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User information manual for digital program to compute mechanical shock and Fourier response spectra for base-excited and viscous-damped single degree-of-freedom oscillator
A user-oriented subroutine package is built around a highly stable explicit integration algorithm for solution of large order systems of ordinary differential equations, as result from discretization of initial-boundary value problems in continuum mechanics. Fast and accurate solutions, for problems in laminar and turbulent, two and three-dimensional viscous flow fields and multi-dimensional transient heat transfer, are presented using this algorithm, as embodied within a general purpose finite element computer program.
Numerical simulation has now become an integral part of engineering design process. Critical design decisions are routinely made based on the simulation results and conclusions. Verification and validation of the reliability of the numerical simulation is therefore vitally important in the engineering design processes. We propose to develop theories and methodologies that can automatically provide quantitative information about the reliability of the numerical simulation by estimating numerical approximation error, computational model induced errors and the uncertainties contained in the mathematical models so that the reliability of the numerical simulation can be verified and validated. We also propose to develop and implement methodologies and techniques that can control the error and uncertainty during the numerical simulation so that the reliability of the numerical simulation can be improved.
A set of nonlinear partial differential equations suitable for the description of a class of turbulent three-dimensional flow fields in select geometries is identified. On the basis of the concept of enforcing a penalty constraint to ensure accurate accounting of ordering effects, a finite element numerical solution algorithm is established for the equation set and the theoretical aspects of accuracy, convergence and stability are identified and quantized. Hypermatrix constructions are used to formulate the reduction of the computational aspects of the theory to practice. The robustness of the algorithm, and the computer program embodiment, have been verified for pertinent flow configurations.
Computerized design criteria for turbomachinery and the constraints imposed by very high rotational fields are presented along with a variety of computerized design criteria of interest to structural designers.
Numerical procedures for accurate determination of elastic stress intensity factors for the general two-dimensional crack problem are reviewed. The elastic perfectly plastic state of crack tip deformation is studied by a finite element procedure. Elastic-plastic fields in the immediate vicinity of a crack tip are determined numerically by finite element procedures based on asymptotic studies of crack tip singularities in plastic materials. The small-scale yielding problem is modeled, and expressions for crack tip opening displacement, shear singularity amplitude, and plastic zone extent are derived. A finite element solution to the large-scale yielding of a circumferentially cracked round tension bar is obtained. The three-dimensional aspects of flawed structures and numerical methods of treating them are studied. Ductile fracture mechanisms, in particular crack tip fracture on the microscale, are discussed.
A finite element solution algorithm is established for a general statement of the time-averaged Navier-Stokes equations governing multi-dimensional turbulent flows. Numerical results are presented which evaluate factors affecting solution accuracy for a broad spectrum of linear and non-linear problem classes.
A one-equation turbulence model based on the turbulent kinetic energy equation is presented. The model is motivated by the success of the Johnson-King model and incorporates a number of features uncovered by Simpson's experiments on separated flows. Based on the results obtained, the model duplicates the success of algebraic models in attached flow regions and outperforms the two-equation models in detached flow regions.
The usage and development of structural finite element processors based on the CSM Testbed's Generic Element Processor (GEP) template is documented. By convention, such processors have names of the form ESi, where i is an integer. This manual is therefore intended for both Testbed users who wish to invoke ES processors during the course of a structural analysis, and Testbed developers who wish to construct new element processors (or modify existing ones).
The development of algebraic multigrid (AMG) methods and their application to certain problems in structural mechanics are described with emphasis on two- and three-dimensional linear elasticity equations and the 'jacket problems' (three-dimensional beam structures). Various possible extensions of AMG are also described. The basic idea of AMG is to develop the discretization sequence based on the target matrix and not the differential equation. Therefore, the matrix is analyzed for certain dependencies that permit the proper construction of coarser matrices and attendant transfer operators. In this manner, AMG appears to be adaptable to structural analysis applications.
Classical structural reliability assessment techniques are based on precise and crisp (sharp) definitions of failure and non-failure (survival) of a structure in meeting a set of strength, function and serviceability criteria. These definitions are provided in the form of performance functions and limit state equations. Thus, the criteria provide a dichotomous definition of what real physical situations represent, in the form of abrupt change from structural survival to failure. However, based on observing the failure and survival of real structures according to the serviceability and strength criteria, the transition from a survival state to a failure state and from serviceability criteria to strength criteria are continuous and gradual rather than crisp and abrupt. That is, an entire spectrum of damage or failure levels (grades) is observed during the transition to total collapse. In the process, serviceability criteria are gradually violated with monotonically increasing level of violation, and progressively lead into the strength criteria violation. Classical structural reliability methods correctly and adequately include the ambiguity sources of uncertainty (physical randomness, statistical and modeling uncertainty) by varying amounts. However, they are unable to adequately incorporate the presence of a damage spectrum, and do not consider in their mathematical framework any sources of uncertainty of the vagueness type. Vagueness can be attributed to sources of fuzziness, unclearness, indistinctiveness, sharplessness and grayness; whereas ambiguity can be attributed to nonspecificity, one-to-many relations, variety, generality, diversity and divergence. Using the nomenclature of structural reliability, vagueness and ambiguity can be accounted for in the form of realistic delineation of structural damage based on subjective judgment of engineers. For situations that require decisions under uncertainty with cost/benefit objectives, the risk of failure should depend on the underlying level of damage and the uncertainties associated with its definition. A mathematical model for structural reliability assessment that includes both ambiguity and vagueness types of uncertainty was suggested to result in the likelihood of failure over a damage spectrum. The resulting structural reliability estimates properly represent the continuous transition from serviceability to strength limit states over the ultimate time exposure of the structure. In this section, a structural reliability assessment method based on a fuzzy definition of failure is suggested to meet these practical needs. A failure definition can be developed to indicate the relationship between failure level and structural response. In this fuzzy model, a subjective index is introduced to represent all levels of damage (or failure). This index can be interpreted as either a measure of failure level or a measure of a degree of belief in the occurrence of some performance condition (e.g., failure). The index allows expressing the transition state between complete survival and complete failure for some structural response based on subjective evaluation and judgment.
