Abstract
A layerwise optimization (LO) approach was previously proposed by the author for the lay-up optimization problem of laminated composites, and has been extended in many applications. Various structural analysis methods, including semi-analytical Ritz method, self-made FEM and commercial FEM, are accommodated in the LO optimization. In such lay-up design problems, they usually cause rapid increase in computation time due to the search for optimum solutions of the multi-dimensional space, when design variables are taken to be the fiber orientation angles directly in all K layers. The LO makes it possible, however, that this multi-dimensional optimization problem can be reduced into only K times repetition of one-dimensional search. The theoretical background, however, has not been discussed enough despite wide applicability and accurate approximation. The present report takes up this basic issue and attempts to clarify the reason why an algorithm of the LO approach works effectively.
