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A novel meshfree radial point interpolation approach which employs a new numerical integration scheme is introduced. The new integration scheme, namely Cartesian Transformation Method, transforms a domain integral into a double integral including a boundary integral and a one-dimensional integral, and thus allowing integration without discretizing domain into sub-domains usually called background mesh in traditional meshfree analysis. A new type of radial basis function that is little sensitive to user-defined parameters is also employed in the proposed approach. The present approach is applied to free vibration and buckling analysis of thin laminated composite plates using the classical Kirchhoff’s plate theory. Various numerical examples with different geometric shapes are considered to demonstrate the applicability and accuracy of the proposed method.

A novel meshfree approach for free vibration and buckling analysis of thin laminated composite plates