Stochastic dynamic analysis of twisted functionally graded plates

Abstract This paper presents a stochastic dynamic analysis of functionally graded plates by following an efficient neural network based approach coupled with the finite element method. An isoparametric quadratic element having eight nodes is considered for the finite element analysis of pre-twisted functionally graded cantilever plates subjected to variation in geometric parameters, material properties and temperature. Both individual and compound effects of stochasticity in the uncertain input parameters are accounted to quantify their influence on the first three natural frequencies, mode shapes, and frequency response functions of functionally graded plates. A sensitivity analysis is conducted to ascertain the relative effects of various prospective sources of uncertainty. Latin hypercube sampling is utilised to train the efficient surrogate models, which are employed as a medium of uncertainty propagation. The comparative performance of artificial neural network and polynomial neural network is assessed in the stochastic dynamic analysis of the pre-twisted functionally graded plates from the viewpoint of accuracy and computational efficiency. The results are validated with respect to direct Monte Carlo simulation based on the finite element model of the functionally graded plates. It is observed that the artificial neural network based algorithm can achieve a significant level of computational efficiency without compromising the accuracy of results. The results presented in this article reveal that the source uncertainties of functionally graded plates have a significant effect on the dynamic responses of the structure.

[1]  Susmita Naskar,et al.  Stochastic natural frequency analysis of damaged thin-walled laminated composite beams with uncertainty in micromechanical properties , 2017 .

[2]  Wael G. Abdelrahman,et al.  Stochastic Finite element analysis of the free vibration of functionally graded material plates , 2008 .

[3]  M. Kadkhodayan,et al.  Three-dimensional thermo-elastic analysis and dynamic response of a multi-directional functionally graded skew plate on elastic foundation , 2017 .

[4]  Mohammad Talha,et al.  Vibration characteristics of functionally graded material plate with various boundary constraints using higher order shear deformation theory , 2016 .

[5]  Sondipon Adhikari,et al.  A Response Surface Modelling Approach for Resonance Driven Reliability Based Optimization of Composite Shells , 2016 .

[6]  Tran Ich Thinh,et al.  VIBRATION AND BUCKLING ANALYSIS OF FUNCTIONALLY GRADED PLATES USING NEW EIGHT-UNKNOWN HIGHER ORDER SHEAR DEFORMATION THEORY , 2016 .

[7]  A. Mellit,et al.  EPNN-based prediction of meteorological data for renewable energy systems , 2023, Journal of Renewable Energies.

[8]  Sondipon Adhikari,et al.  Uncertainty Quantification in Natural Frequency of Composite Plates - An Artificial Neural Network Based Approach: , 2016 .

[9]  Tanmoy Mukhopadhyay,et al.  Metamodel based high-fidelity stochastic analysis of composite laminates: A concise review with critical comparative assessment , 2017 .

[10]  Abbas Karamodin,et al.  Isogeometric analysis of functionally graded plates using a new quasi-3D shear deformation theory based on physical neutral surface , 2017 .

[11]  Sondipon Adhikari,et al.  Free-Vibration Analysis of Sandwich Panels with Randomly Irregular Honeycomb Core , 2016 .

[12]  Sondipon Adhikari,et al.  System reliability analysis of soil slopes with general slip surfaces using multivariate adaptive regression splines , 2017 .

[13]  Tanmoy Mukhopadhyay,et al.  A multivariate adaptive regression splines based damage identification methodology for web core composite bridges including the effect of noise , 2018 .

[14]  S. Adhikari,et al.  Effective elastic properties of two dimensional multiplanar hexagonal nanostructures , 2017 .

[15]  Leonard Meirovitch,et al.  Dynamics And Control Of Structures , 1990 .

[16]  H. Saunders,et al.  Finite element procedures in engineering analysis , 1982 .

[17]  X. L. Chen,et al.  Stability of piezoelectric FGM rectangular plates subjected to non-uniformly distributed load, heat and voltage , 2008, Adv. Eng. Softw..

[18]  R. Luciano,et al.  Some analytical solutions of functionally graded Kirchhoff plates , 2015 .

[19]  R. Luciano,et al.  Free vibrations of Bernoulli-Euler nano-beams by the stress-driven nonlocal integral model , 2017 .

[20]  Rekha S. Singhal,et al.  Comparison of artificial neural network (ANN) and response surface methodology (RSM) in fermentation media optimization: Case study of fermentative production of scleroglucan , 2008 .

[21]  Sondipon Adhikari,et al.  Probabilistic characterisation for dynamics and stability of laminated soft core sandwich plates , 2017 .

