Free vibrations and static analysis of functionally graded sandwich plates with three-dimensional finite elements

Abstract

A three-dimensional modelling of free vibrations and static response of functionally graded material (FGM) sandwich plates is presented. Natural frequencies and associated mode shapes as well as displacements and stresses are determined by using the finite element method within the ABAQUS TM code. The three-dimensional (3-D) brick graded finite element is programmed and incorporated into the code via the user-defined material subroutine UMAT. The results of modal and static analyses are demonstrated for square metal-ceramic functionally graded simply supported plates with a power-law through-the-thickness variation of the volume fraction of the ceramic constituent. The through-the-thickness distribution of effective material properties at a point are defined based on the Mori-Tanaka scheme. First, exact values of displacements, stresses and natural frequencies available for FGM sandwich plates in the literature are used to verify the performance and estimate the accuracy of the developed 3-D graded finite element. Then, parametric studies are carried out for the frequency analysis by varying the volume fraction profile and value of the ceramic volume fraction.

Three-Dimensional Free Vibration Analysis of Thermally Loaded FGM Sandwich Plates

“…As mentioned in the Introduction, a 3D graded finite element has been developed for performing the modal frequency analysis of FGM sandwich plates in [62,63]. To incorporate a variation in the elastic properties of the heterogeneous material into the finite element, the material user-defined subroutine UMAT that establishes the tangent element stiffness matrix was programmed, while the average mass density value was adopted to determine the element mass matrix.…”

“…More details of the implementation of graded elements into the ABAQUS code are found in [30,59] and the ABAQUS manual [56]. In addition, it is important to note that the mass density, averaged over the FGM sandwich plate volume [62,63], was used in the free vibration analysis instead of its spatial representation in the case of thermomechanical analysis.…”

“…In addition, this modeling technique has been extended to 2D plate/shell and 3D models of FGM plates in [60,61], respectively, however, only the static bending analysis has been simulated there. Recently, three-dimensional finite element models of FGM sandwich plates for dynamic modal analyses have been developed in [62,63].…”

“…The aim of this study is to propose an efficient approach for implementing a 3D graded finite element into ABAQUS code to perform a computationally accurate free vibration analysis of thermally loaded FGM sandwich plates. A novel graded finite element has been developed based on the 3D brick graded finite element proposed for the free vibration analysis of 3D FGM sandwich plates in [62,63]. In our study, we extend the functionality of the element to use it for modeling FGM sandwich plates under thermal loading.…”

Material-Oriented Shape Functions for FGM Plate Finite Element Formulation

“…Formulation within three-dimensional theory was applied to static analysis of thick or moderately thick rectangular plates [5] (eight-node brick element), to circular plates on elastic foundation [6] as well as for vibration analysis [7] (8-and 20-node isoparametric elements). Gradation of the finite elements' elastic properties can be also used in the 3D formulation.…”