Probabilistic simulation of uncertainties in thermal structures

Development of probabilistic structural analysis methods for hot structures is a major activity at Lewis Research Center. It consists of five program elements: (1) probabilistic loads; (2) probabilistic finite element analysis; (3) probabilistic material behavior; (4) assessment of reliability and risk; and (5) probabilistic structural performance evaluation. Recent progress includes: (1) quantification of the effects of uncertainties for several variables on high pressure fuel turbopump (HPFT) blade temperature, pressure, and torque of the Space Shuttle Main Engine (SSME); (2) the evaluation of the cumulative distribution function for various structural response variables based on assumed uncertainties in primitive structural variables; (3) evaluation of the failure probability; (4) reliability and risk-cost assessment, and (5) an outline of an emerging approach for eventual hot structures certification. Collectively, the results demonstrate that the structural durability/reliability of hot structural components can be effectively evaluated in a formal probabilistic framework. In addition, the approach can be readily extended to computationally simulate certification of hot structures for aerospace environments

Probability of Failure and Risk Assessment of Propulsion Structural Components

Due to increasing need to account for the uncertainties in material properties, loading conditions, or geometries, a methodology was developed to determine structural reliability and the assess the risk associated with it. The methodology consists of a probabilistic structural analysis by a probabilistic finite element computer code Nonlinear Evaluation of Stochastic Structures Under Stress (NESSUS) and a generic probabilistic material properties model. The methodology is versatile and is equally applicable to high and cryogenic temperature structures. Results obtained demonstrate that the whole issue of structural reliability and risk can be formally evaluated using the methodology developed which is inclusive of uncertainties in material properties, structural parameters and loading conditions. The methodology is described in some detail with illustrative examples

First-passage problems: A probabilistic dynamic analysis for degraded structures

Structures subjected to random excitations with uncertain system parameters degraded by surrounding environments (a random time history) are studied. Methods are developed to determine the statistics of dynamic responses, such as the time-varying mean, the standard deviation, the autocorrelation functions, and the joint probability density function of any response and its derivative. Moreover, the first-passage problems with deterministic and stationary/evolutionary random barriers are evaluated. The time-varying (joint) mean crossing rate and the probability density function of the first-passage time for various random barriers are derived

A methodology for evaluating the reliability and risk of structures under complex service environments

The theoretical basis and numerical implementation of NESSUS (Numerical Evaluation of Stochastic Structures Under Stress), a computer code for probabilistic structural analysis of aerospace components, are described, with an emphasis on the use of NESSUS for reliability and risk assessment. Topics addressed include the structure of probabilistic models of fatigue-crack initiation, risk/cost evaluation, fatigue-fracture analysis, and fatigue-crack initiation. Numerical results from typical applications are presented in graphs and briefly characterized. The usefulness of NESSUS predictions for establishing inspection and retirement schedules and for component certification is indicated

Mapping methods for computationally efficient and accurate structural reliability

The influence of mesh coarseness in the structural reliability is evaluated. The objectives are to describe the alternatives and to demonstrate their effectiveness. The results show that special mapping methods can be developed by using: (1) deterministic structural responses from a fine (convergent) finite element mesh; (2) probabilistic distributions of structural responses from a coarse finite element mesh; (3) the relationship between the probabilistic structural responses from the coarse and fine finite element meshes; and (4) probabilistic mapping. The structural responses from different finite element meshes are highly correlated

Mapping methods for computationally efficient and accurate structural reliability

Mapping methods are developed to improve the accuracy and efficiency of probabilistic structural analyses with coarse finite element meshes. The mapping methods consist of the following: (1) deterministic structural analyses with fine (convergent) finite element meshes; (2) probabilistic structural analyses with coarse finite element meshes; (3) the relationship between the probabilistic structural responses from the coarse and fine finite element meshes; and (4) a probabilistic mapping. The results show that the scatter in the probabilistic structural responses and structural reliability can be efficiently predicted using a coarse finite element model and proper mapping methods with good accuracy. Therefore, large structures can be efficiently analyzed probabilistically using finite element methods

Probabilistic assessment of composite structures

A methodology and attendant computer code were developed and are used to computationally simulate the uncertain behavior of composite structures. The uncertain behavior includes buckling loads, stress concentration factors, displacements, stress/strain, etc., which are the consequences of the inherent uncertainties (scatter) in the primitive (independent random) variables (constituent, ply, laminate, and structural) that describe the composite structures. The computer code is IPACS (Integrated Probabilistic Assessment of Composite Structures). IPACS can simulate both composite mechanics and composite structural behavior. Application to probabilistic composite mechanics is illustrated by its use to evaluate the uncertainties in the major Poisson's ratio and in laminate stiffness and strength. IPACS' application to probabilistic structural analysis is illustrated by its used to evaluate the uncertainties in the buckling of a composite plate, the stress concentration factor in a composite panel, and the vertical displacement and ply stress in a composite aircraft wing segment. IPACS' application to probabilistic design is illustrated by its use to assess the thin composite shell (pipe)

Probabilistic evaluation of fuselage-type composite structures

A methodology is developed to computationally simulate the uncertain behavior of composite structures. Uncertain behavior is the consequence of the random variation (scatter) of the primitive (independent random) variables at the constituent, ply, laminate and structural levels. This methodology is implemented in the IPACS (Integrated Probabilistic Assessment of Composite Structures) computer code. A fuselage-type composite structure is analyzed to demonstrate the code's capability. The probability distribution functions of structural responses are computed. Sensitivity of a given structural response to each primitive variable is also determined from the analyses

Probabilistic SSME blades structural response under random pulse loading

The purpose is to develop models of random impacts on a Space Shuttle Main Engine (SSME) turbopump blade and to predict the probabilistic structural response of the blade to these impacts. The random loading is caused by the impact of debris. The probabilistic structural response is characterized by distribution functions for stress and displacements as functions of the loading parameters which determine the random pulse model. These parameters include pulse arrival, amplitude, and location. The analysis can be extended to predict level crossing rates. This requires knowledge of the joint distribution of the response and its derivative. The model of random impacts chosen allows the pulse arrivals, pulse amplitudes, and pulse locations to be random. Specifically, the pulse arrivals are assumed to be governed by a Poisson process, which is characterized by a mean arrival rate. The pulse intensity is modelled as a normally distributed random variable with a zero mean chosen independently at each arrival. The standard deviation of the distribution is a measure of pulse intensity. Several different models were used for the pulse locations. For example, three points near the blade tip were chosen at which pulses were allowed to arrive with equal probability. Again, the locations were chosen independently at each arrival. The structural response was analyzed both by direct Monte Carlo simulation and by a semi-analytical method

Probability of failure and risk assessment of propulsion structural components

The probabilistic structural analysis method (PSAM) was developed to analyze the effects of fluctuating loads, variable material properties, and uncertain analytical models especially for high performance structures such as the Space Shuttle Main Engine turbopump blades. Risk is calculated after expensive service experience. However, probabilistic structural analysis provides a rational alternative method to quantify uncertainties in the structural performance and durability. NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) was developed as a probabilistic structural analysis computer code which integrates finite element methods and reliability algorithms, capable to predicting the probability distributions of structural response variables such as stress, displacement, natural frequencies, and buckling loads. This computer code is detailed