress Technology), have been developed and are briefly described in this paper.
Chamis, Christos C.↗
Space station integrated wall design and penetration damage control
The analysis code BUMPER executes a numerical solution to the problem of calculating the probability of no penetration (PNP) of a spacecraft subject to man-made orbital debris or meteoroid impact. The codes were developed on a DEC VAX 11/780 computer that uses the Virtual Memory System (VMS) operating system, which is written in FORTRAN 77 with no VAX extensions. To help illustrate the steps involved, a single sample analysis is performed. The example used is the space station reference configuration. The finite element model (FEM) of this configuration is relatively complex but demonstrates many BUMPER features. The computer tools and guidelines are described for constructing a FEM for the space station under consideration. The methods used to analyze the sensitivity of PNP to variations in design, are described. Ways are suggested for developing contour plots of the sensitivity study data. Additional BUMPER analysis examples are provided, including FEMs, command inputs, and data outputs. The mathematical theory used as the basis for the code is described, and illustrates the data flow within the analysis.
Coronado, A. R.↗
The cluster decomposition of the configurational energy of multicomponent alloys
Abstract The cluster expansion method (CEM) is a widely used lattice-based technique in the study of multicomponent alloys. Despite its prevalent use, a clear understanding of expansion terms is lacking. We present a modern mathematical formalism of the CEM and introduce thecluster decomposition—a unique and basis-independent decomposition for functions of the atomic configuration in a crystal. We identify the cluster decomposition as an invariant ANOVA decomposition; and demonstrate how functional analysis of variance and sensitivity analysis can be used to interpret interactions among species. Furthermore, we show how the mathematical structure of the cluster decomposition enables numerical evaluation that scales with the number of clusters and is independent of the number of species. Overall, our work enables rigorous interpretations of interactions among species, provides opportunities to explore parameter estimation beyond linear regression, introduces a numerical efficient implementation, and enables analysis of cluster expansions based on established mathematical and statistical principles.
Chemistry↗
Fundamental analysis of the failure of polymer-based fiber reinforced composites
A mathematical model is described which will permit predictions of the strength of fiber reinforced composites containing known flaws to be made from the basic properties of their constituents. The approach was to embed a local heterogeneous region (LHR) surrounding the crack tip into an anisotropic elastic continuum. The model should (1) permit an explicit analysis of the micromechanical processes involved in the fracture process, and (2) remain simple enough to be useful in practical computations. Computations for arbitrary flaw size and orientation under arbitrary applied load combinations were performed from unidirectional composites with linear elastic-brittle constituent behavior. The mechanical properties were nominally those of graphite epoxy. With the rupture properties arbitrarily varied to test the capability of the model to reflect real fracture modes in fiber composites, it was shown that fiber breakage, matrix crazing, crack bridging, matrix-fiber debonding, and axial splitting can all occur during a period of (gradually) increasing load prior to catastrophic fracture. The computations reveal qualitatively the sequential nature of the stable crack process that precedes fracture.
Kanninen, M. F.↗
Multifunctional Collaborative Modeling and Analysis Methods in Engineering Science
Engineers are challenged to produce better designs in less time and for less cost. Hence, to investigate novel and revolutionary design concepts, accurate, high-fidelity results must be assimilated rapidly into the design, analysis, and simulation process. This assimilation should consider diverse mathematical modeling and multi-discipline interactions necessitated by concepts exploiting advanced materials and structures. Integrated high-fidelity methods with diverse engineering applications provide the enabling technologies to assimilate these high-fidelity, multi-disciplinary results rapidly at an early stage in the design. These integrated methods must be multifunctional, collaborative, and applicable to the general field of engineering science and mechanics. Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple-method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized. The multifunctional methodology presented provides an effective mechanism by which domains with diverse idealizations are interfaced. This capability rapidly provides the high-fidelity results needed in the early design phase. Moreover, the capability is applicable to the general field of engineering science and mechanics. Hence, it provides a collaborative capability that accounts for interactions among engineering analysis methods.
Ransom, Jonathan B.↗
On 3-D inelastic analysis methods for hot section components (base program)
A 3-D Inelastic Analysis Method program is described. This program consists of a series of new computer codes embodying a progression of mathematical models (mechanics of materials, special finite element, boundary element) for streamlined analysis of: (1) combustor liners, (2) turbine blades, and (3) turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain)and global (dynamics, buckling) structural behavior of the three selected components. Three computer codes, referred to as MOMM (Mechanics of Materials Model), MHOST (Marc-Hot Section Technology), and BEST (Boundary Element Stress Technology), have been developed and are briefly described in this report.
