Ben H. Thacker

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.

The Role of Nondeterminism in Verification and Validation of Computational Solid Mechanics Models

Verification and validation (V&V) is an enabling methodology for the development of models that can be used to make engineering predictions with high confidence. Model V&V procedures are needed by government and industry to reduce the time, cost and danger associated with component and full-scale testing of products, materials, and weapons. The development of guidelines and procedures for conducting a V&V program are currently being defined by a broad spectrum of researchers. This paper briefly reviews the main concepts involved in V&V and then focuses on the critical role that nondeterministic analysis plays in the V&V process.

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.

The role of nondeterminism in model verification and validation

Model verification and validation (V&V) is an enabling methodology for the development of computational models that can be used to make engineering predictions with quantified confidence. Model V&V procedures are needed to reduce the time, cost and risk associated with component and full-scale testing of products, materials, and engineered systems. Quantifying the confidence and predictive accuracy of model calculations provides the decision-maker with the information necessary for making high-consequence decisions. Development of guidelines and procedures for conducting a V&V programme are currently being defined by a broad spectrum of researchers. This paper briefly reviews the main concepts involved in model V&V and then focuses on the critical role that nondeterministic analysis plays in the V&V process.

A Probabilistic Model for Internal Corrosion of Gas Pipelines

Locating internal corrosion damage in gas pipelines is made difficult by the presence of large uncertainties in flow characteristics, pre-existing conditions, corrosion resistance, elevation data, and test measurements. This paper describes a preliminary methodology to predict the most probable corrosion damage location along the pipelines, and then update this prediction using inspection data. The approach computes the probability of critical corrosion damage as a function of location along the pipeline using physical models, for flow, corrosion rate, and inspection information as well as uncertainties in elevation data, pipeline geometry and flow characteristics. The probabilistic methodology is based on the internal corrosion direct assessment (ICDA) methodology. The probability of corrosion damage is the probability that the corrosion depth exceeds a critical depth times the probability of the presence of electrolytes such as water. Water is assumed present at locations where the pipeline inclination angle is greater than the critical angle. The corrosion rate is defined to be a linear combination of three candidate corrosion rate models with separate weight factors. Monte Carlo simulation and the first-order reliability method (FORM) implemented in a simple spreadsheet model are used to perform the probability integration. Bayesian updating is used to incorporate inspection information (e.g., in-line, excavation, etc.) and update the corrosion rate model weight factors and thereby refine the prediction of most probable damage location. This provides a systematic method for focusing costly inspections on only those locations with a high probability of damage while allowing future predictions to better reflect field observations.Copyright

Concepts and Terminology of Validation for Computational Solid Mechanics Models

During the past couple of years, a committee under the auspices of the ASME Codes and Standards division has been formed and are meeting regularly. The purpose of the committee is to develop and publish a set of documents that describe a common process for verification and validation of computational solid mechanics models. There are many issues under discussion and many concepts under debate. In this paper we will present some the major concepts and the differing viewpoints focusing on the concept of validation and relate this to the automotive industry in particular.

A Framework to Estimate Uncertain Random Variables

Many engineering applications are characterized by the innate challenge of acquiring experimental data. This lack of available data hampers the selection of the probability density function (PDF) and introduces a level of arbitrariness in the ensuing risk analysis. This paper presents an approach to estimate the uncertainty in the PDF shape. A multiparameter family of candidate PDF shapes is used and the statistical uncertainty associated with the PDF parameters is estimated from the data. Several popular PDF families as well as multiple parameter estimation methods are presented. The confidence bounds on the parameters can be computed and input in commonly used advanced reliability analysis tool to estimate the uncertainty in the computed risk. Practical examples illustrate the approach.