Keywords: discrete Ritz method, potential flow, conformal mapping, variable-stiffness composite plates, buckling, optimization.

Potential flow around two equal-radius cylinders is derived analytically and applied to generate the curvilinear fiber path of variable-stiffness composite 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 variable-stiffness composite plates with two circular holes are studied via discrete Ritz method. A three-dimensional sampling optimization method is then adopted to optimize the curvilinear fiber configurations of variable-stiffness composite plates, and its buckling performances are compared with those of constant stiffness composites with 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 variable-stiffness composite plates with material discontinuity. Moreover, discrete Ritz method exhibits good precision and stability for buckling analysis of variable-stiffness composite plates with complex geometries.

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