Thermal buckling behavior of power and sigmoid functionally graded material sandwich plates using nonpolynomial shear deformation theories

PurposeThe purpose of this article is to carry out the thermal buckling analysis of power and sigmoid functionally graded material Sandwich plate (P-FGM and S-FGM) under uniform, linear, nonlinear and sinusoidal temperature rise.Design/methodology/approachThermal buckling of FGM Sandwich plates namely, FGM face with ceramic core (Type-A) and homogeneous face layers with FGM core (Type-B), incorporated with nonpolynomial shear deformation theories are considered for an analytical solution in this investigation. Effective material properties and thermal expansion coefficients of FGM Sandwich plates are evaluated based on Voigt's micromechanical model considering power and sigmoid law. The governing equilibrium and stability equations for the thermal buckling analysis are derived based on sinusoidal shear deformation theory (SSDT) and inverse trigonometric shear deformation theory (ITSDT) along with Von Karman nonlinearity. Analytical solutions for thermal buckling are carried out using the principle of minimum potential energy and Navier's solution technique.FindingsCritical buckling temperature of P-FGM and S-FGM Sandwich plates Type-A and B under uniform, linear, non-linear, and sinusoidal temperature rise are obtained and analyzed based on SSDT and ITSDT. Influence of power law, sigmoid law, span to thickness ratio, aspect ratio, volume fraction index, different types of thermal loadings and Sandwich plate types over critical buckling temperature are investigated. An analytical method of solution for thermal buckling of power and sigmoid FGM Sandwich plates with efficient shear deformation theories has been successfully analyzed and validated.Originality/valueThe temperature distribution across FGM plate under a high thermal environment may be uniform, linear, nonlinear, etc. In practice, temperature variation is an unpredictable phenomenon; therefore, it is essential to have a temperature distribution model which can address a sinusoidal temperature variation too. In the present work, a new sinusoidal temperature rise is proposed to describe the effect of sinusoidal temperature variation over critical buckling temperature for P-FGM and S-FGM Sandwich plates. For the first time, the FGM Sandwich plate is modeled using the sigmoid function to investigate the thermal buckling behavior under the uniform, linear, nonlinear and sinusoidal temperature rise. Nonpolynomial shear deformation theories are utilized to obtain the equilibrium and stability equations for thermal buckling analysis of P-FGM and S-FGM Sandwich plates.

Theories and Analysis of Functionally Graded Beams

This is a review paper containing the governing equations and analytical solutions of the classical and shear deformation theories of functionally graded straight beams. The classical, first-order, and third-order shear deformation theories account for through-thickness variation of two-constituent functionally graded material, modified couple stress (i.e., strain gradient), and the von Kármán nonlinearity. Analytical solutions for bending of the linear theories, some of which are not readily available in the literature, are included to show the influence of the material variation, boundary conditions, and loads.

In-plane free vibrations of functionally graded sandwich arches using shear and quasi-3D deformation theories

The in-plane vibration problem of functionally graded (FG) sandwich circular arch made up of two layers of power law FGM face sheet and one layer of homogeneous core is investigated. A framework for the vibration analysis of FG sandwich circular arches is presented, and the quasi-3D theories for the arch structures compatible with this framework are established for the first time. The quasi-3D theories take into account the changes of displacement through the thickness of the arch, and satisfy the stress-free boundary conditions naturally. The Lagrange equation is employed to derive the equation of motion, and various boundary conditions are implemented by applying simple algebraic polynomials as admissible functions to discrete the displacement fields of the FG sandwich arches. The comparison study of various high-order shear deformation theories and quasi-3D deformation theories for the FG sandwich circular arches is carried out via different numerical examples. The influences of material distributions and geometric parameters on the vibration characteristics of the FG sandwich circular arches are also presented and discussed for the first time.