Abstract Graph theory has a long history in chemistry. Yet as the breadth and variety of chemical data is rapidly changing, so too do graph encoding methods and analyses that yield qualitative and quantitative insights. Using illustrative cases within a basic mathematical framework, we showcase modern chemical graph theory's utility in Chemists' analysis and model development toolkit. The encoding of both experimental and simulation data is discussed at various levels of granularity of information. This is followed by a discussion of the two major classes of graph theoretical analyses: identifying connectivity patterns and partitioning methods. Measures, metrics, descriptors, and topological indices are then introduced with an emphasis upon enhancing interpretability and incorporation into physical models. Challenging data cases are described that include strategies for studying time dependence. Throughout, we incorporate recent advancements in computer science and applied mathematics that are propelling chemical graph theory into new domains of chemical study. This article is categorized under: Molecular and Statistical Mechanics > Molecular Dynamics and Monte‐Carlo Methods Structure and Mechanism > Computational Materials Science Structure and Mechanism > Molecular Structures
Man/machine interface commands computer-controlled mechanical arm. Remotely-controlled arm has six degrees of freedom and is controlled through "supervisory-control" mode, in which all motions of arm follow set of preprogramed sequences. For simplicity, few prescribed commands are required to accomplish entire operation. Applications include operating computer-controlled arm to handle radioactive of explosive materials or commanding arm to perform functions in hostile environments. Modified version using displays may be applied in medicine.
Topics addressed include: numerical aerodynamic simulation; computational mechanics; supercomputers; aerospace propulsion systems; computational modeling in ballistics; turbulence modeling; computational chemistry; computational fluid dynamics; and computational astrophysics.
The fracture mechanics analysis and computer logic used to perform design life predictions is described. Initial part-through crack defects are analyzed under the conditions of constant-amplitude loading to predict the number of loading cycles applied before breakthrough or failure. A criterion is provided to predict the transition from part-through crack growth characteristics to through crack growth characteristics. A breakthrough criterion is also provided.
The COMOC finite element fluid mechanics computer program system is applicable to diverse problem classes. The two dimensional aerodynamics sequence was established for solution of the potential and/or viscous and turbulent flowfields associated with subsonic flight of elementary two dimensional isolated airfoils. The sequence is constituted of three specific flowfield options in COMOC for two dimensional flows. These include the potential flow option, the boundary layer option, and the parabolic Navier-Stokes option. By sequencing through these options, it is possible to computationally construct a weak-interaction model of the aerodynamic flowfield. This report is the user's guide to operation of COMOC for the aerodynamics sequence.
Cooperative efforts between the Lockheed-Huntsville Computational Mechanics Group and the NASA-MSFC Computational Fluid Dynamics staff has resulted in improved capabilities for numerically simulating incompressible flows generic to the Space Shuttle Main Engine (SSME). A well established and documented CFD code was obtained, modified, and applied to laminar and turbulent flows of the type occurring in the SSME Hot Gas Manifold. The INS3D code was installed on the NASA-MSFC CRAY-XMP computer system and is currently being used by NASA engineers. Studies to perform a transient analysis of the FPB were conducted. The COBRA/TRAC code is recommended for simulating the transient flow of oxygen into the LOX manifold. Property data for modifying the code to represent LOX/GOX flow was collected. The ALFA code was developed and recommended for representing the transient combustion in the preburner. These two codes will couple through the transient boundary conditions to simulate the startup and/or shutdown of the fuel preburner. A study, NAS8-37461, is currently being conducted to implement this modeling effort.
In recent years significant advances have been made for parallel computers in both hardware and software. Now parallel computers have become viable tools in computational mechanics. Many application codes developed on conventional computers have been modified to benefit from parallel computers. Significant speedups in some areas have been achieved by parallel computations. For single-discipline use of both fluid dynamics and structural dynamics, computations have been made on wing-body configurations using parallel computers. However, only a limited amount of work has been completed in combining these two disciplines for multidisciplinary applications. The prime reason is the increased level of complication associated with a multidisciplinary approach. In this work, procedures to compute aeroelasticity on parallel computers using direct coupling of fluid and structural equations will be investigated for wing-body configurations. The parallel computer selected for computations is an Intel iPSC/860 computer which is a distributed-memory, multiple-instruction, multiple data (MIMD) computer with 128 processors. In this study, the computational efficiency issues of parallel integration of both fluid and structural equations will be investigated in detail. The fluid and structural domains will be modeled using finite-difference and finite-element approaches, respectively. Results from the parallel computer will be compared with those from the conventional computers using a single processor. This study will provide an efficient computational tool for the aeroelastic analysis of wing-body structures on MIMD type parallel computers.