Probabilistic Finite Element Research Articles

Implementation and validation of probabilistic models of the anterior longitudinal ligament and posterior longitudinal ligament of the cervical spine

The objective of this investigation was to develop probabilistic finite element (FE) models of the anterior longitudinal ligament (ALL) and posterior longitudinal ligament (PLL) of the cervical spine that incorporate the natural variability of biological specimens. In addition to the model development, a rigorous validation methodology was developed to quantify model performance. Experimental data for the geometry and dynamic properties of the ALL and PLL were used to create probabilistic FE models capable of predicting not only the mean dynamic relaxation response but also the observed experimental variation of that response. The probabilistic FE model uses a quasilinear viscoelastic material constitutive model to capture the time-dependent behaviour of the ligaments. The probabilistic analysis approach yields a statistical distribution for the model-predicted response at each time point rather than a single deterministic quantity (e.g. ligament force) and that response can be statistically compared to experimental data for validation. A quantitative metric that compares the cumulative distribution functions of the experimental data and model response is computed for both the ALL and PLL throughout the time histories and is used to quantify model performance.

Fatigue reliability assessment of steel bridge details integrating weigh-in-motion data and probabilistic finite element analysis

An advanced traffic load model is developed based on weigh-in-motion data. This model takes into account the uncertainties associated with the number of axles, axle weights, axle spacing and transversal position of vehicles. Combined with the traffic load model, a probabilistic finite element analysis approach is proposed to evaluate the time-dependent fatigue reliability levels of steel bridge details. The calculated results are in agreement with those obtained from monitored data. The proposed methodology can be used as a tool accompanying a monitoring program to obtain the fatigue reliability levels associated with the fatigue sensitive bridge details that are not monitored.

Probabilistic optimal safety valuation based on stochastic finite element analysis of steel cable-stayed bridges

This study was intended to efficiently perform the probabilistic optimal safety assessment of steel cable-stayed bridges (SCS bridges) using stochastic finite element analysis (SFEA) and expected life-cycle cost (LCC) concept. To that end, advanced probabilistic finite element algorithm (APFEA) which enables to execute the static and dynamic SFEA considering aleatory uncertainties contained in random variable was developed. APFEA is the useful analytical means enabling to conduct the reliability assessment (RA) in a systematic way by considering the result of SFEA based on linearity and nonlinearity of before or after introducing initial tensile force. The appropriateness of APFEA was verified in such a way of comparing the result of SFEA and that of Monte Carlo Simulation (MCS). The probabilistic method was set taking into account of analytical parameters. The dynamic response characteristic by probabilistic method was evaluated using ASFEA, and RA was carried out using analysis results, thereby quantitatively calculating the probabilistic safety. The optimal design was determined based on the expected LCC according to the results of SFEA and RA of alternative designs. Moreover, given the potential epistemic uncertainty contained in safety index, failure probability and minimum LCC, the sensitivity analysis was conducted and as a result, a critical distribution phase was illustrated using a cumulative-percentile.

Application of probabilistic finite element analysis for crane hook design

PurposeThe purpose of this paper is to report a study in which the feasibility of conducting probabilistic finite element analysis (FEA) for crane hook design has been explored.Design/methodology/approachThis paper presents the results of probabilistic analysis, where in the input random variables are varied and corresponding variations in the output parameters were observed. In this study, material properties and load have been considered as random input variables and the maximum stress, maximum deflection variations were considered as output random variables.FindingsThe probability of occurrence of output variation and the sensitivity of output variables on the input variables are the important results generated from this analysis. By performing this probabilistic analysis, the random selection of factor of safety could be avoided.Research limitations/implicationsThe implementation study has been carried out for a single product.Practical implicationsThe usage of the approach will indicate the importance of probabilistic analysis in product design and development process. This process will enable the organization to compete in the global market.Originality/valueA case study has been reported to indicate the feasibility of performing probabilistic FEA for crane hook design. Hence, the contributions are original.

Relative contributions of design, alignment, and loading variability in knee replacement mechanics

Substantial variation in total knee replacement (TKR) outcomes exists within the patient population. Some of this variability is due to differences in the design of the implanted components and variation in surgical alignment, while other variability is due to differences in the applied forces and torques due to anatomic and physiological differences within a patient population. We evaluated the relative contributions of implant design, surgical alignment, and patient-specific loading variability to overall tibiofemoral joint mechanics to provide insight into which measures can be influenced through design and surgical decisions, and which are inherently dependent on variation within the patient population and should be considered in the robustness of the implant design and surgical procedure. Design, surgical, and loading parameters were assessed using probabilistic finite element methods during simulated stance-phase gait and squat activities. Patient-specific loading was found to be the primary contributor to joint loading and kinematics during low flexion, particularly under conditions of high external loads (for instance, the gait cycle with high internal-external torque), while design and surgical factors, particularly femoral posterior radius and posterior slope of the tibial insert became increasingly important in TKR performance in deeper flexion.

