Stochastic finite element analysis of the free vibration of laminated composite plates

Abstract

Using the Stochastic Finite Element Method (SFEM) to perform reliability analysis of the free vibration of composite plates with material and fabrication uncertainties has received much attention lately. In this work the stochastic analysis is performed using the First Order Reliability Method (FORM-method 2) and the Second Order Reliability Method (SORM). The basic random variables include laminae stiffness properties and material density, as well as the randomness in ply orientation angles. Modeling of the composite behavior utilizes a nine-noded isoparametric Lagrangian element based on the third order shear deformation theory. The developed code utilizes MATLAB capabilities to derive the derivatives of the reduced stiffness and mass matrices symbolically with a considerable reduction in calculation time. Calculating the eigenvectors at the mean values of the variables proves to be a reasonable simplification which significantly increases solution speed. The stochastic finite element code is validated using available data in the literature, in addition to comparisons with results of the well-established Monte Carlo simulation technique with importance sampling. Results show that SORM is an excellent rapid tool in the stochastic analysis of free vibration of composite plates, when compared to the slower Monte Carlo simulation techniques.

Stochastic Finite element analysis of the free vibration of functionally graded material plates

“…The integration is performed over the failure region g < 0. In order to calculate p f , and following our procedure in [6], we shall use two types of analytical approximations that lead to two methods; the First-Order Reliability Method (FORM-Method 2), and the Second-Order Reliability Method (SORM). Both methods will be investigated in their ability to correctly predict the probability of failure and the Most Probable Point (MPP) of the system.…”

“…Here, an element based on the higher-order shear deformation theory (HSDT) is utilized. Development of the element, detailed in [9] and briefly summarized here, employs the parabolic shear deformation theory.…”

“…In this work, our previously developed stochastic finite element SFEM analysis of the free vibration of composite laminates [6] is adopted for FGM plates. This analysis allows the random variables representing material properties to be normal or non-normal, correlated or uncorrelated.…”

Stochastic Thermo-Elastic Stability Analysis of Laminated Composite Plates Resting on Elastic Foundation under Non-Uniform Temperature Distribution

“…Nieuwenhof & Coyette [19] investigated sensitivity analysis to the random parameters such as material and shape parameters using SFEM and independent MCS. Stefanou & Papadrakakis [20], Singh et al [21,22] & Onkar et al [25,26] have used a generalized layer wise stochastic finite element formulation for the buckling analysis of homogeneous and laminated plates with and without centrally loaded circular cutouts having random material properties using FOPT in conjunction with HSDT [25,27].…”

Free Vibration Analysis of Composite Plates via Refined Theories Accounting for Uncertainties

“…The effect of the coefficient of variation of the material properties was investigated. Shaker et al [37] presented the reliability analysis of the free vibration of composite plates via the first-and second-order reliability methods and the stochastic finite element method.…”