Nonlocal Nonlinear Analysis of Functionally Graded Plates Using Natural Neighbor Galerkin Method

Singam, Srividhya and Rajagopal, Amirtham (2018) Nonlocal Nonlinear Analysis of Functionally Graded Plates Using Natural Neighbor Galerkin Method. Masters thesis, Indian Institute of Technology Hyderabad.

Text
Thesis_CE_Mtech_4191.pdf - Submitted Version
Restricted to Repository staff only until 2023.
Download (4MB) | Request a copy

Abstract

Functionally Graded Materials (FGM) are advanced class of engineering composites constituting of two or more distinct phase materials described by continuous and smooth varying composition of material properties in the required direction. The plate is subjected to di�erent loading and boundary conditions. The formulation is developed based on the First order Shear Deformation Theory (FSDT). The mechanical properties are assumed to vary continuously through the thickness of the plate and obey a power law distribution of the volume fraction of the constituents. The variation of volume fraction through the thickness is computed using two di�erent homogenization techniques; namely rule of mixtures and Mori-Tanaka scheme. The results obtained from the two techniques have been compared with the analytical solutions available in literature. In addition to the above a parametric study bringing out the e�ect of boundary conditions, loads and power law index has also been presented. Convergence tests and comparison studies have been carried out to demonstrate the e�ciency of the present formulation. Also in this work, nonlocal nonlinear analysis of functionally graded plates subjected to static loads is studied. The nonlocal nonlinear formulation is developed based on the third-order shear deformation theory (TSDT) of Reddy (1984, 2004). The von K�arm�an nonlinear strains are used and the governing equations of the TSDT are derived accounting for Eringen's nonlocal stress-gradient model (Eringen, 1998). The nonlinear displacement �nite element model of the resulting governing equations is developed, and Newton's iterative procedure is used for the solution of nonlinear algebraic equations. A detailed parametric study to show the effect of side-to-thickness ratio, power-law index, and nonlocal parameter on the load-de ection characteristics of plates have been presented. The stress results are compared with the first-order shear deformation theory (FSDT) to show the accuracy of nonlocal nonlinear TSDT formulation. The above formulation has been presented with Natural Element Method and results are presented. v

[error in script]

IITH Creators: