Stochastic Finite Element Approach 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 Approach to Assess Reliability of Fiber-Reinforced Polymer-Strengthened Concrete Beams

Stochastic Finite Element Approach to Assess Reliability of Fiber-Reinforced Polymer-Strengthened Concrete Beams

Uncertain Eigenvalue Analysis for Graded Porous and Sandwich Arches by Employing Perturbation-Based Stochastic Finite Element Approach

Uncertain Eigenvalue Analysis for Graded Porous and Sandwich Arches by Employing Perturbation-Based Stochastic Finite Element Approach

Stochastic Buckling Analysis of Non-Uniform Columns Using Stochastic Finite Elements with Discretization Random Field by the Point Method

This study examined the discretization random field of the elastic modulus by a point method to develop a stochastic finite element method for the stochastic buckling of a non-uniform column. The formulation of stochastic analysis of a non-uniform column was constructed using the perturbation method in conjunction with the finite element method. The spectral representation was used to generate a random field to employ the Monte Carlo simulation for validation with a stochastic finite element approach. The results of the stochastic buckling problem of non-uniform columns with the random field of elastic modulus by comparing the first-order perturbation technique were in good agreement with those obtained from the Monte Carlo simulation. The numerical results showed that the response of the coefficient of variation of critical loads increased when the ratio of the correlation distance of the random field increased.

Dynamic and Probabilistic Analysis of Shear Deformable Pipeline Resting on Two Parameter Foundation

The nonlinear dynamic deterministic and probabilistic analysis of pipeline undergoing large deflections and resting on Winkler-Pasternak foundation have been done. Dynamic analogues of Euler Bernoulli and Timoshenko Von-Kármán type beam equations are used. The stochastic finite element approach based on the Vanmarcke method combined to Monte Carlo simulations has been used to solve the governing nonlinear equations of soil-pipe interaction. The influence of different parameters of random soil is has been analyzed and the obtained results are compared with those obtained from the literature. It is concluded from the present work that the spatial variability of the soil properties has a great impact on the seismic response of the pipe and the developed model which is based on the accurate method is efficient to determine the real response of the safe and economic pipeline.

Representative Volume Element for Mechanical Properties of Carbon Nanotube Nanocomposites Using Stochastic Finite Element Analysis

AbstractThe aim of this study is to present a representative volume element (RVE) for nanocomposites with different microstructural features using a stochastic finite element approach. To that end, computer-simulated microstructures of nanocomposites were generated to include a variety of uncertainty present in geometry, orientation, and distribution of carbon nanotubes. Microstructures were converted into finite element models based on an image-based approach for the determination of elastic properties. For each microstructure type, 50 realizations of synthetic microstructures were generated to capture the variability as well as the average values. Computer-simulated microstructures were generated at different length scales to determine the change in mechanical properties as a function of length scale. A representative volume element is defined at a length scale beyond which no change in variability is observed. The results show that there is no universal RVE applicable to all properties and microstructures; however, the RVE size is highly dependent on microstructural features. Microstructures with agglomeration tend to require larger RVE. Similarly, random microstructures require larger RVE when compared with aligned microstructures.

A New Dam Reliability Analysis Considering Fluid Structure Interaction

Gravity dam reliability analysis is inherently complex considering the parameters randomness caused by the spatial variability of dam foundation, the coupled influence of seepage and high nonlinearity of dam safety evaluation. Taking the seepage randomness and dam foundation spatial variability into account, a fluid structure interaction (FSI) stochastic finite element approach and a weighted dynamic response surface method (WD-RSM) are proposed based on the integrated 3D engineering geological model. When applying the methods to gravity dam reliability analysis, three technical issues are considered: (1) the influence of dam foundation spatial variability on the gravity safety, (2) the key effect that the FSI makes on the gravity analysis and (3) the available safety evaluation method for the highly nonlinearity problem. The FSI stochastic finite element approach and the WD-RSM are validated using a real case of a gravity dam in operation with karst foundation. The results show the evident negative effect that seepage militated on the dam stability and the consistency and discreteness that spatial variability of dam foundation incarnated, which facilitates understanding the role of seepage and spatial variability.

Stochastic free vibration analysis of angle-ply composite plates – A RS-HDMR approach

This paper presents a generic random sampling-high dimensional model representations (RS-HDMR) approach for free vibration analysis of angle-ply composite plates. A metamodel is developed to express stochastic natural frequencies of the system. A global sensitivity analysis is carried out to address the influence of input random parameters on output natural frequencies. Three different types of input variables (fiber-orientation angle, elastic modulus and mass density) are varied to validate the proposed algorithm. The present approach is efficiently employed to reduce the sampling effort and computational cost when large number of input parameters is involved. The stochastic finite element approach is coupled with rotary inertia and transverse shear deformation based on Mindlin’s theory. Statistical analysis is carried out to illustrate the features of the RS-HDMR and to compare its performance with full-scale Monte Carlo simulation results. The stochastic mode shapes are also depicted for a typical laminate configuration. Based on the numerical results, some new physical insights are drawn on the dynamic behavior of the system.

