Optimization of Perforated Variable-Stiffness Plates Using Energy Element Method and Potential Flow

A novel optimization framework based on potential flow, conformal mapping, energy element method (EEM), and three-dimensional sampling optimization (3DSO) method is proposed for the optimization of variously shaped perforated variable-stiffness composite (VSC) plates. The hypotrochoidal mapping function is adopted to generate the potential flow around a polygonal-type cylinder. By treating the streamlines of potential flow as the curvilinear fiber paths of variously shaped VSC plates with a polygonal hole, the curvilinear fiber paths can bypass the hole. The global fiber orientation angle of a lamina is simulated by the incoming flow angle of the potential flow, and the local fiber orientation angle of the fiber path is determined by the flowfield. First-order shear-deformation-theory-based vibration analysis is conducted for the VSC plates using EEM. EEM performs numerical integration on a complex geometric domain using rectangular energy elements with different scales based on the Gauss–Legendre quadrature, variable-stiffness properties, and a global admissible function. Simulation of energies on a complex geometric domain can be realized by the superposition principle of rectangular energy elements as they allow geometric boundaries to pass through. Vibration characteristics of perforated VSC plates in different shapes are optimized via 3DSO, and compared with those of straight fiber laminates. Significant improvements in the vibrational performance of perforated VSC plates are achieved by utilizing continuous curvilinear fiber paths around the hole.