Life prediction of different commercial dental implants as influence by uncertainties in their fatigue material properties and loading conditions

Probabilistic analyses allow the effect of uncertainty in system parameters to be determined. In the literature, many researchers have investigated static loading effects on dental implants. However, the intrinsic variability and uncertainty of most of the main problem parameters are not accounted for. The objective of this research was to apply a probabilistic computational approach to predict the fatigue life of three different commercial dental implants considering the variability and uncertainty in their fatigue material properties and loading conditions. For one of the commercial dental implants, the influence of its diameter in the fatigue life performance was also studied. This stochastic technique was based on the combination of a probabilistic finite element method (PFEM) and a cumulative damage approach known as B-model. After 6 million of loading cycles, local failure probabilities of 0.3, 0.4 and 0.91 were predicted for the Lifecore, Avinent and GMI implants, respectively (diameter of 3.75mm). The influence of the diameter for the GMI implant was studied and the results predicted a local failure probability of 0.91 and 0.1 for the 3.75mm and 5mm, respectively. In all cases the highest failure probability was located at the upper screw-threads. Therefore, the probabilistic methodology proposed herein may be a useful tool for performing a qualitative comparison between different commercial dental implants.

Geometry strongly influences the response of numerical models of the lumbar spine—A probabilistic finite element analysis

Typical FE models of the human lumbar spine consider a single, fixed geometry. Such models cannot account for potential effects of the natural variability of the spine's geometry. In this study, we performed a probabilistic uncertainty and sensitivity analysis of a fully parameterized, geometrically simplified model of the L3–L4 segment.We examined the impact of the uncertainty in all 40 geometry parameters, estimated lower and upper bounds for the required sample size and determined the most important geometry parameters.The natural variability of the spine's geometry indeed strongly affects intradiscal pressure, range of motion and facet joint contact forces. Deriving generalized statements from fixed-geometry models as well as transferring those results to different cases thus can easily lead to wrong conclusions and should only be performed with extreme caution. We recommend a sample size of≈100 to obtain reasonable accurate point estimates and a sufficient overview of the remaining uncertainties. Yet, only few parameters, especially those determining the disc geometry (disc height, end-plate width and depth) and the facets' position (intra-articular space, pedicle length, facet angles), proved to be truly important. Accurate measurement and modeling of those structures should therefore be prioritized.

Probabilistic Finite Element Prediction of the Active Lower Limb Model

The scope of this paper is to explore the input parameters of a Finite Element (FE) model of an active lower limb that are most influential in determining the size and the shape of the performance envelope of the kinematics and peak contact pressure of the knee tibial insert introduced during a Total Knee Replacement (TKR) surgery. The active lower limb FE model simulates the stair ascent and it provides a more complicated setup than the isolated TKR model which includes the femoral component and the tibial insert. It includes bones, TKR implant, soft tissues and applied forces. Two probabilistic methods are used together with the FE model to generate the performance envelopes and to explore the key parameters: the Monte Carlo Simulation Technique (MCST) and the Response Surface Method (RSM). It is investigated how the uncertainties in a reduced set of 22 input variables of the FE model affect the kinematics and peak contact pressure of the knee tibial insert. The kinematics is reported in the Grood and Suntay system, where all motion is relative to the femoral component of the TKR. Reported tibial component kinematics are tibio-femoral flexion angle, anterior-posterior and medial-lateral displacement, internal-external and varus-valgus rotation (i.e. abduction-adduction), while the reported patella kinematics are patella-femoral flexion angle, medial-lateral shift and medial-lateral tilt. Tibio-femoral and patella-femoral contact pressures are also of interest. Following a sensitivity analysis, a reduced set of input variables is derived, which represent the set of key parameters which influence the performance envelopes. The findings of this work are paramount to the orthopedic surgeons who may want to know the key parameters that can influence the performance of the TKR for a given human activity.

