ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering

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This paper describes the stochastic elastic property evaluation of a resin structure, which is made using the fused deposition modeling (FDM) method, through experimental and numerical tests. The FDM method is an additive manufacturing method, and it enables the fabrication of complex shaped structures at a low cost. However, a resin structure that is made using the FDM method has a complex microstructure, and a multiscale problem must be considered for the evaluation of its mechanical properties. In addition, if the microstructure is not well controlled compared to the structure obtained using a conventional processing technique, a multiscale stochastic problem should be also considered. In this paper, first, the randomness in a resin specimen manufactured using the FDM method is experimentally investigated, and the necessity of considering the microscopic randomness for the mechanical property evaluation of the resin structure is discussed. Next, appropriate numerical modeling for evaluating the probabilistic property of an apparent elastic property of the specimen (as a mechanical property of the resin structure made using the FDM method) is discussed, along with a comparison between the experimental results and the numerical results obtained using the Monte Carlo simulation with several analysis models. Based on the results, the effectiveness of the evaluation using a detailed hierarchical modeling is discussed. In addition, the perturbation-based hierarchical stochastic homogenization analysis is performed, and the applicability of the method is discussed based on the numerical results. This article is available in the ASME Digital Collection at .

This paper describes an efficient computational method for estimating the probabilistic properties of the maximum microscopic stresses in a unidirectional fiber-reinforced composite material against microscopic random variations of fibers locations. Some microscopic geometrical random variations will cause a large variation of the microscopic stresses, even if the influence on the homogenized elastic properties is small. The random variation of the microscopic stresses will have a significant influence on the apparent strength of composites, and therefore, estimation of the random variation will be important for reliability-based design of a composite structure. Further, for more precise analysis, a unit cell containing many inclusions should be employed. When the number of random variables becomes large, a multipoint approximation-based approach will not be appropriate. Therefore, a computational approach with a local surrogate constructed by a successive sensitivity analysis is proposed in this paper. The realizations of the microscopic stresses are estimated with the successive sensitivity-based local surrogate, and the probabilistic properties of the stresses are estimated with using the approximated realizations in the Monte Carlo simulation. As an example, the multiscale stochastic stress analysis of a unidirectional fiber-reinforced composite plate under unidirectional tensile load along the transverse direction is performed with considering randomness in fibers locations. For this problem, probabilistic properties as the expectation and coefficient of variation of the maximum microscopic stresses in resin are estimated. From comparisons between the direct Monte Carlo simulation and the proposed method, validity and effectiveness of the proposed approach are discussed. This article is available in the ASME Digital Collection at .

This paper addresses the effect of microstructure uncertainties on elastic properties of nanocomposites using finite element analysis (FEA) simulations. Computer-simulated microstructures were generated to reflect the variability observed in nanocomposite microstructures. The effect of waviness, agglomeration, and orientation of carbon nanotubes (CNTs) were investigated. Generated microstructures were converted to image-based 2D FEA models. Two hundred different realizations of microstructures were generated for each microstructure type to capture the stochastic response. The results confirm previously reported findings and experimental results. The results show that for a given fiber volume fraction, CNTs orientation, waviness, and agglomeration result in different elastic properties. It was shown that while a given microstructural feature will improve the elastic property, it will increase the variability in the elastic properties. This article is available in the ASME Digital Collection at .

This paper focuses on the computational homogenization of graphene sheet-reinforced composites with randomly dispersed inclusions and uncertainty in the constituent materials. Material uncertainty of the matrix and of the graphene inclusions are considered separately and their relative effect on the homogenized properties is assessed. The uncertainty in the inclusion material is due to structural defects of the graphene lattice and is taken into account using random variables for each component of the elasticity matrix. Moreover, Monte Carlo simulation is used to extract the statistical characteristics of the homogenized properties of the composite material. The results lead to useful conclusions regarding the effect of material and geometrical uncertainty on the macroscopic properties of graphene sheet-reinforced composites. This article is available in the ASME Digital Collection at .

