Limit analysis for plates: a simple loading problem involving a complex exact solution

Abstract

Known exact solutions in limit analysis for rigid perfectly plastic plates are relatively scarce and this has led Wood (1965) to question the soundness of the theory by suggesting that exact solutions may not exist even for apparently simple cases of loading, shape of plate and edge conditions. The alternative explanation for the scarcity is that simple problems may require rather complex exact solutions: this is exemplified in the solution now obtained for a central point load acting on a simply supported rectangular plate, with yielding governed by the square yield criterion. When the aspect ratio (length/breadth) of the rectangle lies in the range 1 to 2.25 approximately, the exact mechanism is relatively complex, involving regions of anticlastic curvature at the corners. From the practical standpoint, the known simple upper bounds of yield-line theory for this problem give the collapse load exactly for aspect ratios greater than about 2.25 and are in error by less than 4 % for smaller aspect ratios.