A variational formulation of the Ritz method is used to establish an eigenvalue problem for the local buckling behavior of composite plates elastically restrained along their four edges (the RRRR plates) and subjected to compression along one axis, and the explicit solution in terms of the rotational restraint stiffness (k) is presented. Based on the different boundary and loading conditions, the explicit local buckling solution for the rotationally restrained plates is further simplified to several special cases (e.g., the SSSS, SSCC, CCSS, SSRR, RRSS, CCRR. and RRCC plates) with a combination of simply supported (S), clamped (C), and/or rotationally restrained (R) edge conditions. The unique deformation shape function combining the harmonic and polynomial functions is proposed by considering the effect of elastic rotational restraint stiffness (k) along the four edges of the orthotropic plate. The explicit local buckling solutions of the RRSS and SSRR cases are validated with the exact transcendental solutions. A parametric study is conducted to evaluate the influences of the rotational restraint stiffness (k) and the aspect ratio (γ) on the local buckling stress resultants of various rotationally restrained plates. The applicability of the explicit solutions of restrained composite plates is illustrated in the discrete plate analysis of two composite structures: short thin-walled composite columns and honeycomb sandwich cores. The local buckling strength values of plate panels in short FRP box columns and core walls between the top and bottom face sheets of sandwich are predicted, and they are in excellent agreement with the numerical finite element solutions and experimental results. The simplicity of the "explicit" local buckling solution of elastically restrained composite plates facilitates analysis, design, and optimization of composite structures.
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