A fast statistical homogenization procedure (FSHP) based on virtual element method (VEM)—previously developed by the authors has been successfully adopted for the homogenization of particulate random composites, via the definition of the representative volume element (RVE), and of the related equivalent elastic moduli. In particular, the adoption of virtual elements of degree one for modeling the inclusions provided reliable results for materials with low contrast, defined as the ratio between mechanical properties of inclusions and matrix. Porous media are then here described as bimaterial systems in which soft circular inclusions, with a very low value of material contrast, are randomly distributed in a continuous stiffer matrix. Several simulations have been performed by varying the level of porosity, highlighting the effectiveness of FSHP in conjunction with virtual elements of degree one. This article is available in the ASME Digital Collection at .

The properties of composite materials with random microstructures are often defined by homogenizing the properties of a representative volume element (RVE). This results in the effective properties of an equivalent homogeneous material. This approach is useful for predicting a global response but smooths the underlying variability of the composite's properties resulting from the random microstructure. Statistical volume elements (SVEs) are partitions of an RVE. Homogenization of individual SVEs produces a population of apparent properties. While not as rigorously defined as RVEs, SVEs can still provide a repeatable framework to characterize mesoscale variability in composite properties. In particular, their statistical properties can be used as the basis for simulation studies. For this work, Voronoi tessellation was used to partition RVEs into SVEs and apparent properties developed for each SVE. The resulting field of properties is characterized with respect to its spatial autocorrelation and distribution. These autocorrelation and distribution functions (PDFs) are then used as target fields to simulate additional property fields, with the same probabilistic characteristics. Simulations based on SVEs may provide a method of further exploring the uncertainty within the underlying approximations or of highlighting effects that might be experimentally measurable or used to validate the use of an SVE mesoscale analysis in a specific predictive model. This work presents an update to an existing simulation technique developed by Joshi (1975, “A Class of Stochastic Models for Porous Media,” Ph.D. thesis, University of Kansas, Lawrence, KS) and initially extended by Adler et al. (1990, “Flow in Simulated Porous Media,” Int. J. Multiphase Flow, 16(4), pp. 691–712). The simulation methodology is illustrated for three random microstructures and two SVE partitioning sizes. This article is available in the ASME Digital Collection at .

To accurately simulate fracture, it is necessary to account for small-scale randomness in the properties of a material. Apparent properties of statistical volume element (SVE) can be characterized below the scale of a representative volume element (RVE). Apparent properties cannot be defined uniquely for an SVE, in the manner that unique effective properties can be defined for an RVE. Both constitutive behavior and material strength properties in SVE must be statistically characterized. The geometrical partitioning method can be critically important in affecting the probability distributions of mesoscale material property parameters. Here, a Voronoi tessellation-based partitioning scheme is applied to generate SVE. Resulting material property distributions are compared with those from SVE generated by square partitioning. The proportional limit stress of the SVE is used to approximate SVE strength. Superposition of elastic results is used to obtain failure strength distributions from boundary conditions at variable angles of loading. This article is available in the ASME Digital Collection at .

The main aim of this work is to study a significance of structural microdefects and their uncertainty in structural steel on its elastoplastic large deformations subjected to tensile test with the use of the generalized stochastic perturbation method. Elastoplastic behavior of the macroscopically homogeneous material is defined by the Gurson–Tvergaard–Needleman (GTN) constitutive model, where Young's modulus and this model constants q₁ and q₂ are consecutively randomized according to the Gauss probability distribution. The stochastic finite element method (SFEM) analysis has been carried out in the system abaqus for the problem of necking under tension to compute the first four probabilistic moments and coefficients of displacements, deformations, and stresses. The tenth-order perturbation scheme has been implemented via statistically optimized least-squares method (LSM) determination of the structural nodal polynomial response functions. A comparison with Monte Carlo simulation (MCS) as well as the semi-analytical integral technique based on the same polynomial bases confirms applicability of the method proposed for the input uncertainty not larger than 0.10. Further numerical experiments with this constitutive law including stochastic nucleation and/or coalescence would be necessary to better understand deformations and stresses of stochastic porous plastic materials. This model may find its applications in various stress states of the plastic materials with voids as well as in numerical simulations of the composite materials with imperfect interphases, for instance, where some parameters exhibit initial Gaussian statistical scattering. This article is available in the ASME Digital Collection at .

