Abridged Petri Nets

A new graphical framework, Abridged Petri Nets (APNs) is introduced for bottom-up modeling of complex stochastic systems. APNs are similar to Stochastic Petri Nets (SPNs) in as much as they both rely on component-based representation of system state space, in contrast to Markov chains that explicitly model the states of an entire system. In both frameworks, so-called tokens (denoted as small circles) represent individual entities comprising the system; however, SPN graphs contain two distinct types of nodes (called places and transitions) with transitions serving the purpose of routing tokens among places. As a result, a pair of place nodes in SPNs can be linked to each other only via a transient stop, a transition node. In contrast, APN graphs link place nodes directly by arcs (transitions), similar to state space diagrams for Markov chains, and separate transition nodes are not needed. Tokens in APN are distinct and have labels that can assume both discrete values ("colors") and continuous values ("ages"), both of which can change during simulation. Component interactions are modeled in APNs using triggers, which are either inhibitors or enablers (the inhibitors' opposites). Hierarchical construction of APNs rely on using stacks (layers) of submodels with automatically matching color policies. As a result, APNs provide at least the same modeling power as SPNs, but, as demonstrated by means of several examples, the resulting models are often more compact and transparent, therefore facilitating more efficient performance evaluation of complex systems.Comment: 17 figure

Flexural–torsional behavior of thin-walled composite space frames

A general analytical model based on the first-order shear deformable beam theory applicable to thin-walled composite space frames with arbitrary lay-ups under external loads is presented. This model accounts for all the structural coupling coming from the material anisotropy. The seven governing equations are derived from the principle of the stationary value of total potential energy. A displacement-based one-dimensional 14 degree-of-freedom space beam model which includes the effects of shear deformation, warping is developed to solve the problem. Numerical results are obtained to investigate the effects of fiber orientation on flexural–torsional responses of thin-walled composite space frame under vertical load

Geometrically nonlinear analysis of thin-walled composite box beams

A general geometrically nonlinear model for thin-walled composite space beams with arbitrary lay-ups under various types of loadings has been presented by using variational formulation based on the classical lamination theory. The nonlinear governing equations are derived and solved by means of an incremental Newton–Raphson method. A displacement-based one-dimensional finite element model that accounts for the geometric nonlinearity in the von Kármán sense is developed. Numerical results are obtained for thin-walled composite box beam under vertical load to investigate the effect of geometric nonlinearity and address the effects of the fiber orientation, laminate stacking sequence, load parameter on axial–flexural–torsional response

A conceptual and computational framework for identifying and predicting the performance of novel airspace concept of operations

Issued as final reportUnited States. National Aeronautics and Space Administratio

Geometrically nonlinear theory of thin-walled composite box beams using shear-deformable beam theory

A general geometrically nonlinear model for thin-walled composite space beams with arbitrary lay-ups under various types of loadings is presented. This model is based on the first-order shear deformable beam theory, and accounts for all the structural coupling coming from both material anisotropy and geometric nonlinearity. The nonlinear governing equations are derived and solved by means of an incremental Newton–Raphson method. A displacement-based one-dimensional finite element model that accounts for the geometric nonlinearity in the von Kármán sense is developed. Numerical results are obtained for thin-walled composite box beams under vertical load to investigate the effects of shear deformation, geometric nonlinearity and fiber orientation on axial–flexural–torsional response

GT2003-38510 COMPARATIVE ASSESSMENT OF DIRECT AND INDIRECT PROBABILISTIC METHODS FOR THERMOMECHANICAL ANALYSIS OF STRUCTURAL COMPONENTS IN GAS TURBINES

ABSTRACT Various sources of uncertainty greatly affect the life of structural components of gas turbines. Probabilistic approaches provide a means to evaluate these uncertainties; however, the accuracy of these approaches often remains unknown. Published quantitative studies of the effectiveness of various uncertainty quantification techniques are usually based on very simple examples. This is contrasted by the large-size finite element models that are used for complex geometries of critical structural parts such as turbine blades or nozzles. In such real-life applications the expenses of the "function calls" (runs of these models) preclude systematic studies of probabilistic methods. These expenses are attributed not only to the actual runs of the model, but to the difficulties in parametrically changing the model as well. Such a "complexity gap" leads to a justifiable concern over whether the trends identified in academic studies are relevant to these industrial applications. As a result, structural engineers end up with the number of function calls that they can afford rather than what would be needed for the required level of accuracy. The present effort intends to bridge this gap by studying a midlevel problem: a simplified notional finite element model of a gas turbine component is presented. Despite its simplicity, the model is designed to reflect the major features of more realistic models. The parametric changes of the model are fully automated, which allows for performing an extensive set of bench- * Research Engineer, School of Aerospace Engineering † Senior Research Engineer, School of Aerospace Engineering ‡ Boeing Professor for Advanced Aerospace Analysis, School of Aerospace Engineering mark tests that help to determine the relative merits of various existing probabilistic techniques for component life assessment Several meta-modeling techniques are investigated and their performance compared based on direct sampling methods. In this context, various Design of Experiments (DoE) methods are studied. The results are used to construct the Response Surface Equations (RSE) as well as the kriging models. It is emphasized that changes in the relative locations of the critical points induced by variation of independent parameters can critically affect the overall fidelity of the modeling; the means of remedying such a degradation in precision are discussed. Finally, it is shown that when the ranges of independent variables are large, kriging generally provides precision that is an order of magnitude better than RSE for the same DoE