Stochastic Finite Element Model Research Articles

Deterministic and stochastic finite element modeling of reinforced concrete beams without stirrups containing plastic wastes

PurposeThe use of waste polyethylene terephthalate (PET) plastics derived from shredded bottles in concrete is not formalized yet, especially in reinforced members such as beams and columns. The disposal of plastic wastes in concrete is a viable alternative to manage those wastes while minimizing the environmental impacts associated to recycling, carbon dioxide emissions and energy consumption.Design/methodology/approachThis paper evaluates the suitability of 2D deterministic and stochastic finite element (FE) modeling to predict the shear strength behavior of reinforced concrete (RC) beams without stirrups. Different concrete mixtures prepared with 1.5%–4.5% PET additions, by volume, are investigated.FindingsTest results showed that the deterministic and stochastic FE approaches are accurate to assess the maximum load of RC beams at failure and corresponding midspan deflection. However, the crack patterns observed experimentally during the different stages of loading can only be reproduced using the stochastic FE approach. This later method accounts for the concrete heterogeneity due to PET additions, allowing a statistical simulation of the effect of mechanical properties (i.e. compressive strength, tensile strength and Young’s modulus) on the output FE parameters.Originality/valueData presented in this paper can be of interest to civil and structural engineers, aiming to predict the failure mechanisms of RC beams containing plastic wastes, while minimizing the experimental time and resources needed to estimate the variability effect of concrete properties on the performance of such structures.

Stochastic finite element modeling of heterogeneities in massive concrete and reinforced concrete structures

AbstractThe lifespan of a reinforced concrete (RC) structure can be greatly influenced by the spatial variability of its material characteristics which, in particular, explains the observed or measured reduction of the tensile strength at first crack when the volume under tension increases. This paper discusses the ability of accounting for the spatial variability of the tensile strength of concrete in RC structures using a stochastic finite element (SFE) method based on random field simulations. In this work, the generation of random fields on the concrete tensile strength aims at computing the force corresponding to the first crack occurrence, and the reduced tensile strength of the structure. The method can be applied in particular to large‐sized structures, which show a pronounced size effect, for different types of loading. The method consists of, first, estimating the mean of the random field, using the analytical approach of the weakest link and localization method (WL ). Then, the discretized random field is defined on a particular 2D or 3D grid, and it is finally projected on the finite element mesh of the studied structure. The study of the parameters that influence the prediction of the cumulative density functions (CDFs) of the rupture force or the tensile strength is highlighted using experimental series of concrete beams having different volumes and subjected to 4‐point bending loading. Moreover, the SFE method is applied to a RC tie‐beam under tensile loading, characterized by a weak stress gradient, which complicates the prediction of crack positions.

Optimal design of stochastic aeroviscoelastic systems in subsonic regime using the doublet lattice

In a concerted effort to mitigate the global environmental impact, various governments and international organizations have put forth strategies aimed at enhancing the efficiency of products and solutions. The aeronautical and aerospace industries have set forth an ambitious target of eliminating their CO2 emissions by the year 2050. To realize this objective, manufacturers are adopting innovative approaches, including the incorporation of new blade engines, utilization of Sustainable Aviation Fuel (SAF), integration of lighter materials, and the adoption of novel geometric wing shapes designed for enhanced efficiency. However, the implementation of structural and aerodynamic modifications, such as those required for aeroelastic systems, can lead to instability effects, notably the flutter phenomenon. Addressing this challenge, one viable strategy involves the application of vibration control techniques. In this context, the use of passive control with viscoelastic materials emerges as an intriguing option due to its cost-effectiveness and ease of application. Additionally, considering the inherent variabilities in structural and aerodynamic parameters within these systems, there is a need for an efficient stochastic modeling methodology to cater to realistic applications of industrial significance. The present study endeavors to model a stochastic aeroviscoelastic system, specifically focusing on a plate-like wing in a subsonic regime. This is achieved through the integration of stochastic finite element modeling and the Doublet Lattice Method (DLM). The study aims to quantify the impact of increased mass and stiffness, particularly related to the addition of layers and the inclusion of damping from the viscoelastic material. The findings of the research demonstrate a noteworthy 31% increase in flutter speed with a corresponding 38% increase in mass. Although the ratio of speed gain to mass gain is below one in this instance, with a partial treatment approach, it can potentially reach 2. This underscores the advantageous nature of treating aeronautical panels with layers of viscoelastic material. Importantly, the engineer possesses the capability to strategically select deterministic parameters to align with specific objectives between the two defined functions.