Wilson, R. B.↗
Advanced methods for 3-D inelastic structural analysis for hot engine structures
Three-dimensional Inelastic Analysis Methods are described. These methods were incorporated into a series of new computer codes embodying a progression of mathematical models (mechanics of materials, specialty finite element, boundary element) for streamlined analysis of hot engine structures such as: (1) combustor liners, (2) turbine blades, and (3) turbine vanes. These models address the effects of high temperatures and thermal/mechanical loadings on the local (stress/strain) and global (displacements, frequencies, amplitudes, buckling) structural behavior of the three respective components. The methods and the three computer codes, referred to as MOMM (Mechanics Of Materials Model), MHOST (MARC-Hot Section Technology), and BEST3D (Boundary Element Stress Technology), have been developed and are briefly described.
Chamis, C. C.↗
Development of Response Surface Models for Rapid Analysis & Multidisciplinary Optimization of Launch Vehicle Design Concepts
Multdisciplinary design optimization (MDO) is an important step in the design and evaluation of launch vehicles, since it has a significant impact on performance and lifecycle cost. The objective in MDO is to search the design space to determine the values of design parameters that optimize the performance characteristics subject to system constraints. Vehicle Analysis Branch (VAB) at NASA Langley Research Center has computerized analysis tools in many of the disciplines required for the design and analysis of launch vehicles. Vehicle performance characteristics can be determined by the use of these computerized analysis tools. The next step is to optimize the system performance characteristics subject to multidisciplinary constraints. However, most of the complex sizing and performance evaluation codes used for launch vehicle design are stand-alone tools, operated by disciplinary experts. They are, in general, difficult to integrate and use directly for MDO. An alternative has been to utilize response surface methodology (RSM) to obtain polynomial models that approximate the functional relationships between performance characteristics and design variables. These approximation models, called response surface models, are then used to integrate the disciplines using mathematical programming methods for efficient system level design analysis, MDO and fast sensitivity simulations. A second-order response surface model of the form given has been commonly used in RSM since in many cases it can provide an adequate approximation especially if the region of interest is sufficiently limited.
Unal, Resit↗
Central Compact Finite‐Difference Scheme With High Spectral Resolution for KdV Equation
This work presents a combination of cell‐node and cell‐centered compact finite difference scheme for the approximation of third derivatives involved in Korteweg–de Vries (KdV) equations. This approach employs a half‐shifted derivative construction at cell centers, avoiding the need for compact interpolation, thereby removing transfer errors; hence, it improves spectral resolution and maintains high‐order accuracy. Fourier analysis is performed to show the spectral properties of the proposed formulation, which provides higher spectral resolutions as compared to node‐based compact schemes. A filtering strategy is incorporated to suppress high‐frequency oscillations without compromising the accuracy of the numerical scheme, and the total variation diminishing Runge Kutta (TVDRK3) method is applied for time integration. Numerical experiments on linear, nonlinear, and coupled KdV systems are conducted, and a comparative analysis with cell‐node compact schemes confirms that the proposed scheme consistently reduces errors by up to an order of magnitude and achieves high spectral resolution properties.
97 MATHEMATICS AND COMPUTING↗
Statistical methods for astronomical data with upper limits. I - Univariate distributions
The statistical treatment of univariate censored data is discussed. A heuristic derivation of the Kaplan-Meier maximum-likelihood estimator from first principles is presented which results in an expression amenable to analytic error analysis. Methods for comparing two or more censored samples are given along with simple computational examples, stressing the fact that most astronomical problems involve upper limits while the standard mathematical methods require lower limits. The application of univariate survival analysis to six data sets in the recent astrophysical literature is described, and various aspects of the use of survival analysis in astronomy, such as the limitations of various two-sample tests and the role of parametric modelling, are discussed.
Feigelson, E. D.↗
Local-global analysis of crack growth in continuously reinfoced ceramic matrix composites
This paper describes the development of a mathematical model for predicting the strength and micromechanical failure characteristics of continuously reinforced ceramic matrix composites. The local-global analysis models the vicinity of a propagating crack tip as a local heterogeneous region (LHR) consisting of spring-like representation of the matrix, fibers and interfaces. Parametric studies are conducted to investigate the effects of LHR size, component properties, and interface conditions on the strength and sequence of the failure processes in the unidirectional composite system.
