Open Access Open Access  Restricted Access Subscription or Fee Access

FEA Simulation for Optimization of Laminated Composite Plate with Cutout in Free Vibrations

Manuraj ., Anadi Misra


Laminated composites have a large application in engineering. The work done in this study is to see
the free vibration response of graphite epoxy composite square plate subjected to different boundary
conditions. Finite element analysis has been done on the software ANSYS. The results obtained by the
simulation have been compared with those obtained from a published data obtained by semianalytical
solution. It is observed that the solutions through ANSYS and that obtained through
analytic solution are in good agreement and hence we see that this can be a valid method for
simulating the problem. The analytic solution to this problem is complex and time consuming, so we
suggest this approach which gives faster and reasonably accurate solution to the problem. The
boundary conditions taken from the reference data are SSCC, SSCS, SSSS and SSCF and the ply
taken is a cross ply with 0/90 lay. Further we see how the 1st mode natural frequency depends upon
the area of the cutout. For a relative study we take readings for square, pentagonal, hexagonal, and
circular shape cutout. For this we investigate different standard ply types with one of the above
boundary conditions. Boundary condition taken is SSCS and the ply-types SP, QI, CP, and AP.
Optimization has been carried out by selection of appropriate interpolation function for the data
points as shown in the graphs. Then Genetic Algorithm is used to determine corresponding area to
minimum and maximum frequency. Mode shapes can be extracted to see the deformation associated
with particular modes. It can be utilized for placement of constraints on the structure.


FEA, laminated composite plate, ANSYS, deformation theory, modal Analysis

Full Text:



Bhardwaj H, Vimal J, Sharma A. Study of free vibration analysis of laminated composite plates with triangular cutouts. Eng Solid Mech. 2015; 3(1): 43–50.

Boscolo M, Banerjee JR. Layer-wise dynamic stiffness solution for free vibration analysis of laminated composite plates. J Sound Vibr. 2014; 333(1): 200–27.

Isanaka BR, Akbar MA, Mishra BP, et al. Free vibration analysis of thin plates: Bare versus Stiffened. Engineering Research Express (ERX). 2020; 2(1): 015014.

Civalek Ö. Free vibration analysis of symmetrically laminated composite plates with first-order shear deformation theory (FSDT) by discrete singular convolution method. Finite Elem Anal Des. 2008; 44(12–13): 725–31.

Kumar D, Singh SB. Effects of boundary conditions on buckling and postbuckling responses of composite laminate with various shaped cutouts. Compos Struct. 2010; 92(3): 769–79.

Dong SB, Pister KS, Taylor RL. On the theory of laminated anisotropic shells and plates. Journal of the Aerospace Sciences. 1962; 29(8): 969–75.

Fan SC, Cheung YK. Flexural free vibrations of rectangular plates with complex support conditions. J Sound Vibr. 1984; 93(1): 81–94.

Kant T, Marur SR, Rao GS. Analytical solution to the dynamic analysis of laminated beams using higher order refined theory. Compos Struct. 1997; 40(1): 1–9.

Khdeir AA, Reddy JN. Free vibrations of laminated composite plates using second-order shear deformation theory. Comput Struct. 1999; 71(6): 617–26.

Mallika A, Rao RN. Topology optimization of cylindrical shells for various support conditions. International Journal of Civil and Structural Engineering. 2011; 2(1): 11–22.

Swamy Monica S, et al. Buckling Analysis of Plate Element Subjected to In Plane Loading Using ANSYS. International journal of Scientific and Engineering Research (IJSER). 2012; 9: 70–79

Pandit MK, Haldar S, Mukhopadhyay M. Free vibration analysis of laminated composite rectangular plate using finite element method. J Reinf Plast Compos. 2007; 26(1): 69–80.

Ramakrishna S, Rao KM, Rao NS. Free vibration analysis of laminates with circular cutout by hybrid-stress finite element. Compos Struct. 1992; 21(3): 177–85.


  • There are currently no refbacks.

Copyright (c) 2021 Journal of Experimental & Applied Mechanics