Investigation of Multi Linear Regression Methods on Estimation of Free Vibration Analysis of Laminated Composite Shallow Shells
( Vol-4,Issue-12,December 2017 )

Ali Dogan, Omer Faruk Cansiz, Kevser Unsalan, Nurullah Karaca


Anisotropy, Finite Element Method (FEM), Multi Linear Regression, Shell Theory, Structural Composites, Free Vibration.


This paper presents regression method’s in estimating the free vibration analysis and compared with SDSST method. In this study, the free vibration analysis of the cross-ply laminated composite cylindrical shallow shells has been studied using shear deformation shallow shell theory (SDSST). First, the kinematic relations of strains and deformation are given. Then, using Hamilton’s principle, governing differential equations are developed for a general curved shell. Finally, the stress-strain relation for the laminated, cross-ply composite shells are obtained. By using some simplifications and assuming Fourier series as a displacement field, the governed differential equations are solved by the matrix algebra for shallow shells. Employing the computer algebra system called MATHEMATICA; a computer program has been prepared for the solution [1]. The results obtained by this solution are compared with the results obtained by (ANSYS) programs. In this article, regression method’s and SDSST method’s abilities in estimating the free vibration with the laminate number, aspect ratio, thickness ratio, curvature ratio and orthotropic ratio variables, are compared with different and similar aspects. In comparing with linear, interaction, quadratic and pure quadratic models, which are constructed with multiple linear regression approach, the quadratic model provides better results.

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[1] MATHEMATICA, Wolfram Research,
[2] Qatu M. S. (2004).Vibration of laminated shells and plates. Elsevier, Netherlands.
[3] Reddy, J. N. (2003). Mechanics of laminated composite plates and shells: Theory and analysis. CRC press, USA.
[4] Dogan A, Arslan H. M, Yerli HR. (2010). Effects of anisotropy and curvature on free vibration characteristics of laminated composite cylindrical shallow shells. Struct Eng Mech. 35(4), 493-510.
[5] Dogan A. and Arslan H. M. (2012). Investigation of the effect of shell plan-form dimensions on mode-shapes of the laminated composite cylindrical shallow shells using SDSST and FEM. Steel and Composite Structures. 12(4), 303-324.
[6] Dong C., Zhang C., Liang Z. and Wang B. (2004). Dimension variation prediction for composites with finite element analysis and regression modeling. Composites Part A. 35, 735-746.
[7] Lee Y. and Lin C. (2003). Regression of the response surface of laminated composite structures. Composite Structures. 62, 91-105.
[8] Satapathy B. K., Majumdar A., Jaggi H. S., Patnaik A. and Tomar B. S. (2011) Targeted material design of flyash filled composites for friction braking application by non-linear regression optimization technique. Computational Materials Science. 50, 3145-3152
[9] Ziari H., Amini A., Goli A. and Mirzaeiyan D. (2018). Predicting rutting performance of carbon nano tube (CNT) asphalt binders using regression models and neural networks. Construction and Building Materials. 160, 415-426.
[10] Oladipo A. A. and Gazi M. (2014). Enhanced removal of crystal violet by low cost alginate/acid activated bentonite composite beads: Optimization and modelling using non-linear regression technique. Journal of Water Process Engineering. 2, 43-52.
[11] Yadollahi M. M., Benli A. and Demirboga R. (2017). Application of adaptive neuro-fuzzy technique and regression models to predict the compressive strength of geopolymer composites. Neural Comput & Applic. 28, 1453-1461.
[12] ANSYS Inc, User manuel Version: 5.3. Theory reference manuel and ANSYS element reference.
[13] MATLAB, The MathWorks Inc., Natick, MA.