Vibration-based structural damage detection strategy using FRFs and machine learning classifiers

In this paper, a damage detection strategy for beam-type structures based on frequency response functions (FRFs) is presented. Five aluminum beams of equal nominal dimensions are used in an experimental program under laboratory conditions to obtain experimental FRF data from both undamaged and damaged conditions. Damages are induced by creating rectangular notches on the beams using saw-cutting. A stochastic finite element model of the beam is developed in MATLAB to construct several training datasets. The damages are modeled by reducing the cross-sectional area at the corresponding damaged elements. Simple damage indexes are proposed as damage-sensitive features. Decision Tree, Support Vector Machines, and Artificial Neural Networks classifiers are trained in the first stage to perform damage detection and localization. Single and multiple damages located in a single zone and more than one zone simultaneously are considered. In the second stage, experimental data not used for training are used for validation. The results from the first stage suggest that the proposed damage indexes can effectively detect and locate structural damage in beams. Among all classifiers, Artificial Neural Networks is the classifier that best performed. High accuracy is achieved to identify the presence of damage (99.3%) and detecting its location on the beam for some of the training datasets (from 80.0% to 97.1%). In the second stage of validation, accuracy, as expected, decreased. However, misclassifications occur mainly for FRF samples in the impact zone, which indicates that the proposed strategy can be efficient to detect damages at locations other than the excitation zone.

Analysis of tunneling-induced ground movements in spatially variable soil under the influence of existing building

Tunnel construction invariably results in ground movement, which is significantly impacted by the spatial variability of soil properties and proximity of existing buildings. However, few studies have examined the coupled effect of these two factors on tunneling-induced ground movement. This study establishes a stochastic finite element model that incorporates both the spatial variability of soil properties and influence of existing buildings. The model is used to perform a series of random analyses, studying the effects of story number, eccentricity, and building length on ground settlements induced by tunneling in soil with spatial variability of Young’s modulus. A probabilistic analysis is conducted to investigate the uncertainties associated with ground settlements. The results of the analysis indicate that the presence of the building enhances the influence of the spatial variability of soil, leading to an increase in the dispersion of ground settlement. For high-rise buildings, the reduction of building eccentricity and length will increase the uncertainty of surface settlement. Neglecting the influence of the existing building in the probability analysis of surface settlement can result in an overestimation of the failure probability.

Physical biology of cell-substrate interactions under cyclic stretch.

Mechanosensitive focal adhesion (FA) complexes mediate dynamic interactions between cells and substrates and regulate cellular function. Integrins in FA complexes link substrate ligands to stress fibers (SFs) and aid load transfer and traction generation. We developed a one-dimensional, multi-scale, stochastic finite element model of a fibroblast on a substrate that includes calcium signaling, SF remodeling, and FA dynamics. We linked stochastic dynamics, describing the formation and clustering of integrins to substrate ligands via motor-clutches, to a continuum level SF contractility model at various locations along the cell length. We quantified changes in cellular responses with substrate stiffness, ligand density, and cyclic stretch. Results show that tractions and integrin recruitments varied along the cell length; tractions were maximum at lamellar regions and reduced to zero at the cell center. Optimal substrate stiffness, based on maximum tractions exerted by the cell, shifted toward stiffer substrates at high ligand densities. Mean tractions varied biphasically with substrate stiffness and peaked at the optimal substrate stiffness. Cytosolic calcium increased monotonically with substrate stiffness and accumulated near lamellipodial regions. Cyclic stretch increased the cytosolic calcium, integrin concentrations, and tractions at lamellipodial and intermediate regions on compliant substrates. The optimal substrate stiffness under stretch shifted toward compliant substrates for a given ligand density. Stretch also caused cell deadhesions beyond a critical substrate stiffness. FA's destabilized on stiff substrates under cyclic stretch. An increase in substrate stiffness and cyclic stretch resulted in higher fibroblast contractility. These results show that chemomechanical coupling is essential in mechanosensing responses underlying cell-substrate interactions.