This paper demonstrates the development of a flexible fault diagnosis methodology that can detect up to ten different faults in the induction motor (IM), simultaneously. The major IM electrical faults, such as the broken rotor bar (BRB), phase unbalance (PUF), and stator winding fault (SWF), and mechanical faults, such as bearing fault (BF), unbalanced rotor (UR), bowed rotor (BR), and misaligned rotor (MR), are considered with different fault severities for the diagnosis. The experiments are conducted with three varying loads and seven different speeds, and the frequency domain vibration and current data are acquired at a relatively low sampling rate of 1 kHz. Several statistical features are extracted and then the best feature-set is selected using the wrapper model. Thereafter, a data classification tool based on the support vector machine (SVM) is used for the fault characterization. Initially, a multi-fault diagnosis is performed by training and testing the SVM at the same operating conditions (i.e., load and speed). The performance of the classifier is found to be very good at all IM operating conditions. The main focus of this study lies in overcoming the fault diagnosis, where the data are unavailable at required operating conditions. This is accomplished by employing interpolation and extrapolation strategies for different loads and speeds. The proposed methodology not only solves practical problem of unavailability of data at different operating conditions but also shows good performance and takes low computation time, which are vital requirements of an online intelligent condition monitoring system. This article is available in the ASME Digital Collection at .

While the area of functional safety for industry has evolved over the years by developing well-renowned standards and methods proven in use, such standards are not present in the field of equipment protection for complex research facilities. Research facilities in particular do typically not apply global, systematic approaches for functional equipment protection, but rather rely on system expert judgment for the individual systems, often leaving out the emergent properties of complex systems of systems. With the increasing demands on research facilities to be highly reliable and available, comparable to industrial facilities, a holistic and systematic method for equipment protection is, if not necessary, highly beneficial. This paper describes the development of a risk management method named functional protection, and benchmarks its lifecycle steps toward the IEC 61508 functional safety standard as well as the ISO 31000 risk management standard. The functional protection method is currently applied for the design and construction of the European Spallation Source in Lund, Sweden. This article is available in the ASME Digital Collection at .

This paper presents a procedure for the reliability analysis of a multistage axial compressor regarding blade-specific roughness effects, based on the survival signature approach. As a result, a time-dependent evolution of the system reliability is obtained along with a prioritization technique for monitoring and regeneration of the rough blade rows by capturing the most critical system components. For this purpose, a one-dimensional flow model is developed and utilized to evaluate the aerodynamic influences of the blade-specific roughness on the system performance parameters, namely the overall pressure ratio and the isentropic efficiency. In order to achieve transparency and high numerical efficiency for time-dependent analyses in practice, the physics-based compressor model is translated into an illustrative, function-based system model. This system model is established by conducting a Monte Carlo simulation along with a variance-based global sensitivity analysis, with the input variables being the row-specific blade roughness. Based on the system model, the roughness impact in different blade-rows is ranked by the relative importance (RI) index, and the corresponding time-dependent reliability of the compressor system in terms of pressure ratio and efficiency is estimated through its survival function. Furthermore, uncertainties in the roughness-induced failure rates of the components are modeled using imprecise probabilities. Consequently, bounds on the reliability function and the importance indices for the blade-surface roughness in each blade row are captured, which enhances the decision-making process for maintenance activities under uncertainty. This article is available in the ASME Digital Collection at .