SOLUTION OF ELASTOPLASTIC BENDING BY FINITE DIFFERENCE METHODS

THE TWO THEOREMS OF LIMIT ANALYSIS, THE STATIC AND THE KINEMATIC THEOREM, ARE OUTLINED AND ADAPTED TO THE PROBLEM OF THE BENDING OF A THIN PLATE WHICH IS ASSUMED TO BE MADE OF PERFECT RIGID PLASTIC MATERIAL SUBJECTED TO SMALL DEFORMATIONS. THESE THEOREMS ARE USED TO ESTIMATE THE UPPER AND LOWER LIMITS OF ULTIMATE LOADING, BUT GIVE NO INDICATION ON PLATE DEFLECTION. A NUMERICAL METHOD IS ALSO PROPOSED FOR SOLVING THE EQUATION REPRESENTING THE ELASTOPLASTIC DEFLECTION OBTAINED BY MEANS OF A GENERAL BEHAVIOUR LAW. THIS METHOD CONSISTS IN SOLVING ITERATIVELY A SERIES OF LINEAR BIHARMONIC PROBLEMS. EXAMPLES OF APPLICATION TO SQUARE PLATES, SUPPORTED OR RESTRAINED, SUBJECTED TO A UNIFORM OR CONCENTRATED LOAD SHOW THE ADVANTAGE OF USING BOTH TECHNIQUES SIMULTANEOUSLY (LIMIT ANALYSIS AND ELASTOPLASTIC CALCULATION) TO OBTAIN THE REAL BEARING CAPACITY OF THE PLATE.