STOCHASTIC MODELING OF MACROMOLECULAR MOTIONS THROUGH POST ARRAYS

The dynamic motions of macromolecules through a microfluidic postarray system are simulated using a three-dimensional stochastic finite element approach. The effects of molecular conformation on the time for a macromolecule to move across the system are investigated. The analyses are first performed on disklike geometries and then extended to a representative carbonic anhydrase (CA) macromolecule model consisting of elastically deformable beam networks. The model predicts that smaller molecules typically take less time to pass through the post array, and that for stiff materials the time inversely increases with the aspect ratio of molecules due to the conformational changes in collisions between the molecules and the obstacles. In addition, the dynamic responses of molecules are highly stochastic. The work has potential applications in designing functional microfluidic devices for separation and purification of macromolecules such as plasmid DNA.

Special Issue on Contaminant Mixtures: Fate, Transport, and Remediation

The fate and transport of mixed contaminants in subsurface environments can be quite complex because of various physical, chemical, and biological processes. In-depth understanding of geochemistry that influences the distribution, speciation, and transport is needed to understand the risk and develop remedial strategies. Joo et al. performed batch experiments to evaluate the sorption of six nonpolar and six polar organic compounds as mixtures to both hydrophilic mineral surfaces [uncoated, iron (hydr) oxide-coated, and aluminum (hydr)oxide-coated sands] and humic acid–mineral complexes with different fractions of organic carbon. The mixture effects on sorption of the nonpolar compounds were found to be not significant, whereas they were found to be significant for polar compounds depending on the mixture compositions and the type of sorbent. This implies the need for accurately quantifying and modeling mixture effects on fate and transport of multiple organic contaminants present at the site. Poly and Sreedeep performed batch sorption experiments and found that the presence of multiple contaminants affect the sorption of individual contaminants. The contaminant fate prediction based on linear isotherm is influenced by the range of concentration for single and multiple contaminants. For lower ranges of concentration, the contaminant fate prediction based on the Freundlich isotherm is greater than that of Langmuir, and vice versa for higher concentration range. Further, the difference in contaminant fate prediction based on Freundlich and Langmuir nonlinear isotherms decreases with an increase in concentration. The fate and transport parameters of soils vary in space because of soil heterogeneity, and such conditions require transport modeling using stochastic approaches. Nezhad and Javadi present an advective and diffusive-dispersive contaminant transport, using a stochastic finite-element approach. The need for expanding such approaches to multiple contaminant conditions is warranted.

Modeling of contaminant transport in soils considering the effects of micro- and macro-heterogeneity

This paper presents development and application of a numerical model for simulation of contaminant transport considering macro- and micro-heterogeneity in soil. Stochastic finite element approach is used to incorporate the effects of the spatial variability of soil hydraulic properties on contaminant fate. The soil micro-heterogeneity effects are modeled with a dual domain concept in which a first order kinetic expression is used to describe the transfer of the solute between the two domains. The model is used to simulate transport of non-reactive solute in a lysimeter under steady-state water flux. Numerical simulation of the problem is carried out for four different scenarios assumed for structure and formation of the soil: a single domain having uniform hydraulic properties (SDU), a dual-domain system with uniform hydraulic properties (DDU), a single domain with spatially variable hydraulic properties (SDV) and a dual-domain system with spatially variable hydraulic properties (DDV). The numerical results are compared with experimental data. The results obtained based on SDU are not in agreement with the measured data. Assuming a dual domain system (DDU) yields satisfactory results but higher accuracy is achieved using DDV scenario. The results show that the combination of the dual domain approach with the stochastic approach improves the numerical predictions. Also, using stochastic finite element approach makes it possible to evaluate variance of concentration as an index of reliability of the result.

A reduced-order stochastic finite element approach for design optimization under uncertainty

This paper presents a computational framework for structural design optimization under uncertainty. The stochastic static response of linear elastic structures is predicted by a spectral stochastic finite element method (SSFEM) based on a polynomial chaos expansion (PCE). Traditional SSFEM approaches lead to large-scale numerical problems and computational costs rendering these methods impractical for design optimization purposes. To mitigate the computational burden, a Galerkin-based multi-point reduced-order model (ROM) is integrated into SSFEM. The ROM basis is spanned by displacements and derivatives of displacements with respect to design and random variables evaluated at adaptively selected calibration points in the design space. The design sensitivity equations are derived and a formal analysis of the computational costs in terms of floating-point operations is presented. The efficiency of the ROM based approach versus traditional SSFEM is studied with the shape optimization of a shell structure. For this example, the results show that the proposed reduced-order modeling scheme can lower the total turnaround time by more than a factor of 30.