Ballarini, Roberto↗
CIE Analysis Process for Engineered Systems
"CIE Analysis Process for Engineered Systems" outlines a comprehensive methodology for integrating Cyber-Informed Engineering (CIE) principles into both new and existing engineered systems. Sponsored by the U.S. Department of Energy’s Office of Cybersecurity, Energy Security, and Emergency Response (DOE CESER), the process aims to achieve cyber-informed decisions by producing functional security requirements for new systems and retrofitting existing systems to mitigate digital risks. The document details a step-by-step approach, including mission and function definition, digital asset awareness, consequence analysis, and mitigation analysis. It emphasizes the importance of documenting mechanical, electrical, programmable, and network components to protect system functions and provides examples and considerations for each step. The ultimate goal is to ensure that engineered systems remain resilient against cyber threats, maintaining safety, performance, and reliability.
42 - ENGINEERING↗
Simulation Environments for Physical Phenomena of Extreme Events
Slides for an external workshop on simulation approaches to risk analysis.
97 MATHEMATICS AND COMPUTING↗
Parametric study of supersonic STOVL flight characteristics
A number of different control devices and techniques are evaluated to determine their suitability for increasing the short takeoff performance of a supersonic short-takeoff/vertical landing (STOVL) aircraft. Analysis was based on a rigid-body mathematical model of the General Dynamics E-7, a single engine configuration that utilizes ejectors and thrust deflection for propulsive lift. Alternatives investigated include increased static pitch, the addition of a close-coupled canard, use of boundary layer control to increase the takeoff lift coefficient, and the addition of a vectorable aft fan air nozzle. Other performance studies included the impact of individual E-7 features, the sensitivity to ejector performance, the effect of removing the afterburners, and a determination of optional takeoff and landing transition methods. The results pertain to both the E-7 and other configurations. Several alternatives were not as well suited to the E-7 characteristics as they would be to an alternative configuration, and vice versa. A large amount of supporting data for each analysis is included.
Rapp, David C.↗
Improving Dose Modeling With Dynamic Modeling Tools [Slides]
Utilities aiming for higher fuel enrichment for power uprates or extended operation times before refueling must conduct a new dose analysis. Current conservative dose estimation standards may cause utilities to exceed regulatory limits for proposed increased fuel enrichment. A more accurate modeling of doses from reactor accidents can lower these conservative assumptions. Prescott et al. (2022) demonstrated that the Event Modeling Risk Assessment using Linked Diagrams (EMRALD) software tool, developed at Idaho National Laboratory (INL), can be coupled with the Modular Accident Analysis Program (MAAP5) for dynamic accident analysis in reactor plants. EMRALD forms models of potential accident scenarios, while MAAP5 simulates the accident progression and dose consequences. By integrating these software tools with utility-specific data, a more precise estimation of dose consequences from plant accidents can be achieved. Preliminary findings indicate that EMRALD provides accurate mean core damage frequencies for generalized accident scenarios. Future work includes expanding the model to account for plant-specific data and mitigation factors.
97 - MATHEMATICS AND COMPUTING↗
Stability analysis of Riccati covariance equations of Kalman filter.
The present paper takes the basic mathematical approach to analyze the stability of Riccati equations. First, a simple stability criterion like that of the linear constant coefficient system is sought for the nonlinear constant Riccati Equation. Then, a complete analysis on the limiting covariance P follows. The analysis is focussed on the main theorem. Finally, the computational aspects of the Riccati equations are analyzed with examples. The application of this analysis is to provide a simple stability criterion for the Kalman filter computation to test and predict filter convergence and thus modify filter parameters accordingly.
Teng, L.↗
Application of optimization techniques to the design of a flutter suppression control law for the DAST ARW-2
The design of a candidate flutter suppression (FS) control law for the symmetric degrees of freedom for the DAST ARW-2 aircraft is discussed. The results illustrate the application of several currently employed control law design techniques. Subsequent designs, obtained as the mathematical model of the ARW-2 is updated, are expected to employ similar methods and to provide a control law whose performance will be flight tested. This study represents one of the steps necessary to provide an assessment of the validity of applying current control law synthesis and analysis techniques in the design of actively controlled aircraft. Mathematical models employed in the control law design and evaluation phases are described. The control problem is specified by presenting the flutter boundary predicted for the uncontrolled aircraft and by defining objectives and constraints that the controller should satisfy. A full-order controller is obtained by using Linear Quadratic Gaussian (LQG) techniques. The process of obtaining an implementable reduced-order controller is described. One example is also shown in which constrained optimization techniques are utilized to explicitly include robustness criteria within the design algorithm.
Adams, W. M., Jr.↗