ANALYTICAL AND MATHEMATICAL MODELLING AND OPTIMIZATION OF FIBER METAL LAMINATES (FMLS) SUBJECTED TO LOW-VELOCITY IMPACT VIA COMBINED RESPONSE SURFACE REGRESSION AND ZERO-ONE PROGRAMMING

Abstract

THIS PAPER PRESENTS ANALYTICAL AND MATHEMATICAL MODELING AND OPTIMIZATION OF THE DYNAMIC BEHAVIOR OF THE FIBER METAL LAMINATES (FMLS) SUBJECTED TO LOW-VELOCITY IMPACT. THE DEFLECTION TO THICKNESS (W/H) RATIO HAS BEEN IDENTIFIED THROUGH THE GOVERNING EQUATIONS OF THE PLATE THAT ARE SOLVED USING THE FIRST-ORDER SHEAR DEFORMATION THEORY AS WELL AS THE FOURIER SERIES METHOD. WITH THE HELP OF A TWO DEGREES-OF-FREEDOM SYSTEM, CONSISTING OF SPRINGS-MASSES, AND THE CHOI’S LINEARIZED HERTZIAN CONTACT MODEL THE INTERACTION BETWEEN THE IMPACTOR AND THE PLATE IS MODELED. THIRTY-ONE EXPERIMENTS ARE CONDUCTED ON SAMPLES OF DIFFERENT LAYER SEQUENCES AND VOLUME FRACTIONS OF AL PLIES IN THE COMPOSITE STRUCTURES. A RELIABLE FITNESS FUNCTION IN THE FORM OF A STRICT LINEAR MATHEMATICAL FUNCTION CONSTRUCTED. USING AN ORDINARY LEAST SQUARE METHOD, RESPONSE REGRESSION COEFFICIENTS ESTIMATED AND A ZERO-ONE PROGRAMMING TECHNIQUE PROPOSED TO OPTIMIZE THE FML PLATE BEHAVIOR SUBJECTED TO ANY TECHNOLOGICAL OR COST RESTRICTIONS. THE RESULTS INDICATED THAT FML PLATE BEHAVIOR IS HIGHLY AFFECTED BY LAYER SEQUENCES AND VOLUME FRACTIONS OF AL PLIES. THE RESULTS ALSO SHOWED THAT, EMBEDDING AL PLIES AT OUTER LAYERS OF THE STRUCTURE SIGNIFICANTLY RESULTS IN A BETTER RESPONSE OF THE STRUCTURE UNDER LOW-VELOCITY IMPACT, INSTEAD OF EMBEDDING THEM IN THE MIDDLE OR MIDDLE AND OUTER LAYERS OF THE STRUCTURE.