Shape Optimization in Laminated Composite Plates

At this stage a substantial body of literature exists for shape optimization involving isotropic materials. The reader is referred to the articles of Haug [1] and Haftka and Grandhi [2] for overviews of the material. One approach to the problem is analytical. Calculus of variation techniques are employed to derive explicit optimality conditions. Choi and Haug [3], Dems and Mroz [4], and Banichuk [5, 6] have adopted this approach. Of note is the recent work of Kikuchi, Chung, Torigaki and Taylor [7] who used variational methods together with an adaptive grid scheme developed by Diaz, Kikuchi and Taylor [8] for shape optimization in linear elastic structures. The works of Braibant and Fleury [9, 10], involving B-splines, should also be cited. Up to now, structural optimization of laminated composites has involved ply orientations and thicknesses as design variables. To the authors' knowledge, no work on shape optimization Of laminated structures has been done. Kicher and Chao [11] considered the optimum design of fiber composite cylinders under combined axial, radial, and torsional loads. Minimum weight was taken as the objective function, with the ply thickness being the design variable. Hirano [12, 13], Park [14], and Tauchert and Adibhatla [15] treated the optimum design of laminated plates under various types of loading. The objective functions used were maximum buckling load, first ply failure (see [16]), and minimum strain energy, respectively. Hirano and Park used fiber angles as design variables, whereas Tauchert and Adibhatla employed both fiber angles and layer thickness as variables. Yiping [17] treated the optimal design of a laminated plate with several elliptical holes under uniaxial tensile loading. Minimizing the maximum value of the Tsai-Wu failure functional (see [18]) was the objective and the fiber angle was the design variable. In all of the above works on composites, mathematical programming techniques were used to obtain the solutions. Other approaches have been used. Bauchau [19] considered the optimal design of rotating graphite-epoxy shafts.