Analytical discrete stacking sequence optimization of rectangular composite plates subjected to buckling and FPF constraints

A special type of new discrete design variables is introduced in order to find optimal stacking sequences for laminated structures. Using the proposed new design variables, we demonstrate how to find analytical (i.e. without any numerical optimization algorithm) optimal solutions for laminates made of plies having three different fibre orientations: 0◦, ±45◦, 90◦. It is proved that the definition of design variables enables us to distinguish two types of optimal solutions, i.e. unimodal and bimodal ones. The form of optimal stacking sequences affects the multiplicity (bimodal problems) or uniqueness (unimodal problems) of the solutions. The decoding procedure between membrane and flexural design variables is also proposed. The results demonstrate the effectiveness, simplicity and advantages of the use of design
variables, especially in the sense of the accuracy, repeatability of results and convergence of the method.