Numerical simulation methods for reinforced concrete columns considering parameter stochasticity

Reinforced concrete column specimens with the same parameters often show differences in bearing capacity and deformation under the same loading path. Most of the existing studies attribute the causes to recording instrumentation errors or randomness in material and bond dimensions, but the method to improve the accuracy of numerical simulation of the reinforced concrete components is still unclear. For a given member, the randomness of material and geometry is an important cause of simulation error, which should be taken into account to improve the simulation accuracy. A weighted least squares estimation (WLS) method is used to fuse the test samples of reinforced concrete member section sizes, reinforcement and concrete with confidence factors as weights. The probability distribution functions of reinforced concrete member section sizes, reinforcement and concrete are calculated by a genetic algorithm method. Based on the existing seismic performance test data of reinforced concrete columns, a stochastic finite element model of reinforced concrete columns is developed for seismic performance analysis using Monte Carlo method through a mixture of two software programs, MATLAB and OpenSees. The numerical seismic performance indexes of eight types of reinforced concrete columns were compared with the test results to verify the importance of introducing stochastic parameters into the model. The results demonstrate the simulation accuracy of the finite element model considering parameter randomness is 88% higher than that of the finite element model without considering parameter randomness, which proves the effectiveness of the numerical simulation method for reinforced concrete columns considering parameter randomness.

Application of Stochastic Finite Element Modeling to Reinforced Lightweight Concrete Beams Containing Expanded Polystyrene Beads

Limited investigations have evaluated the effect of expanded polystyrene (EPS) beads on the structural lightweight concrete properties. EPS offers many features compared to natural or artificial lightweight aggregates including the elimination of aggregate saturation prior to concrete batching, ability to be fabricated on site, consistency in size and quality, and reduced cost. The main objective of this paper is to assess the suitability of finite element (FE) modeling based on deterministic and stochastic approaches to predict the shear strength behavior of reinforced concrete (RC) beams containing EPS additions. Test results showed that the experimental load-deflection properties recorded at failure can be well reproduced using both FE approaches. Nevertheless, the damaged-zone distribution and crack patterns that occur during the loading stages of RC beams cannot be approximated using the deterministic FE approach. In contrast, the stochastic method was quite suitable as it accounted for the concrete heterogeneity and altered spatial mechanical properties (such as compressive strength, splitting tensile strength, and Young’s modulus) due to EPS additions. Such data can be of interest to civil engineers seeking to predict the failure patterns and performance of structural lightweight members while reducing the time and resources needed to account for the concrete’s strength variability during experimental testing.

Relative importance and interactions of parameters of finite-element models of human middle ear.

In the last decades, finite-element models of the middle ear have been widely used to predict the middle-ear vibration outputs. Even with the simplest linear assumption for material properties of the structures in the middle ear, these models need tens of parameters. Due to the complexities of measurements of material properties of these structures, accurate estimations of the values of most of these parameters are not possible. In this study, we benefited from the stochastic finite-element model of the middle ear we had developed in the past, to perform global sensitivity analysis. For this aim, we implemented Sobol' sensitivity analysis which ranks the importance of all uncertain parameters and interactions among them at different frequencies. To decrease the computational costs, we found Sobol' indices from surrogate models that we created using stochastic finite-element results and the polynomial chaos expansion method. Based on the results, the Young's modulus and thickness of the tympanic membrane, Young's modulus and damping of the stapedial annular ligaments, and the Young's modulus of ossicles are among the parameters with the greatest impacts on vibrations of the umbo and stapes footplate. Furthermore, the most significant interactions happen between the Young's modulus and thickness of the tympanic membrane.

