Rotational and ply-level uncertainty in response of composite shallow conical shells

This paper presents the quantification of rotational and ply level uncertainty of random natural frequency for laminated composite conical shells by using surrogate modeling approach. The stochastic eigenvalue problem is solved by using QR iteration algorithm. Sensitivity analysis is carried out to address the influence of different input parameters on the output natural frequencies. The sampling size and computational cost is reduced by employing the present approach compared to direct Monte Carlo simulation. The stochastic mode shapes are also depicted for a typical laminate configuration. Statistical analysis is presented to illustrate the results and its performance.

[1]  Byeongdo Kim,et al.  Comparison study on the accuracy of metamodeling technique for non-convex functions , 2009 .

[2]  Sonja Kuhnt,et al.  Design and analysis of computer experiments , 2010 .

[3]  T. Simpson,et al.  Comparative studies of metamodelling techniques under multiple modelling criteria , 2001 .

[4]  E. Viola,et al.  General higher-order equivalent single layer theory for free vibrations of doubly-curved laminated composite shells and panels , 2013 .

[5]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[6]  Ricardo Perera,et al.  A response surface methodology based damage identification technique , 2009 .

[7]  Sankaran Mahadevan,et al.  A probabilistic approach for representation of interval uncertainty , 2011, Reliab. Eng. Syst. Saf..

[8]  F. Vahabzadeh,et al.  Application of the central composite design and response surface methodology to the advanced treatment of olive oil processing wastewater using Fenton's peroxidation. , 2005, Journal of hazardous materials.

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

[10]  Nicholas Fantuzzi,et al.  The local GDQ method applied to general higher-order theories of doubly-curved laminated composite shells and panels: The free vibration analysis , 2014 .

[11]  David Moens,et al.  Stochastic identification of composite material properties from limited experimental databases, Part II: Uncertainty modelling , 2012 .

[12]  Stanley H. Cohen,et al.  Design and Analysis , 2010 .

[13]  Sudip Dey,et al.  Natural frequencies of delaminated composite rotating conical shells-A finite element approach , 2012 .

[14]  S. Sriramula,et al.  Quantification of uncertainty modelling in stochastic analysis of FRP composites , 2009 .

[15]  Enrico Zio,et al.  Hierarchical propagation of probabilistic and non-probabilistic uncertainty in the parameters of a risk model , 2013 .

[16]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[17]  PeiHao Zhu,et al.  A novel method of dynamic characteristics analysis of machine tool based on unit structure , 2014 .

[18]  Michael S. Eldred,et al.  OVERVIEW OF MODERN DESIGN OF EXPERIMENTS METHODS FOR COMPUTATIONAL SIMULATIONS , 2003 .

[19]  V Ramamurti,et al.  Coriolis effect on the vibration of flat rotating low aspect ratio cantilever plates , 1981 .

[20]  Christopher R. Bowen,et al.  Sensitivity of bistable laminates to uncertainties in material properties, geometry and environmental conditions , 2013 .

[21]  Sondipon Adhikari,et al.  Stochastic free vibration analysis of angle-ply composite plates – A RS-HDMR approach , 2015 .

[22]  Nicholas Fantuzzi,et al.  Static analysis of functionally graded conical shells and panels using the generalized unconstrained third order theory coupled with the stress recovery , 2014 .

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

[24]  Ivo Babuška,et al.  A stochastic multiscale method for the elastodynamic wave equation arising from fiber composites , 2014 .

[25]  Min Xie,et al.  A systematic comparison of metamodeling techniques for simulation optimization in Decision Support Systems , 2010, Appl. Soft Comput..

[26]  P. C. Gehlen,et al.  Computer Experiments , 1996 .

[27]  George Stefanou,et al.  Stochastic finite element analysis of shells with combined random material and geometric properties , 2004 .

[28]  Fanrang Kong,et al.  Multiscale noise tuning of stochastic resonance for enhanced fault diagnosis in rotating machines , 2012 .

[29]  Steffen Marburg,et al.  Uncertainty quantification in natural frequencies and radiated acoustic power of composite plates: Analytical and experimental investigation , 2015 .

[30]  Michael D. Todd,et al.  Statistical modeling of frequency response function estimation for uncertainty quantification , 2013 .

