David S. Riha

A Probabilistically-Based Damage Tolerance Analysis Computer Program for Hard Alpha Anomalies in Titanium Rotors

A probabilistically-based damage tolerance analysis computer program for engine rotors has been developed under Federal Aviation Administration (FAA) funding to augment the traditional safe-life approach. The computer program, in its current form, is designed to quantify the risk of rotor failure due to fatigue cracks initiated at hard alpha anomalies in titanium. The software, DARWIN (Design Assessment of Reliability With Inspection), integrates a graphical user interface, finite element stress analysis results, fracture-mechanics-based life assessment for low-cycle fatigue, material anomaly data, probability of anomaly detection, and inspection schedules to determine the probability-of-fracture of a rotor disk as a function of operating cycles with and without inspections. The program also indicates the relative likelihood of failure of the disk regions. Work is underway to enhance the software to handle anomalies in cast/wrought and powder nickel disks, and manufacturing and maintenance-induced surface anomalies in all disk materials. *Funded under FAA Grant 95-G-04

Geomechanical modeling of an extensional fault-propagation fold: Big Brushy Canyon monocline, Sierra Del Carmen, Texas

Field structural data from the Big Brushy Canyon monocline developed in Cretaceous strata of west Texas are combined with nonlinear finite element modeling to help bridge the gap between geometric, kinematic, and mechanical analysis techniques for understanding the deformation history of reservoir-scale geologic structures. The massive Santa Elena Limestone is offset along a steep normal fault, and fault displacement is accommodated upward by the folding of the Buda Limestone and Boquillas Formation and the thinning in the intervening Del Rio Clay. Mesostructures within competent Buda Limestone beds are concentrated in the monocline limb instead of the hinge and include bed-perpendicular veins that accommodate bed-parallel extension and bedding-plane slip surfaces that offset the veins and accommodate flexural slip. Finite element models were constructed to reproduce the monocline geometry and deformation distribution as well as to assess the effect of material properties and boundary conditions on structural evolution. The initial model configuration replicated the assumed predeformational geometry, included frictional sliding surfaces to allow for bedding-parallel slip, and used a displacement boundary condition at the base of the Santa Elena footwall to simulate fault motion. Geometry and strain evolution were tracked so that (1) fold shape, (2) cumulative extension, and (3) layer-parallel shear strain could be compared to field observations. Iterative model runs successfully matched field data and revealed the importance of benchmarking the model results against monocline geometry, layer-parallel extensional strain, and bedding slip in the natural example. Our results illustrate the potential use of this modeling approach whereby calibration is performed using available data and is followed by strain measurement throughout the model domain to aid in prediction of subseismic faults and fractures. This geomechanical modeling approach provides a powerful tool for site-specific subsurface deformation prediction in hydrocarbon reservoirs that incorporates details of the local mechanical stratigraphy and structural setting.

Capabilities and applications of probabilistic methods in finite element analysis

The ability to quantify the uncertainty of complex engineering structures subject to inherent randomness in loading, material properties, and geometric parameters, is becoming increasingly important in the design and analysis of structures. Probabilistic finite element analysis provides a means to quantify the reliability of complex systems in such areas as aerospace and automotive structures. However, for wide acceptance, probabilistic methods must be interfaced with widely used commercial finite element solvers, such as ABAQUS, ANSYS, and NASTRAN. In addition, the finite element results are generally post-processed to evaluate a measure of useful life with tools that can compute quantities such as fatigue life. In this paper, interfacing and performance issues involved in coupling probabilistic methods, commercial finite element solvers and post finite element solvers are discussed. An example problem consisting of an integration of the NESSUS probabilistic analysis software, the ABAQUS finite element solver and fatigue life assessment is used to demonstrate concepts.

