Most of the spacial discretization techniques so far have been based on finite differences and finite elements. However, new numerical schemes based on collocation by radial basis functions can produce highly accurate results in the static and vibration analysis of composite and sandwich structures.

The paper reviews the basic aspects of collocation with radial basis functions, either alone or in a pseudospectral framework. The crucial aspect of shape parameter choice and optimization is discussed.

The analysis of laminated plates and shells by various shear deformation theories is presented and its use in various laminate configurations is discussed. Single-layer and layerwise approaches are selected for possible, viable, theories to analyse laminated plates and shells with RBF collocation.

The paper discusses results on static deformations and free vibration by the author and colleagues, but also by other contributors on the field.

Several examples are presented and discussed to illustrate the high potential of the methods.

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