An advanced probabilistic structural analysis method for implicit performance functions

Reliability-based design optimization (RBDO) is an effective method for structural optimization due to its ability to take into consideration uncertainties in design variables. Performance measure approach (PMA) based methods are commonly utilized to evaluate the probabilistic constraints of RBDO problems. The advanced mean value (AMV) method is a very commonly used due to its simpleness and effectiveness. However, the AMV method sometimes produces unstable and inefficient results for concave and highly nonlinear limit-state functions. In order to improve robustness and efficiency, many methods have been developed, for example, chaos control based and conjugate gradient-based methods. These methods lead to more stable results as compared with the AMV approach but they are inefficient for use in complex and convex limit-state functions. The RBDO of structural components is often a difficult issue due to complicated constraints. In this paper, a novel hybrid approach, referred to as “hybrid gradient analysis (HGA)” is introduced for the evaluation of both convex and concave constraint functions in RBDO. The HGA method combines AMV and conjugate gradient analysis (CGA). The robustness, simpleness and effectiveness of the proposed HGA method are compared with various PMA methods aimed at reliability such as AMV, chaos control (CC), conjugate mean value (CMV), modified chaos control (MCC), hybrid mean value (HMV) and CGA methods by means of several nonlinear convex/concave limit-state functions and structural RBDO problems. Reliability analysis and RBDO results point out that the HGA approach introduced here is more effective and robust than the well-known approaches.

In this paper, an efficient approach is presented for probabilistic power flow analysis of complex structures with parameter uncertainties. A component-based technique is used to generate Reduced-Order Models (ROMs) of low- to mid-frequency vibration and power flow. Using this framework, two techniques are employed for probabilistic vibration power flow analysis: (1) a Locally Linear Interpolation (LLI) method, which is a new response surface construction method that has been specifically developed for probabilistic vibration analysis and (2) the Advanced Mean Value (AMV) method, which is a more general technique from the reliability literature. The advantages and limitations of the LLI method are examined and compared to those of the AMV method with respect to probabilistic power flow analysis. Numerical results are shown for a simple example system, an L-shaped plate, and for an important engineering application, a ground vehicle structure.

Due to the limited joint position space and the consideration of reducing the moment of inertia and vibration for industrial robot, the design optimization for rotate vector (RV) reducer is becoming a new and urgent problem in industry. Currently, the existing researches focus on deterministic design optimization, which may cause unreliable designs without considering uncertainties. Therefore, the study focuses on the implementation of reliability-based design optimization (RBDO) to the RV reducer. The aim is to make the RV reducer smaller in size while ensuring a higher reliability. Firstly, a modified advanced mean value (MAMV) method is proposed to improve efficiency and robustness of the advanced mean value method, which encounters inefficiency and numerical instability for the concave or highly nonlinear performance measure functions. Secondly, a mathematical model of RBDO for the RV reducer is established. Thirdly, the proposed MAMV method is integrated into double-loop method to optimize the established mathematical model of RBDO with different target reliability. The results show that the proposed MAMV method is efficient compared with other methods. In addition, the volume of the RV reducer is correspondingly reduced by 9.44%, 7.89%, and 5.66% compared with that before optimization when the target reliabilities are 99.38%, 99.87%, and 99.98%.

The robustness and efficiency of inverse reliability methods are important issues in reliability-based design optimization (RBDO) using performance measure approach (PMA). The adaptive modified chaos control (ACC), step length adjustment (SA), and relaxed mean value (RMV) methods were recently implemented to improve the robustness and efficiency of PMA. In this paper, a limited descent mean value (LDMV) method is proposed to improve robustness and efficiency of inverse reliability analysis for either convex or concave probabilistic constraints. The LDMV formula is dynamically adjusted by an adaptive step size based on the advanced mean value method (AMV). The robustness and efficiency of the ACC, SA, RMV, and proposed LDMV methods are compared through six nonlinear performance functions. The results illustrated a similar robust performance between LDMV against RMV and FSL methods and superior to the ACC method. The proposed LDMV improves the robustness and efficiency of the inverse first-order reliability method in comparison with existing reliability methods.

Probabilistic structural analysis methods for space propulsion system components

The development of a three-dimensional inelastic analysis methodology for the Space Shuttle main engine (SSME) structural components is described. The methodology is composed of: (1) composite load spectra, (2) probabilistic structural analysis methods, (3) the probabilistic finite element theory, and (4) probabilistic structural analysis. The progress in the development of generic probabilistic models for various individual loads which consist of a steady state load, a periodic load, a random load, and a spike, is discussed. The capabilities of the Numerical Evaluation of Stochastic Structures Under Stress finite element code designed for probabilistic structural analysis of the SSME are examined. Variation principles for formulation probabilistic finite elements and a structural analysis for evaluating the geometric and material properties tolerances on the structural response of turbopump blades are being designed.