Probabilistic structural analysis using a general purpose finite element program

Abstract This paper presents an accurate and efficient method to predict the probabilistic response for structural response quantities such as stress, displacement, natural frequencies, and buckling loads, by combining the capabilities of MSC / NASTRAN , including design sensitivity analysis and fast probability integration. Two probabilistic structural analysis examples have been performed and ver ified by comparison with Monte Carlo simulation of the analytical solution. The first example consists of a cantilevered plate with several point loads. The random variables are the plate thickness and modulus of elasticity. The quantity of interest is the probabilistic distribution of the tip displacement. The second example is a probabilistic buckling analysis of a simply supported composite plate under in-plane loading. The random variables are the ply material properties, orientation angles, and thickness. The coupling of MSC / NASTRAN and fast probability integration is shown to be orders of magnitude more efficient than Monte Carlo simulation with excellent accuracy.

A PROBABILISTIC ANALYSIS OF A NONLINEAR STRUCTURE USING RANDOM FIELDS TO QUANTIFY GEOMETRIC SHAPE UNCERTAINTIES

Sσ sensitivity with respect to standard deviation COV Coefficient of Variation (= µ/σ) Engineers at Los Alamos National Laboratory (LANL) are currently developing the capability to provide a reliability-based structural evaluation technique for performing weapon reliability assessments. To enhance the analysts confidence with these new methods, an integrated experiment and analysis project has been developed. The uncertainty associated with the collapse response of commercially available spherical marine float is evaluated with the aid of the non-linear explicit dynamics code DYNA3D coupled with the probabilistic code NESSUS. Variations in geometric shape parameters and uncertainties in material parameters are characterized and included in the probabilistic model. Inherent anomalies and variations in geometry and material properties, which were collected from the set of test specimen, are included in the numerical model in the form of random fields and probability density functions (PDF’s). A comprehensive analysis of the parameter correlations is performed to determine appropriate correlation functions to use for the geometric random fields. E Youngs modulus

APPLICATION OF PROBABILISTIC METHODS TO WEAPON RELIABILITY ASSESSMENT

Southwest Research Institute in collaboration with engineers at Los Alamos National Laboratory (LANL) are currently developing capabilities to provide reliability-based structural evaluation techniques for performing weapon component and system reliability assessments in support of eventual weapon certification by analysis. Focus herein is placed on two problems recently studied: 1) The uncertain structural response of an explosive actuated valve-piston assembly, and 2) the quasi-static collapse response of a spherical shell. The probabilistic dynamic response of the piston is evaluated through the coupling of the probabilistic software NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) 2 with the non-linear structural dynamics code, ABAQUS/Explicit 3 . The probabilistic model includes variations in piston mass and geometry, and mechanical properties, such as Youngs Modulus, yield strength, and flow characteristics. The probabilistic response of the shell is evaluated through the coupling of the NESSUS software and the explicit dynamic code DYNA3D 5 . Variations in geometric shape parameters and material properties are considered. Nomenclature

Probabilistic engineering analysis using the NESSUS software

The ability to quantify the uncertainty of complex engineering structures subject to inherent randomness in loading, material properties, and geometric parameters is becoming increasingly important in the design and analysis of structures. Probabilistic analysis provides a means to quantify the reliability of complex systems in such areas as aerospace and automotive industries. Since structural analysis predictions are often based on the results of commercial finite element (FEM) programs (e.g., ABAQUS, ANSYS, and MSC/NASTRAN), probabilistic analysis methods must be linked to such programs to achieve useful reliability results. The NESSUS probabilistic analysis software combines state-of-the-art probabilistic analysis algorithms with general-purpose analysis packages to compute the probabilistic response and the reliability of engineering structures. In this paper, the NESSUS capabilities are presented and demonstrated for several application problems. Introduction and Background Numerical simulation is now routinely used to predict the behavior and response of complex systems. Computational simulation is being increasingly used as performance requirements for engineering structures increase and as a means of reducing testing. Since structural performance is directly affected by uncertainties associated with models or in physical parameters and loadings, the development and Senior Research Engineer, Member AIAA Principal Engineer, Senior Member AIAA Principal Engineer, Member AIAA Staff Engineer, Senior Member AIAA Senior Research Engineer ABAQUS is a registered trademark of Hibbitt, Karlsson, and Sorensen, Inc. ANSYS is a registered trademark of ANSYS, Inc. MSC is a registered trademark of the McNeal-Schwendler Corporation NESSUS is a registered trademark is SwRI. application of probabilistic analysis methods suitable for use with complex numerical models is needed. The traditional method of probabilistic analysis is Monte Carlo simulation. This approach generally requires a large number of simulations to calculate low or high probabilities, and is impractical when each simulation involves extensive finite element computations. Approximate fast probability integration (FPI) methods have been shown to be many times more efficient than Monte Carlo simulation and can often provide sufficient accuracy for engineering predictions. In many situations, the advanced mean value (AMV) procedure, based on FPI, can predict the probabilistic response of complex structures with relatively few response calculations. These methods also provide probabilistic sensitivity measures indicating the input parameters that influence the reliability the most. Beginning with the development of the NESSUS probabilistic analysis computer program, Southwest Research Institute (SwRI) has been addressing the need for efficient probabilistic analysis methods for over fifteen years. NESSUS can be used to simulate uncertainties in loads, geometry, material behavior, and other user-defined random variables to predict the probabilistic response, reliability and probabilistic sensitivity measures of systems. NESSUS provides a built-in finite element structural modeling capability as well as interfaces to many commercially available finite element programs. This paper discusses the current capabilities of the NESSUS software and presents several application problems to demonstrate its effectiveness.

