Abstract
In the present work, for the first time, free vibration response of angle ply laminates with uncertainties is attempted using Multivariate Adaptive Regression Spline (MARS), Artificial Neural Network-Particle Swarm Optimization (ANN-PSO), Gaussian Process Regression (GPR), and Adaptive Network Fuzzy Inference System (ANFIS). The present approach employed 2D C0 stochastic finite element (FE) model based on the Third Order Shear Deformation Theory (TSDT) in conjunction with MARS, ANN-PSO, GPR, and ANFIS. The TSDT model used eliminates the requirement of shear correction factor owing to the consideration of the actual parabolic distribution of transverse shear stress. Zero transverse shear stress at the top and bottom of the plate is enforced to compute higher-order unknowns. C0 FE model makes it commercially viable. Stochastic FE analysis done with Monte Carlo Simulation (MCS) FORTRAN inhouse code, selection of design points using a random variable framework, and soft computing with MARS, ANN-PSO, GPR, and ANFIS is implemented using MATLAB in-house code. Following the random variable frame, design points were selected from the input data generated through Monte Carlo Simulation. A total of four-mode shapes are analyzed in the present study. The comparison study was done to compare present work with results in the literature and they were found in good agreement. The stochastic parameters are Young’s elastic modulus, shear modulus, and the Poisson ratio. Lognormal distribution of properties is assumed in the present work. The current soft computation models shrink the number of trials and were found computationally efficient as the MCS-based FE modelling. The paper presents a comparison of MARS, ANN-PSO, GPR, and ANFIS algorithm performance with the stochastic FE model based on TSDT.
Highlights
The novelty of the article is a probabilistic description of four-mode shapes of hybrid angle ply laminated composite plates with Monte Carlo Simulation (MCS)-finite element model (FEM) and efficient metamodels Gaussian Process Regression (GPR), Multivariate Adaptive Regression Spline (MARS), Particle Swarm Optimization Aided Artificial Neural Network (PSO-Artificial neural networks (ANNs)), and Adaptive Network Fuzzy Inference System (ANFIS) and showing the advantage of metamodels over finite element (FE) model, as in earlier published articles, no or very limited work is found on mode-shape analysis using soft computation metamodels
The present results are based on third-order shear deformation theory using finite element solutions; slight variation is observed with reference papers by Mandal et al [48] and Reddy and Chao [49]
Probability distribution plots, and statistical parameters presented and discussed above show that there is a negligible deviation of GPR, MARS, and ANFIS
Summary
For characterizing the probabilistic behaviour of various mode shape of the present hybrid angle ply laminated composite plate, the employed soft computation metamodel does not require reliability function in advance as in the case of the first-order reliability method (FORM) and second-order reliability method (SORM) Along with it, these metamodels provide inclusive and well-organized sample space which provides an efficient result with negligible loss in accuracy. The novelty of the article is a probabilistic description of four-mode shapes of hybrid angle ply laminated composite plates with MCS-FEM and efficient metamodels GPR, MARS, PSO-ANN, and ANFIS and showing the advantage of metamodels over FE model, as in earlier published articles, no or very limited work is found on mode-shape analysis using soft computation metamodels. The present work is the first attempt on mode shape analysis of a hybrid angle ply laminated composite plate using 2D C0 FE formulation based on TSDT in conjunction with MCS-FEM, GPR, MARS, PSO-ANN, and ANFIS. C1 and C2 are learning parameters that represent the degrees of local search and global search level, respectively. r1 and r2 represent random numbers distributed uniformly between 0 and 1. w is the initial weight that stores previous particle velocity during the optimization problem
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