This study conducts buckling and free vibration analyses of multi-directional functionally graded sandwich plates subjected to various boundary conditions. Two scenarios are considered: a functionally graded (FG) skin with a homogeneous hard core, and an FG skin with a homogeneous soft core. Utilizing refined plate models, which incorporate a parabolic distribution of transverse shear stresses while ensuring zero shear stresses on both the upper and lower surfaces, equations of motion are derived using Hamilton’s principle. Analytical solutions for the buckling and free vibration analyses of multi-directional FG sandwich plates under diverse boundary conditions are developed and presented. The obtained results are validated against the existing literature for both the buckling and free vibration analyses. The composition of metal–ceramic-based FG materials varies longitudinally and transversely, following a power law. Various types of sandwich plates are considered, accounting for plate symmetry and layer thicknesses. This investigation explores the influence of several parameters on buckling and free vibration behaviors.

The thermomechanical bending response of functionally graded sandwich plates has been investigated by the use of the new four variable refined plate theories. The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The no symmetric sandwich plate faces are made of isotropic, two-constituent (ceramic–metal) material distribution through the thickness. The core layer is still homogeneous and made of an isotropic metal material. Several kinds of no symmetric sandwich plates are presented. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order, and the other higher-order theories. Field equations for functionally graded sandwich plates whose deformations are governed by either the shear deformation theories or the classical theory are derived. Displacement and stress functions of the plate for different values of the power-law exponent and thickness to-side ratios are presented. Numerical results for deflections and stresses of functionally graded metal–ceramic plates are investigated.

The bending and free vibration of porous functionally graded (PFG) beams resting on elastic foundations are analyzed. The material features of the PFG beam are assumed to vary continuously through the thickness according to the volume fraction of components. The foundation medium is also considered to be linear, homogeneous, and isotropic, and modeled using the Winkler-Pasternak law. The hyperbolic shear deformation theory is applied for the kinematic relations, and the equations of motion are obtained using the Hamilton’s principle. An analytical solution is presented accordingly, assuming that the PFG beam is simply supported. Comparisons with the open literature are implemented to verify the validity of such a formulation. The effects of the elastic foundations, porosity volume percentage and span-to-depth ratio are finally discussed in detail.

In this paper, a new higher order shear deformation model is developed for static and free vibration analysis of functionally graded beams. The theory account for higher-order variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Based on the present higher-order shear deformation beam theory, the equations of motion are derived from Hamilton’s principle. Navier type solution method was used to obtain frequencies. A static and free vibration frequency is given for different material properties. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

This study delves into the ramifications of manufacturing-induced defects, particularly porosities, on the dynamic behavior of functionally graded material (FGM) beams. These defects possess considerable potential to alter the structural integrity and performance of such elements. The principal objective of this investigation is to examine the free vibration properties of FGM beams incorporating porosities. A power-law formulation is employed to delineate the distribution of Young’s modulus across the beam thickness, while Poisson’s ratio is held constant. Diverse configurations of porosity distribution are thoroughly explored, and the fidelity of the proposed model is rigorously evaluated through comparative assessments. Additionally, this research endeavors to elucidate the effects of variations in porosity distribution rate, power-law index, and thickness ratio on the fundamental frequency of the beams.

In this work, the static and free vibration analysis of functionally graded (FG) porous beams is investigated using a new higher-order shear deformation model (HSD). The porosity that develops naturally during the fabrication of a material is arbitrary in nature. Therefore, in the present study, a variation is considered taking into account three distribution patterns, namely (i) even distribution, (ii) uneven distribution, and (iii) the logarithmic-uneven pattern. Furthermore, the impact of several micromechanical models on the bending and free vibration behavior of the beams was investigated. Different micromechanical models were used to examine the mechanical properties of functionally graded beams, the properties of which change continuously throughout the thickness following a power law. Using the HSD model, the equations of motion are obtained using Hamilton’s principle. To obtain displacements, stresses, and frequencies, the Navier type solution method was employed, and the numerical results were compared to those published in the literature. The impact of porosity and volume fraction index, different micromechanical models, mode numbers, and geometry on the bending and natural frequencies of imperfect FG beams were investigated.