T. Mukhopadhyay

A polynomial chaos expansion based molecular dynamics study for probabilistic strength analysis of nano-twinned copper

Nano-twinned structures are mechanically stronger, ductile and stable than its non-twinned form. Wehave investigated the effect of varying twin spacing and twin boundary width (TBW) on the yield strength of the nano-twinned copper in a probabilistic framework. An efficient surrogate modelling approach based on polynomial chaos expansion has been proposed for the analysis. Effectively utilising 15 sets of expensive molecular dynamics simulations, thousands of outputs have been obtained corresponding to different sets of twin spacing and twin width using virtual experiments based on the surrogates. One of the major outcomes of this work is that there exists an optimal combination of twin boundary spacing and twin width until which the strength can be increased and after that critical point the nanowires weaken. This study also reveals that the yield strength of nanotwinned copper is more sensitive toTBWthan twin spacing. Such robust inferences have been possible to be drawn only because of applying the surrogate modelling approach, which makes it feasible to obtain results corresponding to 40 000 combinations of different twin boundary spacing and twin width in a computationally efficient framework.

Free-Vibration Analysis of Sandwich Panels with Randomly Irregular Honeycomb Core

AbstractAn analytical framework has been proposed to analyze the effect of random structural irregularity in honeycomb core for natural frequencies of sandwich panels. Closed-form formulas have been developed for the out-of-plane shear moduli of spatially irregular honeycombs following minimum potential energy theorem and minimum complementary energy theorem. Subsequently an analytical approach has been presented for free-vibration analysis of honeycomb core sandwich panels to quantify the effect of such irregularity following a probabilistic paradigm. Representative results have been furnished for natural frequencies corresponding to low vibration modes of a sandwich panel with high length-to-width ratio. The results suggest that spatially random irregularities in honeycomb core have considerable effect on the natural frequencies of sandwich panels.

Structural damage identification:A random sampling-high dimensional model representation approach

Structural damage identification and quantification of damage using non-destructive methods are important aspects for any civil, mechanical and aerospace engineering structures. In this study, a novel damage identification algorithm has been developed using random sampling-high dimensional model representation approach. A global sensitivity analysis based on random sampling-high dimensional model representation is adopted for important parameter screening purpose. Three different structures (spring mass damper system, simply supported beam and fibre-reinforced polymer composite bridge deck) have been used for various single and multiple damage conditions to validate the proposed algorithm. The performance of this method is found to be quite satisfactory in the realm of damage detection in structures. The random sampling-high dimensional model representation-based approach for meta-model formation is particularly useful in damage identification as it works well when large numbers of input parameters are involved. In this study, two different optimization methods have been used and their relative capability to identify damage has been discussed. Performance of this damage identification algorithm under the influence of noise has also been addressed in this article.

Probabilistic characterisation for dynamics and stability of laminated soft core sandwich plates

This paper presents a generic multivariate adaptive regression splines-based approach for dynamics and stability analysis of sandwich plates with random system parameters. The propagation of uncertainty in such structures has significant computational challenges due to inherent structural complexity and high dimensional space of input parameters. The theoretical formulation is developed based on a refined C0 stochastic finite element model and higher-order zigzag theory in conjunction with multivariate adaptive regression splines. A cubical function is considered for the in-plane parameters as a combination of a linear zigzag function with different slopes at each layer over the entire thickness while a quadratic function is assumed for the out-of-plane parameters of the core and constant in the face sheets. Both individual and combined stochastic effect of skew angle, layer-wise thickness, and material properties (both core and laminate) of sandwich plates are considered in this study. The present approach introduces the multivariate adaptive regression splines-based surrogates for sandwich plates to achieve computational efficiency compared to direct Monte Carlo simulation. Statistical analyses are carried out to illustrate the results of the first three stochastic natural frequencies and buckling load.

A multivariate adaptive regression splines based damage identification methodology for web core composite bridges including the effect of noise

A novel computationally efficient damage identification methodology for web core fiber-reinforced polymer composite bridges has been developed in this article based on multivariate adaptive regression splines in conjunction with a multi-objective goal-attainment optimization algorithm. The proposed damage identification methodology has been validated for several single and multiple damage cases. The performance of the efficient multivariate adaptive regression splines-based approach for the inverse system identification process is found to be quite satisfactory. An iterative scheme in conjunction with the multi-objective optimization algorithm coupled with multivariate adaptive regression splines is proposed to increase damage identification accuracy. The effect of noise on the proposed damage identification algorithm has also been addressed subsequently using a probabilistic framework. The multivariate adaptive regression splines-based damage identification algorithm is general in nature; therefore, in future it can be implemented to other structures.