Reliable and efficient vibroacoustic loads prediction is often critical in structural design, yet it remains a challenging task for many applications. Spacecraft structures are characterised by extensive use of composite materials, complex connections between components and various non-trivial geometrical features. Accurate treatment necessitates the construction of highly detailed numerical models, traditionally employing deterministic representations. Simultaneously, the broadband acoustic excitation due to the diffuse sound field experienced during launch requires modelling the fluid domain and solving the resulting elasto-acoustic interaction at = multiple frequencies. To alleviate the computational demand implications for large problem sizes, substructuring and reduction techniques for the structural domain are commonplace, component mode synthesis (CMS) being a framework widely adopted in the aerospace industry. Nevertheless, despite ongoing research, the topic still presents a range of difficulties when a universal, robust method of accounting for model uncertainties is sought. In this study, two CMS based approaches are proposed and evaluated. Firstly, the Craig-Bampton stochastic method (CBSM) is improved via a set of modifications enhancing its efficiency, and subsequently adapted for use in a vibroacoustic setting. Optimal perturbation levels and scope of validity of the technique are established against a probabilistic structural analysis (PSA) simulation for a spacecraft structure. Secondly, a novel stochastic finite element method (FEM) is presented. The underlying mathematical foundation is derived so that uncertainty can naturally be controlled at the subsystem level, in partitions of the corresponding condensed mass and stiffness matrices. This decomposition based approach ensures that realisations of the random matrices have key properties such as positive (semi)definiteness strictly preserved, guaranteeing complete robustness. The method is validated with a spacecraft test case, comparing its predictions against PSA, the improved CBSM and experimental data. A coupling scheme with a hierarchical matrix accelerated boundary element method is formulated, resulting in the construction of a complete stochastic vibroacoustic solver.

A probabilistic structural analysis method (PSAM) is described which makes an approximate calculation of the structural response of a system, including the associated probabilistic distributions, with minimal computation time and cost, based on a simplified representation of the geometry, loads, and material. The method employs the fast probability integration (FPI) algorithm of Wu and Wirsching. Typical solution strategies are illustrated by formulations for a representative critical component chosen from the Space Shuttle Main Engine (SSME) as part of a major NASA-sponsored program on PSAM. Typical results are presented to demonstrate the role of the methodology in engineering design and analysis.

ABSTRACTIn this work a probabilistic structural analysis of a container terminal wharf is presented. Through the application of the Monte Carlo Simulations in a finite element structural model, the statistics of the axial forces at the pile heads were evaluated. Considering only ship berthing conditions, but varying equipment type, number and positions, ten external load combinations were analyzed and compared. Both finite element model and probabilistic analysis were performed in ANSYS software, v.16, on its APDL Mechanical and Probabilistic Design System packages respectively. The random input parameters considered were the concrete structure, pavement and rear landfill self-weight, live loads and ship sizes, for which statistical parameters were attributed based on bibliography or data collection. PIANC’s berthing energy method for fender systems design was applied for the evaluation of ship berthing forces acting on the structure. Considering the axial forces as the main parameters in the design of partially embedded piles, the random output parameters obtained were the minimum and maximum axial forces on each simulation. That approach, applied due to the possibility of ANSYS to be programmed through its Parametric Design Language (APDL), proved to be a powerful tool for probabilistic analysis of complex structural systems. The results present a comparison between the statistical parameters and probability density curves for the ten cases analyzed, by which the worst combinations from a probabilistic point of view could be defined. Keywords: Container terminal berth; Probabilistic Analisys; Monte Carlo Method; Finite Element Method; ANSYS.

The principal capabilities of NESSUS (Numerical Evaluation of Stochastic Structures Under Stress), an advanced computer code developed for probabilistic structural response analysis, are reviewed, and its structural reliability assessed. The code combines flexible structural modeling tools with advanced probabilistic algorithms in order to compute probabilistic structural response and resistance, component reliability and risk, and system reliability and risk. An illustrative numerical example is presented.

