A hybrid stochastic sensitivity analysis for low-frequency vibration and low-velocity impact of functionally graded plates

Abstract This paper deals with the stochastic sensitivity analysis of functionally graded material (FGM) plates subjected to free vibration and low-velocity impact to identify the most influential parameters in the respective analyses. A hybrid moment-independent sensitivity analysis is proposed coupled with the least angle regression based adaptive sparse polynomial chaos expansion. Here the surrogate model is integrated in the sensitivity analysis framework to achieve computational efficiency. The current paper is concentrated on the relative sensitivity of material properties in the free vibration (first three natural frequencies) and low-velocity impact responses of FGM plates. Typical functionally graded materials are made of two different components, where a continuous and inhomogeneous mixture of these materials is distributed across the thickness of the plate based on certain distribution laws. Thus, besides the overall sensitivity analysis of the material properties, a unique spatial sensitivity analysis is also presented here along the thickness of the plate to provide a comprehensive view. The results presented in this paper would help to identify the most important material properties along with their depth-wise spatial sensitivity for low-frequency vibration and low-velocity impact analysis of FGM plates. This is the first attempt to carry out an efficient adaptive sparse PCE based moment-independent sensitivity analysis (depth-wise and collectively) of FGM plates under the simultaneous susceptibility of vibration and impact. Such simultaneous multi-objective sensitivity analysis can identify the important system parameters and their relative degree of importance in advanced multi-functional structural systems.

[1]  M. Azhari,et al.  Buckling and free vibration of the FGM thin micro-plate based on the modified strain gradient theory and the spline finite strip method , 2017 .

[2]  R. Dimitri,et al.  Free vibration analysis of arbitrarily shaped Functionally Graded Carbon Nanotube-reinforced plates , 2017 .

[3]  Timon Rabczuk,et al.  A software framework for probabilistic sensitivity analysis for computationally expensive models , 2016, Adv. Eng. Softw..

[4]  Tanmoy Mukhopadhyay,et al.  Genetic programming-assisted multi-scale optimization for multi-objective dynamic performance of laminated composites: the advantage of more elementary-level analyses , 2019, Neural Computing and Applications.

[5]  N. Nguyen‐Thanh,et al.  Static, dynamic and buckling analyses of 3D FGM plates and shells via an isogeometric-meshfree coupling approach , 2018, Composite Structures.

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

[7]  Yiming Fu,et al.  Nonlinear transient response of functionally graded shallow spherical shells subjected to mechanical load and unsteady temperature field , 2014 .

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

[9]  S. Haldar,et al.  Experimental and numerical studies on vibration characteristics of laminated composite skewed shells with cutout , 2019, Composites Part B: Engineering.

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

[11]  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 .

[12]  D. Maiti,et al.  Analytical solution for bending and buckling analysis of functionally graded plates using inverse trigonometric shear deformation theory , 2015 .

[13]  Wei Zhao,et al.  Global sensitivity analysis with a hierarchical sparse metamodeling method , 2019, Mechanical Systems and Signal Processing.

[14]  T. Mukhopadhyay,et al.  Probabilistic micromechanical spatial variability quantification in laminated composites , 2018, Composites Part B: Engineering.

[15]  M. Sadighi,et al.  Low velocity impact response of thick FGM beams with general boundary conditions in thermal field , 2013 .

[16]  A. Palazotto,et al.  Impact Response of Titanium and Titanium Boride Monolithic and Functionally Graded Composite Plates , 2009 .

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

[18]  Carlos Alberto Conceição António,et al.  Uncertainty assessment approach for composite structures based on global sensitivity indices , 2013 .

[19]  Zhenzhou Lu,et al.  Monte Carlo simulation for moment-independent sensitivity analysis , 2013, Reliab. Eng. Syst. Saf..

[20]  Amine Smahat,et al.  Numerical Modeling of an FG Plate Behavior Impacted at Low Velocity in a Temperature Field , 2016 .

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

[22]  A. Palazotto,et al.  Low Velocity Impact Analysis of Functionally Graded Circular Plates , 2006 .

[23]  R. Gunes,et al.  Elastic response of functionally graded circular plates under a drop-weight , 2010 .

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

[25]  C. Sun,et al.  On the Impact of Initially Stressed Composite Laminates , 1985 .

[26]  Zhenzhou Lu,et al.  Moment independent sensitivity analysis with correlations , 2014 .

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

[28]  J. N. Reddy,et al.  Vibration of functionally graded cylindrical shells , 1999 .

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

[30]  Emanuele Borgonovo,et al.  Sampling plans for the estimation of moment-independent importance measures , 2010 .

[31]  S. Dey,et al.  Condition Assessment and Strengthening of Aged Structures: Perspectives Based on a Critical Case Study , 2019, Practice Periodical on Structural Design and Construction.

