Buckling Analysis Of Isotropic Rectangular Plates Using Ritz Method

CHAPTER ONE

INTRODUCTION

1.1 BACKGROUND OF STUDY

Buckling analysis of isotropic rectangular plate has been a subject of study in solid structural mechanics for more than a century. Many exact solutions for isotopic plates have been developed. Steel rectangular plates are widely used in buildings, bridges, automobiles, and ships. Rectangular plate has width size comparable to size of their lengths and so is modeled as two - dimensional plane members unlike beams and columns. Under compression, rectangular plate tends to buckle out of their plane. The buckled shape depends on the loading and support conditions. In both conditions, the plate continues to carry loads in stable manner. Although the buckling analysis of rectangular plates has received the attention of many researchers for several centuries, it's treatment has left much to be done. Most of the available solutions are approximate in nature in that they do not satisfy exactly the prescribed boundary conditions or the governing differential equations or both. In addition, it has been the experience of most structural engineers, that there is no book to which they can turn to for a clear and orderly exposition of the isotopic rectangular plates with one free edge subjected to dynamic boundary condition. These dynamic boundary conditions are also known as non-essential boundary condition. This difficulty led to the use of minimum potential energy approach, which does not satisfy the non essential boundary condition. This approach is widely known as direct variational approach (example is Ritz method). The work of Ibearugbulem (2012) dealt with elastic stability analysis of thin rectangular plate by using Ritz method. He also did not satisfy the non essential boundary conditions for all the plates that have a free edge. It is worthy of note here that, the same work of Ibearugbulem (2012) did satisfy both the essential and non essential boundary conditions for other plates without free edge. The big question here is: is there no how the non essential boundary conditions of plate with free edge can be satisfied? The answer to this question is the main crux of this present work.