Probabilistic micromechanical spatial variability quantification in laminated composites

Abstract

This article presents a probabilistic framework to characterize the dynamic and stability parameters of composite laminates with spatially varying micro and macro-mechanical system properties. A novel approach of stochastic representative volume element (SRVE) is developed in the context of two dimensional plate-like structures for accounting the correlated spatially varying properties. The physically relevant random field based uncertainty modelling approach with spatial correlation is adopted in this paper on the basis of Karhunen-Loève expansion. An efficient coupled HDMR and DMORPH based stochastic algorithm is developed for composite laminates to quantify the probabilistic characteristics in global responses. Convergence of the algorithm for probabilistic dynamics and stability analysis of the structure is verified and validated with respect to direct Monte Carlo simulation (MCS) based on finite element method. The significance of considering higher buckling modes in a stochastic analysis is highlighted. Sensitivity analysis is performed to ascertain the relative importance of different macromechanical and micromechanical properties. The importance of incorporating source-uncertainty in spatially varying micromechanical material properties is demonstrated numerically. The results reveal that stochasticity (/ system irregularity) in material and structural attributes influences the system performance significantly depending on the type of analysis and the adopted uncertainty modelling approach, affirming the necessity to consider different forms of source-uncertainties during the analysis to ensure adequate safety, sustainability and robustness of the structure.

Analytical Solution for Static and Dynamic Analysis of Graphene-Based Hybrid Flexoelectric Nanostructures

“…Recently, Lin et al [27] demonstrated that the nonlinear aeroelastic response and vibration characteristics of the functionally graded (FG) multilayer composite plate reinforced with graphene nanoplatelets, as well as piezoelectric layers when subjected to electromechanical loadings. Naskar and co-authors [28][29][30][31][32] derived new micromechanical analysis for envisaging effective properties of fiber-reinforced composite and functionally graded material by using a novel stochastic representative volume element technique, considering spatial distribution with stochastic analysis and uncertainty quantifications. They have also carried out static and dynamic characteristic including sensitivity and frequency analysis of laminated composite and FG material by using probabilistic and non-probabilistic uncertainty quantification approach.…”

Effect of delamination on the stochastic natural frequencies of composite laminates

“…Figure 3 shows the hybrid surrogate (HDMR) based FE algorithm for uncertainty quantification followed in this paper. A description about Monte Carlo simulation can be found in Naskar et al (2018) [57].…”

“…The aspect of delamination in composites has also received adequate attention in the deterministic domain . Stochastic analysis of composite and sandwich structures considering sourceuncertainty is found to be studied by many researchers including the aspects of multi-scale analysis, optimization and reliability assessment [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58][59]. However, the compound effect of delamination and sourceuncertainty has not been investigated yet for the dynamic responses of composite structures.…”

Quantifying Uncertainty in Structural Responses of Polymer Sandwich Composites: A Comparative Analysis of Neural Networks

“…Therefore, it is essential to consider the material and geometric uncertainty to include the variability and inaccuracies occurring during manufacturing and operating conditions. In general, a surrogate-based uncertainty quantification approach [2][3][4][5][6][7][8][9][10][11][12][13][14][15] can be adopted in case of problems, where efficient solutions [16][17][18][19][20][21][22][23][24] are not available. In this chapter, we aim to present a comparative performance of ANN [25][26][27] and PNN [28] for the uncertainty quantification of sandwich panels.…”