Unifying lamination parameters with spectral-Tchebychev method for variable-stiffness composite plate design

This paper describes an efficient framework for the design and optimization of the variable-stiffness composite plates. Equations of motion are solved using a Tchebychev polynomials-based spectral modeling approach that is extended for the classical laminated plate theory. This approach provides highly significant analysis speed-ups with respect to the conventional finite element method. The proposed framework builds on a variable-stiffness laminate design methodology that utilizes lamination parameters for representing the stiffness properties compactly and master node variables for modeling the stiffness variation through distance-based interpolation. The current study improves the existing method by optimizing the locations of the master nodes in addition to their lamination parameter values. The optimization process is promoted by the computationally efficient spectral-Tchebychev solution method. Case studies are performed for maximizing the fundamental frequencies of the plates with different boundary conditions and aspect ratios. The results show that significant improvements can be rapidly achieved compared to optimal constant-stiffness designs by utilizing the developed framework. In addition, the optimization of master node locations resulted in additional improvements in the optimal response values highlighting the importance of including the node positions within the design variables.