Summary The analysis of the Kirchhoff plate is performed using rational Bézier triangles in isogeometric analysis coupled with a feature‐preserving automatic meshing algorithm. Isogeometric analysis employs the same basis function for geometric design as well as for numerical analysis. The proposed approach also features an automatic meshing algorithm that admits localized geometric features (eg, small geometric details and sharp corners) with high resolution. Moreover, the use of rational triangular Bézier splines for domain triangulation significantly increases the flexibility in discretizing spaces bounded by complicated nonuniform rational B‐spline curves. To raise the global continuity to C1 for the solution of the plate bending problem, Lagrange multipliers are leveraged to impose continuity constraints. The proposed approach also manipulates the control points at domain boundaries in such a way that the geometry is exactly described. A number of numerical examples consisting of static bending and free vibration analysis of thin plates bounded by complicated nonuniform rational B‐spline curves are used to demonstrate the advantage of the proposed approach.

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