[22]  Hyuk-Chun Noh,et al.  Analytical solution for the dynamic response of functionally graded rectangular plates resting on elastic foundation using a refined plate theory , 2015 .

[23]  Ankit K. Gupta,et al.  Nonlinear flexural and vibration response of geometrically imperfect gradient plates using hyperbolic higher-order shear and normal deformation theory , 2017 .

[24]  D. K. Jha,et al.  Assessment of Higher Order Shear and Normal Deformations Theories for Stress Analysis and Free Vibration of Functionally Graded Plates , 2014 .

[25]  Sondipon Adhikari,et al.  Effective in-plane elastic properties of auxetic honeycombs with spatial irregularity , 2016 .

[26]  Susmita Naskar,et al.  On quantifying the effect of noise in surrogate based stochastic free vibration analysis of laminated composite shallow shells , 2016 .

[27]  W. Pedrycz,et al.  A fuzzy ensemble of parallel polynomial neural networks with information granules formed by fuzzy clustering , 2010, Knowl. Based Syst..

[28]  S. Adhikari,et al.  Probing the shear modulus of two-dimensional multiplanar nanostructures and heterostructures. , 2018, Nanoscale.

[29]  A. Chakrabarti,et al.  Static and Dynamic Analysis of Functionally Graded Skew Plates , 2013 .

[30]  S. Mohanty,et al.  Modal Analysis of Functionally Graded Material Plates Using Finite Element Method , 2014 .

[31]  Y. S. Touloukian.  THERMOPHYSICAL PROPERTIES OF HIGH TEMPERATURE SOLID MATERIALS. , 1967 .

[32]  Jie Yang,et al.  Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets , 2018 .

[33]  Wilfrido Rivera,et al.  Neural network and polynomial model to improve the coefficient of performance prediction for solar intermittent refrigeration system , 2016 .

[34]  K. M. Liew,et al.  Free vibration analysis of functionally graded plates using the element-free kp-Ritz method , 2009 .

[35]  M. Janghorban,et al.  FREE VIBRATION OF FUNCTIONALLY GRADED SIZE DEPENDENT NANOPLATES BASED ON SECOND ORDER SHEAR DEFORMATION THEORY USING NONLOCAL ELASTICITY THEORY , 2015 .

[36]  K. Liew,et al.  Active control of FGM plates with integrated piezoelectric sensors and actuators , 2001 .

[37]  R. Luciano,et al.  Analogies between Kirchhoff plates and functionally graded Saint-Venant beams under torsion , 2015 .

[38]  Avadesh K. Sharma,et al.  VIBRATION ANALYSIS OF FUNCTIONALLY GRADED PLATES WITH MULTIPLE CIRCULAR CUTOUTS , 2016 .

[39]  Young-Wann Kim,et al.  TEMPERATURE DEPENDENT VIBRATION ANALYSIS OF FUNCTIONALLY GRADED RECTANGULAR PLATES , 2005 .

[40]  B. Manohar,et al.  An artificial neural network analysis of porcine pancreas lipase catalysed esterification of anthranilic acid with methanol , 2005 .

[41]  Sondipon Adhikari,et al.  Stochastic dynamic stability analysis of composite curved panels subjected to non-uniform partial edge loading , 2018 .

[42]  Sondipon Adhikari,et al.  Effective in-plane elastic moduli of quasi-random spatially irregular hexagonal lattices , 2017 .

[43]  Vishnu Pareek,et al.  Artificial neural network modeling of a multiphase photodegradation system , 2002 .

[44]  L. Rayleigh,et al.  The theory of sound , 1894 .

[45]  S. Adhikari,et al.  Frequency domain homogenization for the viscoelastic properties of spatially correlated quasi-periodic lattices , 2019, International Journal of Mechanical Sciences.

[46]  K. R. Jagtap,et al.  Stochastic nonlinear free vibration analysis of elastically supported functionally graded materials plate with system randomness in thermal environment , 2011 .

[47]  S. Dey,et al.  Low Velocity Impact Responses of Functionally Graded Plates , 2017 .

[48]  S. Adhikari,et al.  Effective mechanical properties of multilayer nano-heterostructures , 2017, Scientific Reports.

[49]  Tanmoy Mukhopadhyay,et al.  Optimisation of Fibre-Reinforced Polymer Web Core Bridge Deck—A Hybrid Approach , 2015 .

[50]  Sung-Kwun Oh,et al.  A design of granular-oriented self-organizing hybrid fuzzy polynomial neural networks , 2013, Neurocomputing.

[51]  Eleni Chatzi,et al.  Metamodeling of dynamic nonlinear structural systems through polynomial chaos NARX models , 2015 .