Effect of Stiffness Uncertainties on the Flutter of a Cantilever Wing

This paper deals with the investigation of the influence of spanwise distribution of bending and torsion stiffness uncertainties on the flutter behavior of an aeroelastic wing using a stochastic finite element approach. The analysis adopted a numerical algorithm to simulate unsteady, nonlinear, incompressible flow (based on the unsteady vortex lattice method) interacting with linear aeroelastic structure in the absence of uncertainties. The airflow and wing structure are treated as elements of a single dynamic system. Parameter uncertainties are represented by a truncated Karhunen-Love expansion. Both perturbation technique and Monte Carlo simulation are used to establish the boundary of stiffness uncertainty level, at which the wing exhibits flutter in the form of limit-cycle oscillations and above which the wing experiences dynamic instability. The analysis also includes the limitation of perturbation solution for a relatively large level of stiffness uncertainty.

Inversion of Robin coefficient by a spectral stochastic finite element approach

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.

Stochastic modeling of transient contaminant transport

A stochastic perturbation-based formulation for transient contaminant transport in the vadose zone was developed and implemented. The proposed methodology provides an efficient way to incorporate the small-scale variability of soil properties into large-scale models using effective parameters. A finite element solution of the stochastic differential equation for transient contaminant transport was formulated. The mean concentration value and its variance at each node were evaluated. The advantage of the proposed stochastic finite element approach is that only a few soil parameters are required to describe the variability of its stochastic properties. In addition, the proposed approach is neither site-specific nor contaminant-specific. A one-dimensional transient contaminant transport was simulated and the stochastic results were compared to deterministic and experimental results. The stochastic perturbation-based numerical formulation predicted the velocity of spreading of the contaminant much closer to the experimental measurements, as compared to the deterministic approach.

Consideration of Parameter Scattering in Thermo-Mechanical Characterization of Advanced Packages

Much progress has been made in the simulation and verification of the thermo-mechanical behavior of plastic packages. On the other hand, until now there is a lack in the consideration of the scatter or uncertainty, respectively, of certain characteristics. A comparatively large scatter of local material properties or random geometrical imperfections can often be observed within the material compounds of electronic packages. The partial randomness of certain input parameters creates uncertainties in the finite element determination of mechanical quantities which are provided for thermo-mechanical reliability optimization and life time prediction. In the following the STOFEM stochastic finite element approach based on perturbation theory is applied as a part of the finite element simulation. It is used to find out some additional effects arising from uncertainties in the modeling, slightly varying parameters or probabilistic influences, respectively. In a second part of the paper, another approach to the consideration of random variations is discussed. It is based on the randomization of initially deterministic relations.

Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach

This paper presents an efficient procedure for characterizing the solution of evolution equations with stochastic coefficients. These typically model the behavior of physical systems whose properties are modeled as spatially or temporally varying stochastic processes described within the framework of probability theory. The concepts of projection, orthogonality and weak convergence are exploited in a manner which directly mimics deterministic finite element solutions except that, in the stochastic case, inner products refer to expectation operations. Specifically, the Karhunen–Loève expansion is used to discretize these processes into a denumerable set of random variables, thus providing a denumerable function space in which the problem is cast. The polynomial chaos expansion is then used to represent the solution in this space, and the coefficients in the expansion are evaluated as generalized Fourier coefficients via a Galerkin procedure in the Hilbert space of random variables.

Convergence rates for finite elementapproximations of stochastic partial differential equations

We study convergence rates for generalized random variables, ihese results will be applied to study a stochastic finite element approach to stochastic partial differential equations

Interpretation of pavement deflection measurement data using an elastodynamic stochastic approach

Pavement deflection measurements, together with backcalculation procedures, are widely used to estimate the layer moduli of pavement-subgrade systems. Sensitivity analysis of a sample problem indicates that conclusions drawn from static analyses with regards to deflection sensitivity to variation in layer moduli may apply when characterizing uncertainty associated with the interpretation of the falling weight deflectometer (FWD) data. The uncertainty associated with the values of the backcalculated parameters from deflection data is investigated in this paper using an elastodynamic, stochastic finite element approach. The results of the simulations indicate that, in order to properly estimate surface layer moduli, loading frequencies higher than that of excitation by typical FWD loading are required. The low sensitivity of deflection uncertainty to random variations in surface modulus, when compared with that associated with subgrade modulus, is demonstrated to contribute to high variations in backcalculated surface modulus from measured surface deflections. Although focus is placed on uncertainties in elastic modulus and deflection, the methodology presented in the paper can be used to quantify uncertainties associated with other layer properties and pavement responses.Key words: stochastic, finite element, pavement deflection, elastodynamic, backcalculation, layer moduli, falling weight deflectometer test.