Reliability of Spread Footing Performance in Desiccated Clay

AbstractTo advance the use of reliability-based design procedures, it is necessary to evaluate the sources of the design parameter uncertainty including inherent variability, measurement error, and transformation uncertainty. The results of a probabilistic evaluation of undrained footing bearing performance are discussed in the context of an extensive test site characterization described in a companion paper. Kriged cone tip resistance values are transformed into design parameters using a second-moment probabilistic approach and compared with the parameters obtained from the laboratory test analyses on specimens retrieved from the test site. The spatial, measurement, and transformation uncertainty are incorporated into probabilistic finite-element and bearing capacity analyses in which the results are compared against a full-scale load test performed at the test site. The results indicate that the reliable assessment of the spread footing response depends to a large degree on the assumed strength anisotro...

Probabilistic finite element analysis of a craniofacial finite element model

We employed a probabilistic finite element analysis (FEA) method to determine how variability in material property values affects stress and strain values in a finite model of a Macaca fascicularis cranium. The material behavior of cortical bone varied in three ways: isotropic homogeneous, isotropic non-homogeneous, and orthotropic non-homogeneous. The material behavior of the trabecular bone and teeth was always treated as isotropic and homogeneous. All material property values for the cranium were randomized with a Gaussian distribution with either coefficients of variation (CVs) of 0.2 or with CVs calculated from empirical data. Latin hypercube sampling was used to determine the values of the material properties used in the finite element models. In total, four hundred and twenty six separate deterministic FE simulations were executed.We tested four hypotheses in this study: (1) uncertainty in material property values will have an insignificant effect on high stresses and a significant effect on high strains for homogeneous isotropic models; (2) the effect of variability in material property values on the stress state will increase as non-homogeneity and anisotropy increase; (3) variation in the in vivo shear strain values reported by Strait et al. (2005) and Ross et al. (2011) is not only due to variations in muscle forces and cranial morphology, but also due to variation in material property values; (4) the assumption of a uniform coefficient of variation for the material property values will result in the same trend in how moderate-to-high stresses and moderate-to-high strains vary with respect to the degree of non-homogeneity and anisotropy as the trend found when the coefficients of variation for material property values are calculated from empirical data. Our results supported the first three hypotheses and falsified the fourth.When material properties were varied with a constant CV, as non-homogeneity and anisotropy increased the level of variability in the moderate-to-high strains decreased while the level of variability in the moderate-to-high stresses increased. However, this is not the pattern observed when CVs calculated from empirical data were applied to the material properties where the lowest level of variability in both stresses and strains occurred when the cranium was modeled with a low level of non-homogeneity and anisotropy. Therefore, when constant material property variability is assumed, inaccurate trends in the level of variability present in modest-to-high magnitude stresses and strains are produced.When the cranium is modeled with the highest level of accuracy (high non-homogeneity and anisotropy) and when randomness in the material properties is calculated from empirical data, there is a large level of variability in the significant strains (CV=0.369) and a low level of variability in the modest-to-high magnitude stresses (CV=0.150). This result may have important implications with regard to the mechanical signals driving bone remodeling and adaptation through natural selection.

A probabilistic three-dimensional finite element study on simply-supported composite floor beams

Composite steel-concrete beams are commonly used as flooring in buildings. The composite action between slab and steel joist is typically provided by shear connectors welded to the top of the steel joist and embedded in the concrete. This paper investigates the effects of material uncertainties on the numerically simulated structural response of simply-supported beam tests reported in the literature by means of Monte Carlo simulation (MCS). The numerical analyses are performed using a three-dimensional finite element model developed using the commercial software ABAQUS and capable of predicting the response of composite steel-concrete members as well as the influence of the shear connectors without having to rely on shear connection load-slip curves obtained from push-out tests. All materials are assumed to behave in a non-linear fashion. Contact regions between the concrete and steel elements are simulated using surface-to-surface and embedment techniques. The statistical information on the structural response obtained from MCS using different realisation sizes is compared and discussed. For the particular case studies considered in this paper it can be concluded that even a reduced number of realisations can already provide meaningful statistical representations of the structural response of the considered composite floor beams.

Study on Design Method of Series Traction Rod of Heavy Machinery

Abstract The integrated design method of series traction rod of heavy machinery was studied. Based on topology optimization, parameter optimization design and reliability analysis, its integrated design method was proposed. Its topology optimization design and parameter optimization design were done. Moreover, based on probabilistic finite element method, the influence of the randomness of the design parameters to its maximum deflection and maximum equivalent stress was studied. The method and basis are supported for design and development of series traction rod of heavy machinery.

