Efficient large deflection analysis of rectangular plates with general transverse form of displacement

Thin, elastic, rectangular plates are analysed. Each plate has symmetry about the transverse centre line, but the transverse form of displacement can take any form, depending on the degree of support (if any) along each longitudinal edge, and on the manner of loading. Classical plate theory is used (Love-Kirchhoff hypothesis), and large deflections compared to the thickness are accommodated. The lateral displacement is expressed as a series, each term of which involves the product of a sinusoidal term in the longitudinal direction, and a polynomial term in the transverse direction. The von Karman/Marguerre compatibility equation is satisfied, and equilibrium found at each load stage by directly minimising the total potential energy. The method is presented, and is then used to analyse a wide variety of different plate types. The method is shown to be very efficient, and accurate, by comparison with previous work. The results clearly show the subtle variations in transverse form of displacement for the various examples considered. (C) 1999 Elsevier Science Ltd. All rights reserved.