Free vibration and mechanical buckling of plates with in-plane material inhomogeneity - a three dimensional consistent approach

TL;DR

This paper presents a three-dimensional consistent finite element approach to analyze free vibration and buckling of inhomogeneous plates with in-plane material grading, avoiding shear correction factors and locking issues.

Contribution

It introduces a novel 3D consistent spectral element method for plates with in-plane material inhomogeneity, providing accurate eigenvalue analysis without shear correction factors.

Findings

Material gradient affects buckling and vibration frequencies.

Boundary conditions significantly influence critical buckling load.

The method efficiently handles in-plane material grading and complex geometries.

Abstract

In this article, we study the free vibration and the mechanical buckling of plates using a three dimensional consistent approach based on the scaled boundary finite element method. The in-plane dimensions of the plate are modeled by two-dimensional higher order spectral element. The solution through the thickness is expressed analytically with Pade expansion. The stiffness matrix is derived directly from the three dimensional solutions and by employing the spectral element, a diagonal mass matrix is obtained. The formulation does not require ad hoc shear correction factors and no numerical locking arises. The material properties are assumed to be temperature independent and graded only in the in-plane direction by a simple power law. The effective material properties are estimated using the rule of mixtures. The influence of the material gradient index, the boundary conditions and the geometry of the plate on the fundamental frequencies and critical buckling load are numerically investigated.