Tooth Base Geometrical Variability Effect on the Vibration Behavior of the Stator

The magnetic pressure generated in the stator of electric machines can be a significant source of noise and vibration. The vibration behavior of the stator and such mechanical structures primarily depends on their geometry. Although the stator is often considered a simple structure, its teeth are not included in this assumption. In this paper, we endeavor to evaluate the impact of stator geometrical variability on the vibration behavior of electric machines. Our sensitivity study reveals that natural frequencies and frequency response functions are highly sensitive to geometrical variability. To account for this, we conducted a variability propagation study using a stochastic finite element model. Our findings show negligible variability on the natural frequencies but a high variability on the frequency response functions, even with low input variability. As anticipated, our study highlights the critical role of accounting for geometrical variability to enhance the accuracy of finite element models and strengthen their predictive power. However, the main contribution of this work is that the vibration behavior of the stator is not coupled, implying that the impact on natural frequencies does not necessarily reflect the same effect on the frequency response function.

Inaccuracies of deterministic finite-element models of human middle ear revealed by stochastic modelling

For over 40 years, finite-element models of the mechanics of the middle ear have been mostly deterministic in nature. Deterministic models do not take into account the effects of inter-individual variabilities on middle-ear parameters. We present a stochastic finite-element model of the human middle ear that uses variability in the model parameters to investigate the uncertainty in the model outputs (umbo, stapes, and tympanic-membrane displacements). We demonstrate: (1) uncertainties in the model parameters can be magnified by more than three times in the umbo and stapes footplate responses at frequencies above 2 kHz; (2) middle-ear models are biased and they distort the output distributions; and (3) with increased frequency, the highly-uncertain regions spatially spread out on the tympanic membrane surface. Our results assert that we should be mindful when using deterministic finite-element middle-ear models for critical tasks such as novel device developments and diagnosis.

In-field measurement and numerical modelling of air leakage in concrete: From laboratory specimen to structural full-scale

This work estimates air leakage through concrete porosity for structures by using data obtained in field combined with stochastic finite element (SFE) modelling. For this purpose, a methodology is proposed to evaluate permeability under representative over-pressurization conditions based on in-field measurements under vacuum. This makes it possible to investigate the air leakage through the inner wall of a 1:3 scaled nuclear vessel named the VeRCoRs mock-up. Measurements are made for over 80 points scattered on the external face of the inner wall of the structure. Based on the data collected, a statistical analysis quantifies the spatial variation of permeability and contributes to the building of an SFE model of air leakage at the structural scale. Measured and predicted data are in good agreement on the service life of the structure. This shows the relevance of combining in-field measurements during an operational phase and the SFE modelling for better evaluation of the structural performance. The lessons learnt from the present work could be useful for the assessment of all structures with durability or mechanical issues that induce a continuous loss of tightness.

Impacts of Random Atomic Defects on Critical Buckling Stress of Graphene under Different Boundary Conditions.

Buckled graphene has potential applications in energy harvest, storage, conversion, and hydrogen storage. The investigation and quantification analysis of the random porosity in buckled graphene not only contributes to the performance reliability evaluation, but it also provides important references for artificial functionalization. This paper proposes a stochastic finite element model to quantify the randomly distributed porosities in pristine graphene. The Monte Carlo stochastic sampling process is combined with finite element computation to simulate the mechanical property of buckled graphene. Different boundary conditions are considered, and the corresponding results are compared. The impacts of random porosities on the buckling patterns are recorded and analyzed. Based on the large sampling space provided by the stochastic finite element model, the discrepancies caused by the number of random porosities are discussed. The possibility of strengthening effects in critical buckling stress is tracked in the large sampling space. The distinguishable interval ranges of probability density distribution for the relative variation of the critical buckling stress prove the promising potential of artificial control by the atomic vacancy amounts. In addition, the approximated Gaussian density distribution of critical buckling stress demonstrates the stochastic sampling efficiency by the Monte Carlo method and the artificial controllability of porous graphene. The results of this work provide new ideas for understanding the random porosities in buckled graphene and provide a basis for artificial functionalization through porosity controlling.