[32]  M. Eslami,et al.  Free vibration of FGM Lévy conical panels , 2014 .

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

[34]  Susmita Naskar,et al.  Non-probabilistic analysis of laminated composites based on fuzzy uncertainty quantification , 2017 .

[35]  A. Sofiyev,et al.  On the vibration and stability of FGM cylindrical shells under external pressures with mixed boundary conditions by using FOSDT , 2019, Thin-Walled Structures.

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

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

[38]  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 .

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

[40]  Leigang Zhang,et al.  Borgonovo moment independent global sensitivity analysis by Gaussian radial basis function meta-model , 2018 .

[41]  P. Bishay,et al.  Sensitivity analysis of a smart soft composite robotic finger design using geometrically nonlinear laminated composite finite beam elements , 2018, Materials Today Communications.

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

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

[44]  S. Dey,et al.  Stochastic dynamic analysis of twisted functionally graded plates , 2018, Composites Part B: Engineering.

[45]  S. Dey,et al.  Effect of oblique angle on low velocity impact response of delaminated composite conical shells , 2014 .

[46]  Ariosto Bretanha Jorge,et al.  A modified topological sensitivity analysis extended to the design of composite multidirectional laminates structures , 2018, Composite Structures.

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

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

[49]  Larry Lessard,et al.  Load sharing in single-lap bonded/bolted composite joints. Part II: Global sensitivity analysis , 2015 .

[50]  Binoy Krishna Roy,et al.  Stochastic dynamic behaviour of hydrodynamic journal bearings including the effect of surface roughness , 2018, International Journal of Mechanical Sciences.

[51]  Emanuele Borgonovo,et al.  Global sensitivity measures from given data , 2013, Eur. J. Oper. Res..

[52]  Anupam Chakrabarti,et al.  A hybrid approach for global sensitivity analysis of FRP composite multi-bolt joints , 2019, Composite Structures.

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

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

[55]  Francesca Pianosi,et al.  Comparison of variance-based and moment-independent global sensitivity analysis approaches by application to the SWAT model , 2017, Environ. Model. Softw..

[56]  K. Asemi,et al.  A STUDY ON LOW VELOCITY IMPACT RESPONSE OF FGM RECTANGULAR PLATES WITH 3D ELASTICITY BASED GRADED FINITE ELEMENT MODELING , 2015 .

[57]  Susmita Naskar,et al.  Spatially varying fuzzy multi-scale uncertainty propagation in unidirectional fibre reinforced composites , 2019, Composite Structures.

[58]  P. K. Karsh,et al.  Stochastic low-velocity impact on functionally graded plates: Probabilistic and non-probabilistic uncertainty quantification , 2019, Composites Part B: Engineering.

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

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

[61]  Tapabrata Ray,et al.  Sensitivity analysis of inverse algorithms for damage detection in composites , 2017 .

[62]  J. Reddy,et al.  The elasto-plastic impact analysis of functionally graded circular plates under low-velocities , 2011 .

[63]  Serge Abrate,et al.  FUNCTIONALLY GRADED PLATES BEHAVE LIKE HOMOGENEOUS PLATES , 2008 .

[64]  Bruno Sudret,et al.  Adaptive sparse polynomial chaos expansion based on least angle regression , 2011, J. Comput. Phys..

[65]  H. Hua,et al.  Free vibration analysis of rotating functionally graded double-tapered beam including porosities , 2019, International Journal of Mechanical Sciences.

[66]  Moshe Eisenberger,et al.  Vibration analysis of variable thickness plates and shells by the Generalized Differential Quadrature method , 2016 .

[67]  Naif Alajlan,et al.  Sensitivity and uncertainty analysis for flexoelectric nanostructures , 2018, Computer Methods in Applied Mechanics and Engineering.

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

[69]  Krishna Murari Pandey,et al.  Stochastic buckling analysis of sandwich plates: The importance of higher order modes , 2019, International Journal of Mechanical Sciences.

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

[71]  Wei Zhang,et al.  Free vibration of FGM sandwich doubly-curved shallow shell based on a new shear deformation theory with stretching effects , 2017 .

[72]  Michael D. Gilchrist,et al.  Designing the energy absorption capacity of functionally graded foam materials , 2009 .

[73]  Yong Li,et al.  Nonlinear dynamic response for functionally graded shallow spherical shell under low velocity impact in thermal environment , 2011 .

[74]  Susmita Naskar,et al.  Effect of delamination on the stochastic natural frequencies of composite laminates , 2018, Composites Part B: Engineering.

[75]  Ö. Civalek,et al.  Free vibration analysis of laminated and FGM composite annular sector plates , 2019, Composites Part B: Engineering.