The quantification of uncertainties in the mechanical response of composite structures can be a computationally demanding task. This is due both to the number of uncertain parameters in a real study ...case and the complexity of the model to be analysed. In this paper, an efficient global/local approach to estimate the uncertainties of the quantities of interest in specific regions of interest with limited computational effort is proposed. This is achieved by refining only locally the model taking advantage of Refined Structural Theories. At the same time, since the variance of the uncertain parameters is usually relatively small, the stochastic analysis is dealt with a sensitivity study carried out both in the global and in the local model. In this way, it is possible to assess the influence of global and local uncertain parameters in the same submodeling analysis. The methodology presented is applied to several study cases of interest. The results focus on obtaining probabilistic distributions of the stress field that can be later used in failure criteria to evaluate the subsequent distribution of the failure index. Furthermore, a damage tolerance study case is investigated, showing good correlation with the reference Monte Carlo simulations.
•Uncertainty Quantification via a stochastic perturbation method.•Computationally efficient methodology to assess damage initiation.•Good correlations with reference Monte Carlo simulations.
In engineering practice, the evaluation of seismic reliability of high-rise reinforced concrete structure relies on the probabilistic modelling of material properties. However, the measured data of ...material parameters in engineering practice is usually inadequate to determine the probability model accurately, especially for the problems involving spatial variability. Traditional parametric reliability analysis methods can be biased for this kind of problem. Therefore, a nonparametric seismic reliability analysis method is proposed based on the Bayesian compressive sensing – stochastic harmonic function method and the probability density evolution method. In this method, the conditional random fields are generated and applied to represent material properties of concrete. As a result, the seismic reliability of a high-rise reinforced concrete shear wall model structure is analyzed using the probability density evolution method.
•A novel stochastic homotopy method is proposed to solve static problems involving arbitrarily distributed random variables.•The optimal homotopy series expansion is obtained by minimizing the ...stochastic residual error.•The proposed method shows better convergency and efficiency than the aPC method in the case of non-Gaussian random field.•This method is successfully applied to the stochastic static analysis of the large-scale engineering structure.
The modelling of realistic engineering structures with uncertainties often involves various probabilistic distribution types, which bring forward higher requirements for the generality of stochastic analysis methods. This paper proposes a novel stochastic homotopy method to evaluate the static response of the structure with random variables of arbitrary distributions. In this method, a homotopy series expansion is used to approximate the stochastic static response, and the optimal form of the expansion can be determined by minimizing the residual error about the stochastic static equilibrium equation regardless of distribution types of random variables. The numerical results of a logarithmic function and a thin plate show that the new method exhibits excellent accuracy and stability compared to the homotopy stochastic finite element method depending on the sample selection. Compared with the arbitrary polynomial chaos method (aPC), the proposed method is more efficient under equivalent accuracy. On the other hand, as the expansion order increases, this new method shows better convergence than the aPC method and the perturbation stochastic finite element method in the case of non-Gaussian distributed random variables of large fluctuation. In addition, a cable-stayed bridge example illustrates the application of the proposed method on the large-scale structure.
•A novel homotopy based stochastic FE model updating method is proposed to deal with the correlation of static measurement data firstly.•The Karhunen–Loeve expansion is used to express the correlated ...measurement displacements by independent random variables.•It is very significant to check the consistence of the correlation coefficients of the responses of updated model with those of the measured data.•The proposed method can effectively update structural model in the case of correlated measurement errors.
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.
Seismic analysis of dam-foundation systems is inherently complex due to uncertainties in material properties. This study investigates the effects of material randomness and heterogeneity on the ...seismic response of gravity dam-foundation systems using the stochastic spectral finite element method (SSFEM) based on the Karhunen Loève expansion and the polynomial chaos expansion. The Pine Plane dam is taken as an analysis example. First, the appropriate Karhunen Loève expansion modes and polynomial chaos order are determined for SSFEM by comparing them with the Monte-Carlo simulations. Subsequently, the seismic response of the dam is analyzed in the stochastic and deterministic models, respectively. Results indicate that material randomness and heterogeneity may reduce the seismic response of gravity dams, and the deterministic model may overestimate dynamic responses. Subsequently, the parametric analysis of the correlation length, which measures the spatial correlation between variables in different positions and indicates the size of heterogeneity material patches, is conducted. It is demonstrated that the correlation length would not significantly affect the mean responses, but a larger correlation length leads to greater dispersions in responses. Finally, the effects of randomness in the foundation are investigated. The heterogeneities in the foundation affect the response of the dam in the high-frequency range. Therefore, the uncertainty in material properties should be fully considered in a structural assessment and risk analysis.
•Parameters of SSFEM are determined in stochastic simulation for the Pine Plane dam.•The effect of the correlation length on the seismic response of gravity dam-foundation system is analyzed.•The effect of randomness in the foundation on the seismic response is analyzed.
In this paper, a stochastic homogenization method that couples the state-of-the-art computational multi-scale homogenization method with the stochastic finite element method, is proposed to predict ...the statistics of the effective elastic properties of textile composite materials. Uncertainties associated with the elastic properties of the constituents are considered. Accurately modeling the fabric reinforcement plays an important role in the prediction of the effective elastic properties of textile composites due to their complex structure. The p-version finite element method is adopted to refine the analysis. Performance of the proposed method is assessed by comparing the mean values and coefficients of variation for components of the effective elastic tensor obtained from the present method against corresponding results calculated by using Monte Carlo simulation method for a plain-weave textile composite. Results show that the proposed method has sufficient accuracy to capture the variability in effective elastic properties of the composite induced by the variation of the material properties of the constituents.
