Raymond P. Daddazio

Refined Stratified Sampling for efficient Monte Carlo based uncertainty quantification

Abstract A general adaptive approach rooted in stratified sampling (SS) is proposed for sample-based uncertainty quantification (UQ). To motivate its use in this context the space-filling, orthogonality, and projective properties of SS are compared with simple random sampling and Latin hypercube sampling (LHS). SS is demonstrated to provide attractive properties for certain classes of problems. The proposed approach, Refined Stratified Sampling (RSS), capitalizes on these properties through an adaptive process that adds samples sequentially by dividing the existing subspaces of a stratified design. RSS is proven to reduce variance compared to traditional stratified sample extension methods while providing comparable or enhanced variance reduction when compared to sample size extension methods for LHS – which do not afford the same degree of flexibility to facilitate a truly adaptive UQ process. An initial investigation of optimal stratification is presented and motivates the potential for major advances in variance reduction through optimally designed RSS. Potential paths for extension of the method to high dimension are discussed. Two examples are provided. The first involves UQ for a low dimensional function where convergence is evaluated analytically. The second presents a study to asses the response variability of a floating structure to an underwater shock.

Simulating the Response of Composite Reinforced Floor Slabs Subjected to Blast Loading

The threat of terrorist attack against civil infrastructure in the US and other countries has led to the need to better understand the response of structures and structural components to an impulsive air blast overpressure. One scenario that is present in many cities is delivery trucks entering basement or street level loading/unloading areas. A bomb present in one of these delivery trucks could cause considerable damage to the floor slab (and consequently the building) above the blast by causing a vertical uplift, a condition that the slab was not designed to resist. Traditional methods to retrofit floor slabs to resist an upwards blast pressure require that additional tension sustaining reinforcing bars (rebars) be placed near the slab upper surface. This reinforcing method is costly, difficult to produce, and adds additional weight to the overall structure in building retrofit situations. Another approach to reinforcing the slab is to bond light-weight, high strength fiber composite material to the slab upper surface as a means of resisting the tensile forces from the slab upward motion. This paper presents results from an effort to simulate the response of a reinforced concrete floor slab with a fiber composite retrofit subjected to a blast overpressure. The simulations were performed using the Weidlinger Associates’ FLEX [1] finite element code for structural response calculations. The MAZ [2] computational fluid dynamics code was used to generate blast pressure. This paper will discuss the modeling effort used to predict the response of fiber composite retrofitted slabs and compare the computational analysis to test results1 .Copyright

Response of AISC Steel Column Sections to Blast Loading

One dozen American Institute of Steel Construction (AISC) W14 steel columns were tested at the Energetic Materials Research and Testing Center (EMRTC), New Mexico Institute of Mining and Technology in Socorro, New Mexico with loading from typical size vehicle bomb threats at very close to moderately close standoffs. Pretest predictions of structural response were performed using standard SDOF methods and the Weidlinger Associates, Inc. (WAI) FLEX finite element code. Loads acting on the columns were determined from the U. S. Army developed CONWEP code using the Kingery-Bulmash equations for the pretest predictions. Seven tests included individual columns with axial loading and blast loading applied simulataneously. One test included 5 columns built into a frame with moment connections at the top of the columns and base plate connections at the base of the columns. The columns were instrumented with accelerometers and pressure transducers. The tests were designed to produce various levels of damage from mild to severe. This paper will compare the pretest and posttest predictions using both the SDOF and FLEX finite element methods with the actual test results. The comparison between actual loading and CONWEP loading will also be discussed. Conclusions will be drawn with regard to the use of CONWEP loading for this type of threat at various standoffs. Also, the use of SDOF and FLEX finite element methods to predict the response of AISC W14 steel columns will be compared.Copyright

SOME PRACTICAL APPLICATIONS OF THE USE OF SCALE INDEPENDENT ELEMENTS FOR DYNAMIC ANALYSIS OF VIBRATING SYSTEMS

Abstract Discrete deterministic methods such as finite elements offer great flexibility in analyzing the dynamic response of vibrating systems. However, these methods can easily grow beyond available computer resources as frequencies of interest grow higher. In this paper we present a new approach for the frequency domain dynamic analysis of structures. A theory is developed for the analysis of systems which are uniform along a single coordinate axis, but otherwise arbitrary in geometry and material composition. This approach, termed the scale independent element, is shown to be an accurate, efficient and general method for the analysis of vibrating systems. This technique extends the applicability of discrete deterministic finite element based modeling to higher frequencies and is capable of bridging the gap to frequency regimes where statistical energy methods become applicable.