All engineering design problems can be characterized by the underlying assumptions around which the problem is formulated. The effect of these assumptions - including everything from general assumptions defining an operating environment to detailed assumptions regarding material properties - is variability in system performance, and resulting deviations from expected performance. Assumptions are made to eliminate uncertainties that would prevent the quantification of design performance. Probabilistic methods have been developed in recent decades to convert such deterministic problem formulations into probabilistic formulations to model and assess the effects of these known uncertainties and thus relax restrictive assumptions. Until very recently, however, the computational expense of probabilistic analysis of a single design has made its application impractical for all but very simplistic design problems. Consequently, probabilistic optimization has been considered prohibitively expensive, particularly for complex multidisciplinary systems. Today a number of enabling technologies are available to support probabilistic design analysis and optimization for complex engineering design problems, including: flexible software frameworks that allow integration and automation of a complex multidisciplinary process; probabilistic analysis and optimization tools that allow uncertainty to be modeled and performance variation to be measured and reduced; large scale parallel processing capabilities leading to greatly increased efficiency; and advanced surrogate modeling capabilities to replace complex nonlinear analyses with computationally efficient approximation models. Along with steady increases in computing power, the combination of these enabling technologies can facilitate effective probabilistic analysis and optimization for complex design problems. In this paper we focus primarily on two of these enabling technologies. We present a comprehensive probabilistic design optimization formulation, a six sigma based approach that incorporates variability within all elements of the formulation - input design variable bound formulation, output constraint formulation, and robust objective formulation. We discuss the applicability of kriging, one surrogate modeling approach that supports the approximation of complex nonlinear analyses, for facilitating probabilistic multidisciplinary design optimization. These enabling technologies, as implemented within the commercial software framework provided by iSIGHT, including capability to facilitate parallel processing, are demonstrated for a multidisciplinary conceptual ship design problem.

Probabilistic Analysis Tools for Surface Ships Under Seaway and Extreme Dynamic Loads

The recent tailing dam failure in Brazil has again emphasized the need of performing robust stability analysis prior to construction. This paper demonstrates the probabilistic dynamic stability analysis of tailing dams considering an existing rock-fill tailing dam in India. The stability analysis was performed using 2D finite element-based package RS2. In the probabilistic analysis, the strength parameters such as cohesion (c) and the friction angle (φ) were considered as random variables. In total, 3000 numbers of samples were generated assuming a normal distribution. Monte Carlo simulation was used to evaluate the probability of failure (PoF) and reliability index. Strength reduction method was used for the finite element analyses. A pseudo-static seismic loading was incorporated in the strength reduction analysis to check the seismic stability of the dam. A factor of safety (FoS) of 1.15 was observed from the deterministic analysis for downstream slope. For the same case, the probabilistic analysis provided a mean FoS of 1.19 with 5.46% probability of failure. The FoS values and the locations of the critical failure surface obtained by the limit equilibrium method and finite element method were compared. The observed FoS values were found to be higher than the values specified in the IS 7894-1975 (reaffirmed in 1997) and ANCOLD (1999). In the case of pseudo-static approach, the maximum displacement of 0.53 m was observed in the slope. Furthermore, nonlinear dynamic stability analysis was performed to simulate a true earthquake event. The permanent deformation of the slope after the earthquake was found to be 0.40 m. The zone of failure observed in both pseudo-static and nonlinear dynamic stability analyses was found to be the same. Overall, the results revealed that the spatial variability of the soil significantly influences the FoS values.

Probabilistic fatigue analysis of all-ceramic crowns based on the finite element method

In this paper, the mean-centered first-order second-moment (FOSM) method is employed to perform probabilistic push-over analysis (POA) of structural and/or soil-structure systems. Approximations of first and second statistical moments (FSSMs) of engineering demand parameters (EDPs) of structural and/or geotechnical systems with random material parameters are computed based on finite-element (FE) response and response sensitivity analysis (RSA) results. The FE RSA is performed accurately and efficiently by using the direct differentiation method (DDM) and is employed to evaluate the relative importance (RI) of the various modeling material parameters in influencing the variability of the EDPs. The proposed approximate methodology is illustrated through probabilistic POA results for nonlinear inelastic FE models of: (1) a three-story reinforced-concrete (RC) frame building and (2) a soil-foundation-structure interaction system consisting of a RC frame structure founded on layered soil. FSSMs of EDPs computed through the FOSM method are compared with the corresponding accurate estimates obtained via Monte Carlo simulation. Results obtained from exact (or local) and averaged (or global) response sensitivities are also compared. The RI of the material parameters describing the systems is studied in both the deterministic and probabilistic sense, and presented in the form of tornado diagrams. Effects of statistical correlation between material parameters are also considered and analyzed by the FOSM method. A simple approximation of the probability density function and cumulative distribution function of EDPs due to a single random parameter at a time (while all the other parameters are fixed to their mean values) is also proposed. Conclusions are drawn on both the appropriateness of using local RSA for simplified probabilistic POA and on the application limits of the FOSM method. It is observed that the FOSM method combined with the DDM provides accurate estimates of FSSMs of EDPs for low-to-moderate level of inelastic structural or system behavior and useful qualitative information on the RI ranking of material parameters on the structural or system response for high level of inelastic behavior.