Efficient System Reliability Analysis of Earth Slopes Based on Support Vector Machine Regression Model

This chapter presents a surrogate-based approach for system reliability analysis of earth slopes considering random soil properties under the framework of limit equilibrium method of slices. The support vector machine regression (SVR) model is employed as a surrogate to approximate the limit-state function based on the Bishops simplified method coupled with a nonlinear programming technique of optimization. The value of the minimum factor of safety and the location of the critical slip surface are treated as the output quantities of interest. Finally, Monte Carlo simulation in combination with Latin hypercube sampling is performed via the SVR model to estimate the system failure probability of slopes. Based on the detailed results, the performance of the SVR-based proposed procedure seems very promising in terms of accuracy and efficiency.

Free vibration analysis of angle-ply composite plates with uncertain properties

In this paper a random sampling-high dimensional model representations (RSHDMR) approach is employed to analyze free vibration of angle-ply composite plates with stochastic properties. A metamodel is developed and sensitivity analysis is carried out. The present approach is found efficient to reduce the sampling effort and computational cost when large number of random input parameters are involved. Statistical analysis is carried out incorporating its performance with full scale Monte Carlo Simulation results. Encouraging agreements between the direct Monte Calois simulation and results from the proposed reduced RS-HDMR apaproach were obtained. I. Introduction OMPOSITE materials are extensively used in aircraft industries due to its weight sensitivity, cost-effective, high specific stiffness. Because of its inherent complexity, laminated composite structures can be difficult to manufacture accurately according to its exact design specifications, resulting in undesirable uncertainties. The random structural uncertainties involve material and geometric properties, fibre parameters of the individual constituent laminae. These variables are statistical in nature; therefore, the properties of composite materials should be quantified probabilistically. As a consequence, the behavior of composite structures shows a scatter from its average value. Traditionally, an ad-hoc factor of safety is used in the design to account for the difficulty in predicting the structural behavior. However, this approach of designer may result in either an ultraconservative or an unsafe design. In general, uncertainties can be categorized into three types, namely aleatoric, epistemic and prejudicial, respectively. The total uncertainty of a system is the combination of these three types of uncertainties. In general, Monte Carlo simulation technique is popularly utilized to generate the randomized output frequency to deal with large number of samples. Although the uncertainty in material and geometric properties can be computed by the MCS method, it is inefficient and expensive. To mitigate this lacuna, random sampling - High-dimensional model representations (RS-HDMR) is employed for quantitative model assessment and analysis tool which maps high-dimensional input-output system relationship very efficiently

UNCERTAINTY QUANTIFICATION OF DYNAMIC CHARACTERISTICS OF COMPOSITES – A FUZZY APPROACH

The quantification of uncertainty in composite structures has intuitively significant threat to ensure structural reliability. Due to inherent complexities, composite structures are difficult to manufacture accurately according to its exact design specifications resulting in unavoidable uncertainties. Typical uncertainties are inadvertently induced due to intralaminate voids, incomplete curing of resin, excess resin between plies, excess matrix voids, porosity, variations in material properties and fibre parameters. In general, random field models are extensively used to represent a spatially varying function. Different probabilistic approaches (Monte Carlo simulation, perturbation methods, random matrix, and generalized polynomial chaos with Karhunen-Loève expansion) are employed for composites. In a probabilistic setting, uncertainty associated with the system parameters can be modelled as random variables or stochastic processes using the so-called parametric approach. But in real-life situation due to the availability of limited sample data (crisp inputs), it will be more practical or realistic to follow non-probabilistic approach rather than probabilistic approach. In the present study, fuzzy approach is introduced to carry out the uncertainty propagation in natural frequencies of laminated composite plates using Gram-Schmidt Polynomial Chaos (PC). The proposed PC fuzzy model is integrated with finite element to predict the possible two extreme bound of responses for different degree of fuzziness. The fuzzy variable is represented as a set of interval variables via membership function. The most significant input parameters are identified and then fuzzified. Fuzzy analysis of the first three natural frequencies for typical laminate configuration is presented to illustrate the results and its performance.