Modeling 2-D spatial variation in slope reliability analysis using interpolated autocorrelations

This paper deals with slope reliability analysis incorporating two-dimensional spatial variation. Two methods, namely the method of autocorrelated slices and the method of interpolated autocorrelations, are proposed for this purpose. Investigations are carried out based on the limit equilibrium method of slices. First-order-reliability-method (FORM) is coupled with deterministic slope stability analysis using the constrained optimization approach. Systematic search for the probabilistic critical slip surface has been carried out in this study. It is shown that both methods work well in modeling 2-D spatial variation. The results of slope reliability analysis are validated by Monte Carlo simulations. Failure probabilities obtained by FORM agree well with simulation results. It is found that 2-D spatial variation significantly influences the reliability analysis, and that the reliability index is more sensitive to vertical autocorrelation distance than to horizontal autocorrelation distance. Based on this study, failure probability is found significantly overestimated when spatial variation is ignored. Finally, the possible use of the method of interpolated autocorrelations in a probabilistic finite element analysis is suggested.

BUCKLING ANALYSIS OF COMPOSITE LONG CYLINDERS USING PROBABILISTIC FINITE ELEMENT METHOD

The buckling behaviours of filament-wound carbon fibre-epoxy composite long cylinders subjected to ex-ternal hydrostatic pressure are researched by using deterministic and probabilistic finite element analyses. The critical buckling pressures predicted by deterministic finite element analysis and Monte Carlo simulation and response surface method of ANSYS probabilistic design system are compared with the experimental results. The effects of uncertainties of material properties and physical dimensions on the critical buckling pressure are also researched. The results show that the deterministic and probabilistic finite element analyses predict the similar critical buckling pressures, which are a little higher than the experimental results. The probability of buckling predicted by using response surface method is correct according to the experi-mental buckling pressure. The thickness of composite layers, transversal modulus, inside radius and longitudinal modulus have significant effects on the performance of composite long cylinders, whereas shear modulus, Poisson's ratio, winding angle of outer layers, winding angle of inner layers and unsupported length have small influences. http://dx.doi.org/10.5755/j01.mech.17.5.721

Probabilistic analysis of composite pressure vessel for subsea blowout preventers

The buckling behaviour of filament-wound carbon fibre–epoxy composite pressure vessel with aluminium liner for subsea blowout preventer is investigated by using probabilistic finite element analysis method and hydrostatic pressure test. The critical buckling pressure which is predicted by means of Monte Carlo Simulation (MCS) and Response Surface Method (RSM) of ANSYS probabilistic design system is compared with the experimental results. The influences of uncertainties of material properties and pressure vessel dimensions on the critical buckling pressure are researched. The results show that RSM and MCS predict the similar probability of buckling behaviour, which is lower than the calculated probability. The longitudinal modulus of composite material and thickness of composite layers have significant influences on the performance of composite pressure vessel, whereas winding angle, inside radius, shear modulus, Poisson’s ratio, unsupported length and transverse modulus have small influences. In addition, the results of finite element analysis by means of PDS and hydrostatic pressure test indicate good matches.

Probabilistic modeling of microstructure evolution using finite element representation of statistical correlation functions

A probabilistic finite element scheme is presented for simulating evolution of polycrystalline microstructures during deformation. The microstructure is described using conditional orientation correlation function (COCF), defined as the probability density of occurrence of a crystal orientation g′ at a distance r from a given orientation g. The COCF is represented using three interconnected layers of finite element meshes in the g′, r and g spaces. As the microstructure evolves, the reoriented neighborhood and strain fields close to an orientation (g) are captured by updating probability fields in these finite element meshes. For this purpose, a novel total Lagrangian approach has been developed that allows evolution of probability densities while satisfying normalization constraints, probability interdependencies and symmetries. The improvement in prediction of texture and strains achieved by the COCF approach over ODF-based methods is quantified through deformation analysis of a planar polycrystalline microstructure.

