Determination of Forces and Moments Per Unit Length in Symmetric Exponential FG Plates with a Quasi-Triangular Hole

Hamid Abdolalian,Eduard-Marius Craciun,Luciano Feo,Mohammad Hossein Bayati Chaleshtari,Mohammad Jafari

doi:10.3390/sym12050834

Abstract

In this study, the resultant forces and moments acting on infinite symmetric FGPs with a triangular hole subject to uniaxial tensile load were examined via an analytical method using the complex variable approach. The mechanical properties of graded plates are hypothesized to vary throughout the thickness exponentially. The impact of various factors, namely hole orientation, hole aspect ratio as well as the hole corner curve on stress distribution and moment resultants is considered. In order to approve the credibility of the analytical approach, its outcomes are compared to numerical results acquired from ABAQUS finite element modeling. This comparison showed a favorable agreement level among the acquired analytical and numerical outcomes. Based on these results, the mentioned factors entail a considerable effect on the distribution of resultant forces and moments at the proximity of the hole and the load bearing tolerance of functional grated plates with holes may be enhanced by suitable selection of the aforementioned parameters.

Highlights

Openings and holes are vital sections of structural models, and control of their adverse effects on the structure stability and failure probability around these geometric discontinuities is crucial to design procedures
The hole geometry was modeled with the following values for the studied parameters: β = 0◦, c = 1(aspect ratio of the hole) and ω = 0.125
This study provided an analytical approach on the basis of Lekhnitskii’s formalism and a conformal mapping to assess the stress distribution of FGPs consisting of triangular holes

Summary

Introduction

Openings and holes are vital sections of structural models, and control of their adverse effects on the structure stability and failure probability around these geometric discontinuities is crucial to design procedures. Rezaeepazhand and Jafari [6] used a mapping function derived from Lekhnitiskii’s theory to get the stress concentration factor of different rectangular holes and curvature radii in anisotropic plates. Sharma [12] obtained stress functions to determine stress distribution at the proximity of special holes within infinitely laminated plates under arbitrary biaxial loading at infinity by utilizing Muskhelishvili’s complex variable method. The complex variable approach was utilized to examine the impact of factors, namely the dispersion of materials characteristics and the load angle of resultant and of moments. Mohammadi and Dirang [16] obtained the stress concentration in FGPs containing a circular hole for biaxial loading They used an exponential function to model their plate in a radial direction. The hole is not subjected to external loading and we consider that the plate is greater than the hole

Analytical Formulations

Numerical Results

Results

Conclusions