Variance Decomposition in the Presence of Epistemic and Aleatory Uncertainty

Variance-based global sensitivity analysis is a powerful approach for understanding the importance of model input variables or groups of variables in driving model output variation. However, input variance is often attributable to both aleatory (irreducible) and epistemic (reducible) uncertainties. This paper presents an approach whereby variance decomposition is used in conjunction with probabilistic analysis. Epistemic uncertainty associated with a model’s probabilistic response is decomposed based on probability distribution uncertainty, deterministic model uncertainty, and other epistemic uncertainty sources. The proposed methodology allows for the identification of the epistemic uncertainty sources having the largest contributions to the uncertainty in the model’s response. As demonstrated in the numerical example, the proposed methodology may be used to support resource allocation decisions in modeling and simulation activities.

Geological Stress State Calibration and Uncertainty Analysis

The stress state is an important controlling factor on the slip behavior of faults and fractures in the earth’s crust and hence on the productivity of faulted and fractured hydrocarbon reservoirs. Uncertain or poorly constrained estimates of stress states can lead to high risk both in drilling and production costs. Current methods for stress tensor estimation rely on slip vector field data, however, this information is not generally available from datasets that are commonly used in the oil and gas industry. This work presents an approach whereby predicted slip tendency is used as a proxy for fault displacement, which can easily be extracted from datasets routinely used by the oil and gas industry. In doing so, a calibration approach is developed in order to estimate the parameters governing the underlying stress state by calibrating slip tendency predicted by the 3DStress® software to match measured slip displacement. A Bayesian approach is employed, and several uncertainty sources are accounted for in the estimation process, including the impacts of limited data and correlated data taken from geologically similar measurement locations.

A Probabilistic Treatment of Expert Knowledge and Epistemic Uncertainty in NESSUS

The risk assessment in many engineering applications is hampered by a lack of hard data. Under these conditions the selection of probability density function (PDF) seems arbitrary. Quite often the data are not only sparse but also vague expert knowledge or conflicting. Several non-probabilistic methods have been proposed in the literature to perform a risk assessment under these conditions. We propose to use probabilistic techniques using uncertain PDFs. The uncertainty on the PDF is characterized by treating the parameters in the PDF as random variables. We expand the classical Bayesian updating scheme to make use of vague or imprecise interval data. Each expert is considered to be a sample from a parent distribution of experts. Consequently, a conflict between experts is accounted for through the likelihood function. The uncertain PDFs can be used in both simulation-based and MPP-based reliability methods. Because of the uncertainty on the PDF of the random variables, the risk or reliability index itself will be a random variable. Design decisions are made on the basis of the risk assessment and an incorrect risk assessment increases the total cost of the design. Since a cost can be associated with either an over or underestimation of the risk, an optimal reliability index can be determined, which minimizes this cost. The probabilistic framework we present in this paper establishes a direct link between the amount and quality of the available data and the optimal reliability estimate. This link allows the decision maker to weigh expected value of additional data collection efforts against the expected optimal reliability index improvement.