Framework for Identification and Prediction of Corrosion Degradation in a Steel Column through Machine Learning and Bayesian Updating

In recent years, structural health monitoring, starting from accelerometric data, is a method which has become widely adopted. Among the available techniques, machine learning is one of the most innovative and promising, supported by the continuously increasing computational capacity of current computers. The present work investigates the potential benefits of a framework based on supervised learning suitable for quantifying the corroded thickness of a structural system, herein uniformly applied to a reference steel column. The envisaged framework follows a hybrid approach where the training data are generated from a parametric and stochastic finite element model. The learning activity is performed by a support vector machine with Bayesian optimization of the hyperparameters, in which a penalty matrix is introduced to minimize the probability of missed alarms. Then, the estimated structural health conditions are used to update an exponential degradation model with random coefficients suitable for providing a prediction of the remaining useful life of the simulated corroded column. The results obtained show the potentiality of the proposed framework and its possible future extension for different types of damage and structural types.

A two-stage approach to stochastic finite element model updating using FRF data

Stochastic model updating techniques are used to update an FE model of a structure so that the updated model can predict the mean as well as the variability of the structure's dynamic characteristics. Most of the current approaches and studies employ modal data to update the uncertain parameters related to the mass and stiffness matrices. Model updating using FRFs has an advantage over modal data that it avoids modal analysis errors and can be used to update the damping matrix. There is limited work on using FRFs for stochastic model updating and on identifying variability of the damping matrix. The existing methods simultaneously update the parameters related to the mass, stiffness, and damping matrices. These methods may encounter numerical challenges due to large differences in the order of magnitude of these matrices. In some situations, only the mass and stiffness matrices are to be updated to accurately predict the undamped dynamics of the structure and hence the damping identification is not necessary. In these situations, the existing methods cannot be used to update only the mass and stiffness matrices because the modelling and identification of the damping are necessary for updating with FRF-based methods. To address these limitations, this paper proposes a two-stage approach to stochastic model updating using normal FRFs. Normal FRFs represent the estimates of the FRFs, excluding the effect of the damping in the structures. Stage-I updates the mean and variability of the uncertain parameters related to the mass and stiffness matrices using normal FRFs. Stage-II updates the mean and variability of the uncertain parameters related to the damping matrix using the difference between the complex and normal FRFs. Separating updating of the damping matrix from updating of the mass and stiffness matrices improves the conditioning of the sensitivity matrices and eliminates the numerical challenges associated with updating the matrices with different orders of magnitude. For the situations where the variability in the undamped dynamics only needs to be predicted, stage-I of the proposed method can be used. Numerical studies on a damped cantilever beam and an aeroplane model (DLR-AIRMOD structure) are presented to validate the method. Experimental validation of the proposed method is carried out using nominally identical samples of a damped acrylic beam. The performance of the method is also compared with an existing complex FRF based method to highlight the effectiveness of the proposed method.

Homotopy based stochastic finite element model updating with correlated static measurement data

This paper focuses on studying the impaction of the correlation between the measurement data on structural model updating. A new homotopy based stochastic finite element model updating frame is constructed to cope with the correlated static measurement data. To judge whether considering the correlation of the measurement data, the sensitivity analysis of structural responses about structural parameters is implemented firstly. Then the discrete Karhunen–Loeve expansion is utilized to transform the correlated measurement data into a linear combination of multiple independent random variables. Furthermore, a novel stochastic model updating equation about the correlated static measurement data is set up, and is solved by the homotopy stochastic finite element method. It is significant to check the consistence of the correlation coefficients of the responses of the updated model with those of the measured data when the correlation actually exists. In this case, the proposed approach can effectively update the structural model.

