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In this paper, the first-order shear deformation theory (FSDT) is employed to derive analytical solutions for the buckling analysis of functionally graded material—porous—functionally graded material (FGM-porous-FGM) sandwich plate resting on Pasternak elastic foundation. The top and bottom layers of the plate consist of functionally graded materials that vary according to the exponential law along the thickness direction, while the core layer is composed of a porous material. The governing equations are derived by using the principle of minimum total potential energy. Based on the Navier’s solution, the displacements are obtained to satisfy the boundary conditions. The results are then compared with existing published literature showing the accuracy of the proposed solutions. Moreover, parametric studies investigate the effects of material parameters, geometric dimensions, foundation coefficients and face-core-face thickness ratios on the critical buckling load of the rectangular FGM-porous-FGM sandwich plate. In the case of uniaxial loading, the critical bucking load is almost twice for the case of biaxial loading, no matter the value of volume fraction index. For all the cases of face-core-face thickness ratio, the biaxial critical buckling load linearly depends on the porosity coefficient. The porosity coefficient is crucial when and only when the volume of the core is almost eight times bigger than the volume of the face layer. Optimization studies are then presented in order to: (i) maximize the critical buckling load and (ii) optimize the input variables corresponding to a given value of the critical buckling load. The proposed study aims to provide valuable insights into the design and application of FGM-porous-FGM sandwich plates in various engineering fields, contributing to the development of more resilient and efficient structural components.
Duong et al. (Sun,) studied this question.