[52]  R. Luciano,et al.  Functionally graded Timoshenko nanobeams: A novel nonlocal gradient formulation , 2016 .

[53]  R. Luciano,et al.  On torsion of random composite beams , 2015 .

[54]  G. Rao,et al.  Free Vibration Analysis of Functionally Graded Beams , 2012 .

[55]  Anupam Chakrabarti,et al.  Efficient lightweight design of FRP bridge deck , 2015 .

[56]  Sondipon Adhikari,et al.  Effect of cutout on stochastic natural frequency of composite curved panels , 2016 .

[57]  S. H. Mirtalaie,et al.  Free Vibration Analysis of Functionally Graded Moderately Thick Annular Sector Plates Using Differential Quadrature Method , 2011 .

[58]  R. K. Sharma,et al.  Modeling vibration frequencies of annular plates by regression based neural network , 2009, Appl. Soft Comput..

[59]  Sondipon Adhikari,et al.  A polynomial chaos expansion based molecular dynamics study for probabilistic strength analysis of nano-twinned copper , 2016 .

[60]  Anupam Chakrabarti,et al.  Structural damage identification: A random sampling-high dimensional model representation approach , 2016 .

[61]  Mohammad Talha,et al.  Stochastic vibration characteristics of finite element modelled functionally gradient plates , 2015 .

[62]  Tinh Quoc Bui,et al.  A moving Kriging interpolation-based meshfree method for free vibration analysis of Kirchhoff plates , 2011 .

[63]  C. Eswara Reddy,et al.  Free Vibration Behaviour of Functionally Graded Plates Using Higher-Order Shear Deformation Theory , 2014 .

[64]  Sondipon Adhikari,et al.  Rotational and ply-level uncertainty in response of composite shallow conical shells , 2015 .

[65]  Anupam Chakrabarti,et al.  Optimum design of FRP bridge deck: an efficient RS-HDMR based approach , 2015 .

[66]  Sondipon Adhikari,et al.  Uncertainty Quantification in Laminated Composites: A Meta-model Based Approach , 2018 .

[67]  Susmita Naskar,et al.  Uncertain natural frequency analysis of composite plates including effect of noise – A polynomial neural network approach , 2016 .

[68]  M. H. Yas,et al.  Free vibration analysis of functionally graded annular plates by state-space based differential quadrature method and comparative modeling by ANN , 2012 .

[69]  Erasmo Carrera,et al.  Free vibration analysis of functionally graded shells by a higher-order shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations , 2013 .

[70]  A. Saidi,et al.  Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation , 2011 .

[71]  Sondipon Adhikari,et al.  Stochastic mechanics of metamaterials , 2017 .

[72]  Chun-Fei Hsu,et al.  Intelligent control of chaotic systems via self-organizing Hermite-polynomial-based neural network , 2014, Neurocomputing.

[73]  Diana V. Bambill,et al.  Vibration Analysis of Axially Functionally Graded Rotating Timoshenko Beams with General Variation of Cross Section, with DQM and FEM , 2013 .

[74]  M B Kasiri,et al.  Modeling and optimization of heterogeneous photo-Fenton process with response surface methodology and artificial neural networks. , 2008, Environmental science & technology.

[75]  R. Luciano,et al.  Exact solutions of isotropic viscoelastic functionally graded Kirchhoff plates , 2014 .

[76]  Di Wu,et al.  Stochastic static analysis of Euler-Bernoulli type functionally graded structures , 2018 .

[77]  P. K. Karsh,et al.  Spatial vulnerability analysis for the first ply failure strength of composite laminates including effect of delamination , 2018 .

[78]  M. Shariyat,et al.  Low-velocity impact analysis of the hierarchical viscoelastic FGM plates, using an explicit shear-bending decomposition theory and the new DQ method , 2014 .

[79]  Sondipon Adhikari,et al.  Probabilistic Analysis and Design of HCP Nanowires: An Efficient Surrogate Based Molecular Dynamics Simulation Approach , 2016 .

[80]  Xin Yu,et al.  Convergence of gradient method with penalty for Ridge Polynomial neural network , 2012, Neurocomputing.

[81]  E. Carrera,et al.  Analysis of functionally graded material plates using triangular elements with cell-based smoothed discrete shear gap method , 2013, 1306.4811.

[82]  Ivan Maric,et al.  Optimization of self-organizing polynomial neural networks , 2013, Expert Syst. Appl..

[83]  Sung-Kwun Oh,et al.  Polynomial neural networks architecture: analysis and design , 2003, Comput. Electr. Eng..

[84]  Jyoti Vimal,et al.  Free vibration analysis of moderately thick functionally graded skew plates , 2014 .