On the Shear Buckling of Clamped Narrow Rectangular Orthotropic Plates

Seyed Rasoul Atashipour,Ulf Arne Girhammar

doi:10.1155/2015/569356

Seyed Rasoul Atashipour, Ulf Arne Girhammar

Open Access

https://doi.org/10.1155/2015/569356

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Abstract

This paper deals with stability analysis of clamped rectangular orthotropic thin plates subjected to uniformly distributed shear load around the edges. Due to the nature of this problem, it is impossible to present mathematically exact analytical solution for the governing differential equations. Consequently, all existing studies in the literature have been performed by means of different numerical approaches. Here, a closed-form approach is presented for simple and fast prediction of the critical buckling load of clamped narrow rectangular orthotropic thin plates. Next, a practical modification factor is proposed to extend the validity of the obtained results for a wide range of plate aspect ratios. To demonstrate the efficiency and reliability of the proposed closed-form formulas, an accurate computational code is developed based on the classical plate theory (CPT) by means of differential quadrature method (DQM) for comparison purposes. Moreover, several finite element (FE) simulations are performed via ANSYS software. It is shown that simplicity, high accuracy, and rapid prediction of the critical load for different values of the plate aspect ratio and for a wide range of effective geometric and mechanical parameters are the main advantages of the proposed closed-form formulas over other existing studies in the literature for the same problem.

Highlights

The shear buckling analysis of clamped composite plates is of great importance in design of many types of engineering structures
A differential quadrature (DQ) code is developed for comparison purposes to prove the high accuracy of the proposed closed-form formulas for predicting the critical buckling load of the rectangular orthotropic plates in shear with clamped edges
It should be pointed out that the assumptions of the classical plate theory (CPT) are incorporated into the simulations performed by ANSYS

Summary

Introduction

The shear buckling analysis of clamped composite plates is of great importance in design of many types of engineering structures. All the above-mentioned numerical studies have some deficiencies like convergence difficulties and being time-consuming compared to analytical and closedform solutions It is not easy and time-efficient to predict the critical shear buckling loads and investigate the effect of various parameters by the use of numerical solution approaches. To the best of authors’ knowledge, no closed-form solution can be found in the literature for the shear buckling of composite rectangular plates with finite dimensions. To fill this apparent void, the present work is carried out to provide efficient and reliable explicit formulas for rapid prediction of the fundamental critical shear buckling loads of clamped orthotropic rectangular plates. Other failure modes, such as the shear strength, are not included in the analysis

Definition of the Problem and Governing Equations

An Efficient Closed-Form Solution

Differential Quadrature Solution

Numerical Results and Discussion

Conclusions