A theoretical and experimental investigation of the thermal buckling of flat rectangular plates

The thesis presents a theoretical and experimental investigation of the buckling of flat rectangular plates when subjected to symmetrical and asymmetrical temperature distributions over their lateral surfaces. These temperature distributions induce thermal stresses. Under certain conditions the compressive component of the induced thermal stresses causes the plate to buckle out of its own plane. The evaluation of the critical temperature, which initiates buckling, is carried out in two successive steps. 1. A solution of the biharmonic equation that governs the distribution of thermal stresses under stable conditions is obtained. 2. This stable state distribution of thermal stresses is utilised to obtain an approximate solution of the equation governing the stability of flat plates with internal varying stresses. This gives the value of the critical temperature at the onset of buckling. The subject matter of the thesis is divided into four parts PART I is a review of the published literature covering rigorous and approximate methods which have been used to determine the stable state distribution of thermal stresses and the evaluation of the critical buckling temperature. It also includes considerations of plate deflections in the post-buckling range with particular reference to the growth of the plate centre deflection with increasing values of plate temperature differential. PART II deals exclusively with the theoretical analysis and evaluation of the critical buckling temperature. It includes, as its first consideration, the determination of the steady state distribution of thermal stresses in the plate. An approximate solution of the biharmonic equation, governing the distribution of stresses is presented using the Kantorovitch. Method. This is followed by an original application of the Rayleigh-Ritz Method, to obtain an approximate solution of the biharmonic equation giving the thermal stresses in a polynomial form. This is followed by an investigation of the effects of plate aspect ratio and the degree of asymmetry of the temperature distributions on the value of critical temperature. The cases considered have, to the author's knowledge, not been investigated hitherto. The numerical work associated with the theoretical analysis was carried out on a 'Deuce' Computer using Alpha Code and General Interpretive Programmes. PART III presents the experimental work carried out in substantiation of the theoretical methods used in Part II. This covers the determination of the critical buckling temperatures and deformations of aluminium alloy plates, of aspect ratios ranging from one to three, subjected to symmetrical and asymmetrical temperature distributions. PART IV discusses, critically examines and summarises the comparison and correspondence obtained between the theoretically predicted and experimentally determined values of critical temperatures and deformations. It is shown that good agreement exists. The thesis concludes with six appendices which present detailed analyses and calculations followed by a bibliography