Reliability analysis of pipe whip impacts

Improved response surface method and its application to stiffened plate reliability analysis

Reliability analysis of smart laminated composite plates under static loads using artificial neural networks

In this study, the drag torque was predicted considering the uncertainties in geometry and material properties of automotive wheel bearing seals. For this, the deformation of the seals was firstly analyzed using numerical analysis based on the finite element method. Three types of experiments for material properties of rubber were conducted to improve the reliability of deformation analysis for the rubber seals. In addition, hyperelastic analysis was conducted using the experimental results. To consider the geometrical and material uncertainties of the seals, Monte Carlo simulation was performed considering variations in dimension and rubber properties. As Monte Carlo simulation to analyze the deformation of the seals takes a very high computational cost, a response surface was created using design of experiment (DOE) and then Monte Carlo simulation was performed using this response surface. Based on the simulation results, sensitivity analysis was conducted to analyze design variables that affect the drag torque of the rubber seal. Finally, variation in the drag torque of the automotive wheel bearing seals was evaluated using the results of Monte Carlo simulation.

The reliability of a simple turbomachinery model was calculated to demonstrate the application of a newly developing system integration tool, Probabilistic Design and Analysis Framework(PRODAF), along with efficient probabilistic methods using a response surface method. The model represents a system consisting of hypothetical turbine components. The parts include a blade, disk, and shaft with an applied angular velocity. All the components were modeled with the properties of the nickel alloy, Inconel 718. A response surface was calculated for the system of components to improve probabilistic computational efficiency. In addition, a fast probability integration method, Advanced First Order Reliability Method (AFORM), was used for the probabilistic analysis in order to provide an efficient analysis as possible. Geometric dimensions, the applied load, and material yield strength were varied for this study. The probability of failure was determined using the maximum first principal stress response and the material yield strength. A simple G function using the difference between strength and loading stress was used to determine failure limits. The probabilistic sensitivity of the failure response relative to the individual variables was determined also with material yield strength having the greatest influence. The model was recreated with every iteration of the probabilistic analysis in order to vary the geometry. As a result, the response surface method has a significant impact on improving computational efficiency and enabling reliability analysis with rapid turnaround.

Objectives: Quantification of uncertainties and its implications on stability assessment of geotechnical problems can very well be captured through probabilistic analysis in which parameters are considered to be random variables. Thus, randomness of the response of the system is also captured and safety assessment is reported in terms of a safety index, commonly called as “reliability index”. In this study, probabilistic approach in conjunction with conventional deterministic approach is used for the analysis of a deep excavation problem and advantages of probabilistic approach are highlighted. Methods/Statistical Analysis: Probabilistic analysis requires establishment of connection between input parameters and output responses, for which response surface method (RSM) concepts can effectively be utilized. RSM helps developing regression model between input and output which can be used for the probabilistic analysis through First Order Reliability Method (FORM). Advanced finite element numerical tool, i.e., PLAXIS 3D is utilized for the purpose of the analysis. Findings: Considering this typical case of deep excavation problem, it is highlighted that probabilistic analysis when used in conjunction with the deterministic approach, it brings rationality in decision making while dealing with uncertainty and provides mathematical basis for treating uncertainty. Application/Improvements: Conventionally, stability analyses of a deep excavation system are carried out through limit equilibrium based approaches and the parameter used to define extent of stability is factor of safety. With advent of computers and finite element or finite difference based computing facilities, strength reduction technique is adopted to estimate the factor of safety. These numerical tools also help in predicting the deformation pattern and judging the serviceability requirements. In either case, the soil parameters used as input in the numerical tools are taken a constant value uniformly. Choice of appropriate value of design input parameter is based on past experience, good engineering judgment and confidence in the adopted analysis methodology. Due to various uncertain sources involved in the estimation of the input properties of a natural material like soil, such as, natural variability, testing errors, model transformation, it is impractical to assign a single value to design parameter. Deterministic approach, which involves single value of design parameters for stability assessment is considered to be simple and straight forward. It is demonstrated that quantification of uncertainties and its influence on stability assessment of deep excavation problem can be captured in probabilistic framework.