Probabilistic optimal safety with minimum life-cycle cost based on stochastic finite element analysis of steel cable-stayed bridges

This study was intended to efficiently perform the probabilistic safety and optimal design assessment of steel cable-stayed bridges (SCS bridges) using stochastic finite element analysis (SFEA) and expected life-cycle cost (LCC) concept. To that end, advanced probabilistic finite element algorithm (APFEA) which enables to execute the static and dynamic SFEA considering aleatory uncertainties contained in random variable was developed. APFEA is the useful analytical means enabling to conduct the reliability assessment (RA) in a systematic way by considering the result of SFEA based on linearity and nonlinearity of before or after introducing initial tensile force. Appropriateness of APFEA was verified in such a way of comparing the result of SFEA of a simple structure and the result of numerical analysis using Monte Carlo Simulation (MCS) program. The probabilistic method of SCS bridges was set, taking into account of analytical parameters. The dynamic response characteristic by probabilistic method was evaluated using ASFEA, and RA was carried out based on analysis result, thereby quantitatively calculating the probabilistic safety. The optimal design of SCS bridges was determined based on the expected LCC according to the results of SFEA and RA of alternative designs. Moreover, given the potential epistemic uncertainty contained in safety index, failure probability and minimum LCC, the sensitivity analysis was conducted and as a result, a critical distribution phase was illustrated using a cumulative-percentile.

Safety assessment of infrastructures using a new Bayesian Monte Carlo method

A recently developed Bayesian Monte Carlo (BMC) method and its application to safety assessment of structures are described in this paper. We use a one-dimensional BMC method that was proposed in 2009 by Rajabalinejad in order to develop a weighted logical dependence between successive Monte Carlo simulations. Our main objective in this research is to show that the extended BMC can dramatically improve simulation efficiency by using prior information from modelling and outcomes of preceding simulations. We provide theory and numerical algorithms for an extended BMC method for multi-dimensional problems, integrate it with a probabilistic finite element model and apply these coupled models to assessment of reliability of a flood defence for the 17th Street Flood Wall system in New Orleans. This is the first successful demonstration of the BMC method to a complex system. We provide a comparison of the numerical efficiency for the BMC, Monte Carlo (MC) and Dynamic Bounds methods that are used in reliability assessment of complex infrastructures.

Reliability assessment of 3D space frame structures applying stochastic finite element analysis

Throughout design development of satellite structure, stress engineer is usually challenged with randomness in applied loads and material properties. To overcome such problem, a risk-based design is applied which estimates satellite structure probability of failure under static and thermal loads. Determining probability of failure can help to update initially applied factors of safety that were used during structure preliminary design phase. These factors of safety are related to the satellite mission objective. Sensitivity-based analysis is to be implemented in the context of finite element analysis (probabilistic finite element method or stochastic finite element method (SFEM)) to determine the probability of failure for satellite structure or one of its components.

Advances in Finite Element Simulations of Elastosonography for Breast Lesion Detection

Among the available tools for the early diagnosis of breast cancer, the elastographic technique based on ultrasounds has many advantages such as the noninvasive measure, the absence of ionizing effects, the high tolerability by patients, and the wide diffusion of the ecographic machines. However this diagnostic procedure is strongly affected by many subjective factors and is considered not reliable enough even to reduce the number of biopsies used to identify the nature of lesions. Therefore in the literature experimental and numerical simulations on physical and virtual phantoms are presented to test and validate procedures and algorithms and to interpret elastosonographic results. In this work, first a description of the elastographic technique and a review of the principal finite element (FE) models are provided and second diagnostic indexes employed to assess the nature of a lump mass are presented. As advances in FE simulations of elastosonography, axisymmetric phantom, and anthropomorphic models are described, which, with respect to the literature, include some features of breast mechanics. In particular deterministic analyses were used to compare the various details of virtual elastograms and also to investigate diagnostic indexes with respect to the regions where strains were considered. In order to improve the reliability of the elastosonographic procedure, univariate and multivariate sensitivity analyses, based on a probabilistic FE approach, were also performed to identify the parameters that mostly influence the deformation contrast between healthy and cancerous tissues. Moreover, synthetic indicators of the strain field, such as the strain contrast coefficient, were evaluated in different regions of interest in order to identify the most suitable for lesion type assessment. The deterministic analyses show that the malignant lesion is characterized by a uniform strain inside the inclusion due to the firmly bonding condition, while in the benign inclusion (loosely bonded) a strain gradient is observed independently from the elastic modulus contrast. The multivariate analyses reveal that the strain contrast depends linearly on the relative stiffness between the lesion and the healthy tissue and not linearly on the interface friction coefficient. The anthropomorphic model shows other interesting features, such as the layer or curvature effects, which introduce difficulties in selecting a reference region for strain assessment. The results show that a simple axisymmetric model with linear elastic material properties can be suitable to simulate the elastosonographic procedure although the breast curvature and layer distinction play a significant role in the strain assessment.