Post-buckling strength of simply supported corroded square plates subjected to in-plane compression

Steel plates have been widely used in various structures, including building structures, bridges, ocean platforms, and industrial equipment. The post-buckling strength of steel plates can be substantially affected by corrosion. This study quantifies the influence of corrosion on post-buckling strength of simply supported corroded steel plates. To do so, stochastic numerical analysis is adopted, and the reliability of an established stochastic finite element model is initially verified by comparing it with the analytical results. This study also investigates the feasibility of the derived results for steel plates with different width/thickness (b/t) ratios. A variable Θ is introduced to represent the reduction factor of compression strength of corroded plates. The analytical formulas for predicting the upper and lower bounds of Θ are proposed, and the probabilistic distribution model of Θ is suggested. The method to determine the equivalent width/thickness (b/teqv) ratio of corroded steel plates is proposed. With the premise that the post-buckling strength remains unaffected, the corroded steel plates can be treated as uncorroded when the b/teqv ratio is substituted for the original b/t ratio. Conclusion of this study can establish a foundation for the buckling behavior of corroded steel plates.

Stochastic analysis on the lateral buckling of a HPHT pipeline considering the spatial variability of seabed

Complex geological processes and depositional environments could bring great spatial variability of the engineering properties of seabed sediments, which may further cause uncertainty in the global buckling predictions of high-pressure high-temperature (HPHT) pipelines. Unlike previous investigations with the deterministic method, a stochastic finite element (SFE) model is established for predicting the lateral buckling of a pipeline considering the spatial variability of the seabed. A flow chart of the Monto Carlo simulation for the lateral buckling of pipeline is provided. The SFE results for the simplified homogeneous seabed are compared with the existing analytical solutions for model verifications. Monte Carlo simulation results indicate that the mean values of the critical temperature rise for triggering the lateral buckling of a pipeline on the spatially varied seabed are generally larger than the deterministic predictions. It is found that the critical temperature rise may reach its maximum value when the horizontal scale of fluctuation ranges from the value of the discrete-element size to that of the imperfection wavelength. As the horizontal scale of fluctuation increases, the buckling probability increases significantly, which could be up to about 50% while the horizontal scale of fluctuation approaching a quite large value or even infinity.

3D mesoscale analysis of concrete containing defect damages during different freeze-thaw cycles

The damage process of concrete containing air pore and aggregate gradation defects under freeze-thaw (FT) cycles was parametrically studied by an ABAQUS coupled thermo-mechanical mesoscale numerical analyses platform. It was a stochastic finite element model (SFEM) developed by Python script program. The effectiveness of mesoscale model was verified by comparing 96 concrete samples divided to 4 groups with air pore and aggregate defects exposed to 0 to 90 FT cycles. The damage function of concrete for FT cycles was described by Weibull distribution equations. The analyses showed that air pore defects had a significant impact on concrete mechanical characteristics under FT cycles. When FT cycle number (n) reached 90, the strength loss of specimens with no defect was about 37.5%. When air pore content was 5% with non-uniform grading of aggregate, the strength loss of specimen was 61.6%. This showed that FT cycle damage effect on concrete was obvious which was more prominent for higher values of n.

Three-scale modeling and probabilistic progressive damage analysis of woven composite laminates

This article investigates the three-scale mechanical response and damage progression of woven composite laminates by probabilistic progressive damage analysis. Micro-scale, meso-scale, and macro-scale stochastic finite element models of woven composite laminates were established to consider the random fiber distribution in yarns and stochastic nature of material properties. Based on Monte-Carlo method, three-scale probabilistic progressive damage model was proposed to predict damage progression and probabilistic distribution of strengths for woven composite laminates. Good agreement between the predictions of elastic properties and strengths and experimental results has been achieved, demonstrating the validity of proposed three-scale probabilistic progressive damage model.