A four-unknown higher-order shear deformation theory for the analysis of bending in sigmoid-FGM plates - Djidar, Fatima Zohra; Hebali, Habib (Vojnotehnički glasnik / Military Technical Courier, 2025)
An In this paper, the bending analysis of sigmoid functionally graded materials (S-FGM) plates is presented using four-variable high-order shear deformation theory. In this present theory, the number of unknown functions has simply been reduced from five to four compared to other shear deformation theories, it does not require shear correction factors and satisfies the conditions of zero shear stresses for the top and bottom surface of the plate, knowing that the variation of shear stresses is parabolic through the thickness. The equilibrium equations of this present theory are derived from the principle of virtual work, and the Navier solution is used to solve these equations. For this S-FGM plate, according to the power law, the materials are distributed in terms of volume fractions of the constituents, and their properties are gradually varied in the thickness direction. This analytical study gave very satisfactory results, and the comparison between the numerical results obtained from the present theory and those obtained from the classical plate theory (CPT) and high-order shear deformation theories (HSDTs) demonstrated the simplicity, accuracy, and reliability of this presented theory in analyzing the static bending behavior of thick S-FGM plates.