A unified framework for stochastic predictions of mechanical properties of polymeric nanocomposites

Static and frequency optimization of folded laminated composite plates using an adjusted Differential Evolution algorithm and a smoothed triangular plate element

“…In addition, unlike the work done by Vu et al [58][59][60] and Silani et al [61], which focus on mechanical properties of composite material and take random distribution of fibers into account, the paper aims to find the optimum orientation for fibers with assumed fiber's distribution. As a result, the algorithm to generate the random distribution of fibers is not considered in the paper.…”

Stochastic analysis of the interphase effects on the mechanical properties of clay/epoxy nanocomposites

“…Here the focus is only to study the effect of interphase layer on the Young's modulus of clay/epoxy nanocomposites and hence, we only considered the Young's modulus and thickness of the interphase layer as the stochastic inputs and set the other parameters to be deterministic inputs with their mean value (the clay aspect ratio is considered to be 300 [34,35] and the Young's modulus and Poisson's ratio of the epoxy and clays are considered as 1.96 GP a, ν = .25, 221.5 GP a and ν = .25 [36,34] respectively). To evaluate the effect of other inputs on the Young's modulus of clay/epoxy nanocomposites, refer to [24,25]. Based on MD simulations and analytical results available in the literature the thickness and the Young's modulus of the interphase layer vary from 0.5 nm to 2 nm [17,37] and 0.35 Gpa to 1.96 GP a [11], respectively.…”

“…In similar approches, Vu-Bac et al [24] proposed a stochastic framework based on sensitivity analysis (SA) methods to quantify the key input parameters influencing the Young's modulus of polymer (epoxy) clay nanocomposites (PCNs). Silani et al [25] presented a numerical investigation of the mechanical properties of exfoliated clay/epoxy nanocomposites.…”

A software framework for probabilistic sensitivity analysis for computationally expensive models

“…The mapping technique is performed by the following algorithm Table 3 Penalized spline regression model result summary. At first, the quadratic regression without mixed terms [10,22] quadr_regsn.m is used to approximate the Branin data. As shown in Table 2 , the COD R 2 is less than 0.8.…”

“…Thus, the so-called surrogate-based approach is employed as an approximation of the real model for sensitivity analysis. In [10] , the authors presented a penalized spline regression model for a single continuous predictor. Since predictor variables have nonlinear relationships with the model output, the regression models considering multiple smooth functions [11] are adopted in this article to approximate the observed data.…”