[31]  Abdullah H. Sofiyev,et al.  On the buckling of composite conical shells resting on the Winkler–Pasternak elastic foundations under combined axial compression and external pressure , 2014 .

[32]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

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

[34]  Sondipon Adhikari,et al.  Stochastic natural frequency of composite conical shells , 2015 .

[35]  Sudip Dey,et al.  Finite element analysis of bending-stiff composite conical shells with multiple delamination , 2012 .

[36]  Dimos C. Charmpis,et al.  The need for linking micromechanics of materials with stochastic finite elements: A challenge for materials science , 2007 .

[37]  Anupam Chakrabarti,et al.  Structural Damage Identification Using Response Surface-Based Multi-objective Optimization: A Comparative Study , 2015, Arabian Journal for Science and Engineering.

[38]  N. Aslan,et al.  Application of response surface methodology and central composite rotatable design for modeling and optimization of a multi-gravity separator for chromite concentration , 2008 .

[39]  Erasmo Carrera,et al.  Static analysis of doubly-curved anisotropic shells and panels using CUF approach, differential geometry and differential quadrature method , 2014 .

[40]  W. Djoudi,et al.  Optimization of copper cementation process by iron using central composite design experiments , 2007 .

[41]  Slawomir Koziel,et al.  Computational Optimization, Methods and Algorithms , 2016, Computational Optimization, Methods and Algorithms.

[42]  Rubens Sampaio,et al.  Dynamics of thin-walled composite beams: Analysis of parametric uncertainties , 2013 .

[43]  Abdullah H. Sofiyev,et al.  On the solution of the buckling problem of functionally graded truncated conical shells with mixed boundary conditions , 2015 .

[44]  Nicholas Fantuzzi,et al.  Accurate inter-laminar recovery for plates and doubly-curved shells with variable radii of curvature using layer-wise theories , 2015 .

[45]  Li Wanyou,et al.  A numerical solution for vibration analysis of composite laminated conical, cylindrical shell and annular plate structures , 2014 .

[46]  N.G.R. Iyengar,et al.  Buckling Of Laminated Plates with Random Material Characteristics , 1998 .

[47]  Christian Berggreen,et al.  Reliability Analysis of a Composite Wind Turbine Blade Section Using the Model Correction Factor Method: Numerical Study and Validation , 2013, Applied Composite Materials.

[48]  George S. Springer,et al.  Design of Composite Laminates by a Monte Carlo Method , 1993 .

[49]  André I. Khuri,et al.  Response surface methodology , 2010 .

[50]  J. Borkowski.  Spherical prediction-variance properties of central composite and Box-Behnken designs , 1995 .

[51]  C. R. L. Murthy,et al.  Spatial Wavelet Approach to Local Matrix Crack Detection in Composite Beams with Ply Level Material Uncertainty , 2013, Applied Composite Materials.

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

[53]  Mohammad Mohammadi Aghdam,et al.  Free vibration analysis of rotating functionally graded carbon nanotube-reinforced composite truncated conical shells , 2014 .

[54]  Kenan Y. Sanliturk,et al.  A new triangular composite shell element with damping capability , 2014 .

[55]  Jahan B. Ghasemi,et al.  Comparative study of Box–Behnken, central composite, and Doehlert matrix for multivariate optimization of Pb (II) adsorption onto Robinia tree leaves , 2013 .

[56]  K. M. Liew,et al.  Vibration of pretwisted cantilever shallow conical shells , 1994 .

[57]  Sudip Dey,et al.  Free vibration analyses of multiple delaminated angle-ply composite conical shells – A finite element approach , 2012 .

[58]  Mohamad S. Qatu,et al.  Natural frequencies for cantilevered doubly-curved laminated composite shallow shells , 1991 .

[59]  Dirk Vandepitte,et al.  Stochastic identification of composite material properties from limited experimental databases, part I: Experimental database construction , 2012 .

[60]  Nicholas Fantuzzi,et al.  Stress and strain recovery for functionally graded free-form and doubly-curved sandwich shells using higher-order equivalent single layer theory , 2015 .

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

[62]  G. Rahimi,et al.  Experimental, numerical and analytical investigation of free vibrational behavior of GFRP-stiffened composite cylindrical shells , 2015 .

[63]  S. Adhikari,et al.  Stochastic free vibration analyses of composite shallow doubly curved shells – A Kriging model approach , 2015 .