This paper applies the genetic algorithm and consequential convex approximation programming to deal with problems of minimizing the strain energy of a linear elastic fiber reinforced composite laminate in a state of plane stress. The directions of fibers are used as design variables. From the numerical results, an evaluation of two optimization techniques is performed. | Vietnam Journal of Mechanics, VAST , Vol. 26 , 2004, No. 4 (247 - 256) APPLYING THE GENETIC ALGORITHM AND THE CONSEQUENTIAL CONVEX APPROXIMATION PROGRAMMING FOR COMPOSITE STRUCTURE OPTIMIZATION NGUYEN TH OI TRUNG , NGO THANH PHONG Department of Math ematics and Informatics, University of Natural Sciences- VNU-HCM ABSTRACT . This paper applies the genetic algorithm and consequential convex approximation programming to deal with problems of minimizing the strain energy of a linear elastic fiber reinforced composite laminate in a state of plane stress. The directions of fibers are used as design variables. From the numerical results, an evaluation of two optimization techniques is performed. 1 Introduction F iber reinforced composite materials are ideal for structural applications where high stiffness and strength are required at low weight . Aircraft and spacecraft are typical weight sensitive structure, in which composite materials are cost effective. To obtain the full advantage of the fiber reinforcement, fibers must be distributed and oriented optimally with respect to t he actual strain field. Ho11·?ver , due to the objective function and constrains are implicit depending on the desiv J. variables, it is impossible to use the traditional optimization methods such as t he external penalty, the internal penalty, the Lagrange multiply methods , etc . to solve directly. We must use new methods such as the genetic algorithm and t he sequential convex approximation programming to solve. 2 Behavior theory of the composite lamina te in t h e p la n e stress state [1] Elastic equation in the principle a xis (2 .1) 217 where the red µIVVJ():) LArrvi::-;iup~f!EVTO:) Relation~ \:Mu ·'e1:i ™1ff'ifo8 V(jJ ;'fs'lh,!s · ' -~Hp inciple and · 1· ~i'l\ \'I•/ \'1''.1(-) 'il.,J" .'I'"-)t 'H1''':.:> global axis ,/'' J>L ;.,.-. ~,;.»_' J ·"-· ·-· -·' ,. J,ft . .L\ . . . [R], where ,, 'QU' ~ the1 ·reduced sitiH'He~s 1 .
