Buckling Optimization of Variable-Stiffness Composite Plates with Two Circular Holes Using Discrete Ritz Method and Potential Flow

Potential flow around two equal-radius cylinders is derived analytically and applied to generate the curvilinear fiber path of variable-stiffness composite (VSC) plates with two circular holes. As complex variable theory and conformal mapping are used to generate the potential flow around two equal-radius cylinders, the location and size of the two equal-radius circular holes are arbitrary. By changing the angle of incoming flow, the global fiber angle of a variable-stiffness lamina can be simulated and the local fiber orientation angle at any point is determined by the global potential flow field. Buckling performance of variously-shaped VSC plates with two circular holes are investigated via a novel numerical method - discrete Ritz method (DRM). DRM combines the extended interval integral, Gauss quadrature, and variable stiffness within a rectangular domain and builds a discrete energy system to simulate the plate, which allows the geometric boundaries of the plate to vary. The strain energy of a plate is modeled in the rectangular domain, discretized using Gauss points, and is characterized by variable stiffness, which characterizes both the material distribution and plate geometry simultaneously. After that, a three-dimensional sampling optimization (3DSO) method is adopted to optimize the curvilinear fiber configurations of VSC plates, and its buckling performances are compared with those of constant stiffness composites (CSC) with optimal straight fibers. Significant improvements on load-carrying capacity can be achieved compared to straight ones, demonstrating that using potential flow is one of the most efficient way to generate curvilinear optimal fiber path with maximum load-carrying capacity for VSC plates with material discontinuity. Moreover, DRM exhibits good precision and stability for buckling analysis of VSC plates with complex geometries.