Mapping model validation metrics to subject matter expert scores for model adequacy assessment

This paper develops a novel approach to incorporate the contributions of both quantitative validation metrics and qualitative subject matter expert (SME) evaluation criteria in model validation assessment. The relationship between validation metrics (input) and SME scores (output) is formulated as a classification problem, and a probabilistic neural network (PNN) is constructed to execute this mapping. Establishing PNN classifiers for a wide variety of combinations of validation metrics allows for a quantitative comparison of validation metric performance in representing SME judgment. An advantage to this approach is that it semi-automates the model validation process and subsequently is capable of incorporating the contributions of large data sets of disparate response quantities of interest in model validation assessment. The effectiveness of this approach is demonstrated on a complex real-world problem involving the shock qualification testing of a floating shock platform. A data set of experimental and simulated pairs of time history comparisons along with associated SME scores and computed validation metrics is obtained and utilized to construct the PNN classifiers through K-fold cross validation. A wide range of validation metrics for time history comparisons is considered including feature-specific metrics (phase and magnitude error), a frequency metric (shock response spectra), a time-frequency metric (wavelet decomposition), and a global metric (index of agreement). The PNN classifiers constructed using a Parzen kernel for the class conditional probability density function whose smoothing parameter is optimized using a genetic algorithm performs well in representing SME judgment.

Health monitoring of complex structures

A basic step in the monitoring of health of any structure is detection of damage levels and location of the damage in the system. Several damage detection schemes have been proposed in recent years. Published applications of these methods are typically for simplified models of realistic structures. This leaves open the question of the accuracy and efficiency of the available damage detection methods when applied to large and complex structural models. This paper will investigate the accuracy of different damage detection techniques to complex structural models. A typical multi- jointed steel bridge, which is damaged by cracks of different sizes, is considered. The damage will be simulated analytically in the structural model, and the damage detection algorithms will be applied to both the damaged and the undamaged structures. Three damage detection algorithms are investigated, namely the change of stiffness, the change of flexibility and the damage index methods. Some modifications and extensions of the change of stiffness and change of flexibility methods were incorporated in this study. These extensions helped inaccurate comparisons between different methods. It was found that all three algorithms produced adequate damage detection results. More analytical studies are recommended. Also, experimental testing for complex structures is recommended.

Stress resultant based elasto-viscoplastic thick shell model

The current paper presents enhancement introduced to the elasto-viscoplastic shell formulation, which serves as a theoretical base for the finite element code EPSA (Elasto-Plastic Shell Analysis) [1–3]. The shell equations used in EPSA are modified to account for transverse shear deformation, which is important in the analysis of thick plates and shells, as well as composite laminates. Transverse shear forces calculated from transverse shear strains are introduced into a rate-dependent yield function, which is similar to Iliushins yield surface expressed in terms of stress resultants and stress couples [12]. The hardening rule defined by Bieniek and Funaro [4], which allows for representation of the Bauschinger effect on a moment-curvature plane, was previously adopted in EPSA and is used here in the same form. Viscoplastic strain rates are calculated, taking into account the transverse shears. Only non-layered shells are considered in this work.

Boundary Element Methods in Probabilistic Acoustic Scattering Problems

Boundary Element Methods (BEM) are suited to a wide range of engineering problems, especially those of a semi-infinite nature. Examples of such problems can be found in the fluid-structure interactions of acoustic radiation and scattering problems and in the soil-structure interactions of earthquake and machine foundation problems. The required input parameters, dynamic loads, and system properties for such problems are not in general well defined and can be considered random variables. Probabilistic structural analysis through the use of the BEM has been introduced by Ettouney et al. [8,9]. In this work, we extend the use of this probabilistic approach to area of fluid-structure interaction by applying this technique to the problem of acoustic scattering from structures.