A bi-value coding parameterization scheme for the discrete optimal orientation design of the composite laminate

The discrete optimal orientation design of the composite laminate can be treated as a material selection problem dealt with by using the concept of continuous topology optimization method. In this work, a new bi-value coding parameterization (BCP) scheme of closed form is proposed to this aim. The basic idea of the BCP scheme is to 'code' each material phase using integer values of +1 and -1 so that each available material phase has one unique 'code' consisting of +1 and/or -1 assigned to design variables. Theoretical and numerical comparisons between the proposed BCP scheme and existing schemes show that the BCP has the advantage of an evident reduction of the number of design variables in logarithmic form. The benefit is particularly remarkable when the number of candidate materials becomes important in large-scale problems. Numerical tests with up to 36 candidate material orientations are illustrated for the first time to indicate the reliability and efficiency of the BCP scheme in solving this kind of problem. It proves that the BCP is an interesting and valuable scheme to achieve the optimal orientations for large-scale design problems. Besides, a four-layer laminate example is tested to demonstrate that the proposed BCP scheme can easily be extended to multilayer problems.