This paper proposes a novel stochastic finite element scheme to solve partial differential equations defined on random domains. A geometric mapping algorithm first transforms the random domain into a ...reference domain. By combining the mesh topology (i.e. the node numbering and the element numbering) of the reference domain and random nodal coordinates of the random domain, random meshes of the original problem are obtained by only one mesh of the reference domain. In this way, the original problem is still discretized and solved on the random domain instead of the reference domain. A random isoparametric mapping of random meshes is then proposed to generate the stochastic finite element equation of the original problem. We adopt a weak-intrusive method to solve the obtained stochastic finite element equation. In this method, the unknown stochastic solution is decoupled into a sum of the products of random variables and deterministic vectors. Deterministic vectors are computed by solving deterministic finite element equations, and corresponding random variables are solved by a proposed sampling method. The computational effort of the proposed method does not increase dramatically as the stochastic dimension increases and it can solve high-dimensional stochastic problems with low computational effort, thus the proposed method avoids the curse of dimensionality successfully. Four numerical examples are given to demonstrate the good performance of the proposed method.
•A general framework is proposed for solving deterministic/stochastic PDEs on random domains.•A random isoparametric mapping approach is developed to assemble stochastic matrices and stochastic vectors.•The stochastic finite element equation is solved by an efficient numerical algorithm.•The curse of dimensionality of high-dimensional stochastic problems is well avoided.
A hybrid methodology based on numerical and non-destructive experimental schemes, which is able to predict the structural level strength of composite laminates is proposed on the current work. The ...main objective is to predict the strength by substituting the up to failure experiments with non-destructive experiments where the investigated specimen is loaded up to 20% of its maximum load. A significant gap exists between the 20% and the 100% load which is proposed to be treated by high fidelity physics-based numerical models, deep learning techniques, and non-catastrophic experiments. Thus, a deep learning algorithm is developed, based on the convolutional neural networks and trained by probabilistic failure analysis datasets which result from the utilization of the stochastic finite element method. Also, the Monte Carlo dropout technique is embedded into the developed convolutional neural network to estimate the uncertainty induced by the investigated variations between the simulated and experimental data. The current paper provides a thorough description of the proposed methodology and a practical example which demonstrates the validity of the method.
This paper proposes a non-intrusive stochastic finite element method for slope reliability analysis considering spatially variable shear strength parameters. The two-dimensional spatial variation in ...the shear strength parameters is modeled by cross-correlated non-Gaussian random fields, which are discretized by the Karhunen–Loève expansion. The procedure for a non-intrusive stochastic finite element method is presented. Two illustrative examples are investigated to demonstrate the capacity and validity of the proposed method. The proposed non-intrusive stochastic finite element method does not require the user to modify existing deterministic finite element codes, which provides a practical tool for analyzing slope reliability problems that require complex finite element analysis. It can also produce satisfactory results for low failure risk corresponding to most practical cases. The non-intrusive stochastic finite element method can efficiently evaluate the slope reliability considering spatially variable shear strength parameters, which is much more efficient than the Latin hypercube sampling (LHS) method. Ignoring spatial variability of shear strength parameters will result in unconservative estimates of the probability of slope failure if the coefficients of variation of the shear strength parameters exceed a critical value or the factor of slope safety is relatively low. The critical coefficient of variation of shear strength parameters increases with the factor of slope safety.
•A non-intrusive stochastic finite element method is developed.•Slope reliability with spatially varying shear strength parameters is studied.•The proposed method is much more efficient than the LHS method.•Ignoring spatial variability may underestimate the probability of slope failure.•Variation of probability of slope failure highly depends on factor of safety.
Stochastic methods have recently been the subject of increased attention in Computational Mechanics for their ability to account for the stochasticity of both material parameters and geometrical ...features in their predictions. Among them, the Galerkin Stochastic Finite Element Method (GSFEM) was shown to be particularly efficient and able to provide accurate output statistics, although at the cost of intrusive coding and additional theoretical algebraic efforts. In this method, distributions of the stochastic parameters are used as inputs for the solver, which in turn outputs nodal displacement distributions in one simulation. Here, we propose an extension of the GSFEM—termed the A posteriori Finite Element Method or APFEM—where uniform distributions are taken by default to allow for parametric studies of the inputs of interest as a postprocessing step after the simulation. Doing so, APFEM only requires the knowledge of the vertices of the parameter space. In particular, one key advantage of APFEM is its use in the context of Bayesian inferences, where the random evaluations required by the Bayesian setting (usually done through Monte Carlo) can be done exactly without the need for further simulations. Finally, we demonstrate the potential of APFEM by solving forward models with parametric boundary conditions in the context of (i) metamaterial design and (ii) pitchfork bifurcation of the buckling of a slender structure; and demonstrate the flexibility of its use for Bayesian inference by (iii) inferring friction coefficient of a half plane in a contact mechanics problem and (iv) inferring the stiffness of a brain region in the context of cancer surgical planning.
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