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SUMMARYAn adaptable curved quadrilateral element based on quadratic B-splines is developed for finite element analysis of membrane vibration problems. The approximated displacement field in each element is divided into corners, edges and internal modes. The number of knots on the edges of elements are distinct in any integer power of 2. The elements of different resolutions can be thus connected smoothly under the constraint from the 'two-scale relation' of splines bases. The displacement compatibility on the interconnected edges between adjacent elements is satisfied along the whole edge. The advantages of the proposed element also result in a more adaptable element meshing strategy for structural discretization. Some numerical examples are studied as verification and demonstration of the present work.

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