Transient responses and natural frequencies of sandwich beams with inhomogeneous functionally graded (FG) core are investigated. To serve this purpose, we propose a novel truly meshfree method in which the displacement field is approximated by the radial point interpolation method (RPIM) regardless of predefined mesh, and the domain integrals are evaluated by the so-called Cartesian transformation method (CTM) to obviate the need for a background cell. The effective properties of the FG core are obtained either by the rule of mixture or by the Mori–Tanaka micromechanics scheme, while the penalty technique is adopted to treat the material discontinuities at the interface between the core and the two face sheets. The accuracy and the efficiency of the present formulation are demonstrated by examining a series of numerical examples. The results are compared to those obtained by alternative methods, and excellent agreements are obtained.
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