Reliability analysis of nonlinear structural systems using response surface method

Influence of micro-scale uncertainties on the reliability of fibre-matrix composites

The effect of interference of corrosion pits on the failure probability of a reinforced concrete beam

Effect of Pit Distance on Failure Probability of a Corroded RC Beam

Uncertain material properties on wave dispersion behaviors of smart magneto-electro-elastic nanobeams

Miter gate is a type of navigation lock gate which is used to allow the passage of inland navigation across different levels in a river system. Aging miter gates have come down with structural degradation due to fatigue and corrosion bringing about a deterioration of structural resistance, influencing the integrity and life cycle costs. Therefore, it is essential to re-assess our belief in the structural safety and perform maintenance accordingly to optimize the operation and maintenance costs. This study demonstrates an approach to update the reliability of aging miter gates under the effect of fatigue and corrosion. The failure probability calculated in this study is founded on a probabilistic crack propagation analysis which considers the uncertainty in material properties, weld geometry, and fatigue loading. The time-dependent capacity of a miter gate is assessed including the influence of corrosion fatigue and corrosion growth rate. The procedure is then used for an example where the probability of failure of a miter gate welded joint is updated based on inspection outcomes. The reliability updating approach presented here can be used for risk-based maintenance optimization of lock gates.

Thermal protection system (TPS) is one of the most important subsystems for vehicle reentry. Because of the uncertainties in thermal loads, material properties, and manufacture tolerances, the thermal response of TPS has strong randomness, which brings great challenges to the engineering design and reliability evaluation. Because the uncertain aerodynamic heating loads are stochastic processes in time history, it is difficult to model them in the conventional surrogate models that usually take scalar random variables as input. This paper thus proposes an effective characterization method that can represent the uncertainties of aerodynamic heating by a set of random variables using Karhunen–Loève expansion. The random variables that describe the uncertainty of thermal loads, material properties, and geometric thickness are taken as inputs for probabilistic analyses. A kriging surrogate model is constructed to solve the transient heat conduction with high accuracy. Taking a typical multilayer TPS as an example, the probabilistic thermal analyses are carried out considering different degrees of heat rate uncertainties. The results show that the uncertainties of aerodynamic heating intensify the randomness of the thermal response of TPS, and thus have a great impact on the thermal reliability. The sensitivities of temperature response to various uncertain parameters are investigated as well, which provide a reference for system design and reliability improvement.

Fuzzy stochastic finite element method for the hybrid uncertain temperature field prediction

The paper describes a computational simulation approach for durability, damage tolerance (D&DT) and reliability of composite wind turbine blade structures in presence of uncertainties in material properties. This computer-based prediction methodology combines composite mechanics with finite element analysis, damage and fracture tracking capability, probabilistic analysis and a robust design algorithm to reduce weight of turbine bales without loss in structural durability and reliability. A composite turbine blade was first assessed with finite element based multi-scale progressive failure analysis to determine failure modes and locations as well as the fracture load. Analysis D&DT results were validated with static test performed at Sandia National Laboratories. The work was followed by detailed weight analysis to identify contribution of various materials to the overall weight of the blade. The methodology ensured that certain types of failure modes, such as delamination progression, are contained to reduce risk to the structure. Probabilistic analysis indicated that composite shear strength has a great influence of the blade ultimate load under static loading. Weight was reduced by 12% with robust design without loss in reliability or D&DT. It was achieved by replacing a small volume of key materials with foam.

The paper presents a semi-empirical based response surface approach for structural reliability analysis of steel plates with non-uniform corrosion represented by random fields. The approach consists of using a semi-empirical design equation as simplified response surface model, which is then calibrated iteratively by means of the results of non-linear finite element analyses at the design points calculated by the First Order Reliability Method. This technique has been successfully applied to problems formulated in terms of discrete random variables and is now applied to problems involving spatial variability of structural parameters represented by random fields. The approach is first illustrated with an example of the ultimate strength of plates with random imperfections and material properties and then applied to plates with random fields of corrosion discretized using the Expansion Optimal Linear Estimation method. The results obtained by the semi-empirical based response surface approach and by coupling directly the First Order Reliability Method and the finite element code are compared.