Microstructural/geometric imperfection sensitivity on the vibration response of geometrically discontinuous bi-directional functionally graded plates (2DFGPs) with partial supports by using FEM

Varun Katiyar , Ankit Gupta , Abdelouahed Tounsi

Abstract

In the present article, the vibration response of a geometrically imperfect bi-directional functionally graded plate (2D-FGP) with geometric discontinuities and micro-structural defects (porosities) has been investigated. A porosity model has been developed to incorporate the effective material properties of the bi-directional FGP which varies in two directions i.e., along the axial and transverse direction. The geometric discontinuity is also introduced in the plate in the form of a circular cut-out at the center of the plate. The structural kinematic formulation is based on the non-polynomial trigonometric higher-order shear deformation theory (HSDT). Finite element formulation is done using C° continuous Lagrangian quadrilateral four-noded element with seven degrees of freedom per node. The equations of motion have been derived using a variational approach. Convergence and validation studies have been documented to confirm the accuracy and efficiency of the present formulation. A detailed investigation study has been done to evaluate the influence of the circular cut-out, geometric imperfection, porosity inclusions, partial supports, volume fraction indexes (along with the thickness and length), and geometrical configurations on the vibration response of 2D-FGP. It is concluded that after a particular cut-out dimension, the vibration response of the 2D FGP exhibits non-monotonic behavior.

Key Words

bi-directional functionally graded plates (2D-FGPs); circular cut-outs; geometric imperfection; microstructure defects; partial supports; vibration response

Address

Varun Katiyar, Ankit Gupta — School of Engineering, Shiv Nadar Institution of Eminence, Deemed to be University, Gautama Buddha Nagar, India
Abdelouahed Tounsi — 1)YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea 2)Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia

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