A layerwise finite element formulation for free vibration analysis of functionally graded sandwich shells

Three-dimensional free vibration analyses of functionally graded laminated shells under thermal environment by a hierarchical quadrature element method

This paper presents an analytical solution for the free vibration of functionally graded material (FGM) sandwich plates in a thermal environment. An equivalent‐single‐layer (ESL) plate theory with four variables is used to obtain the solution. Two types of sandwich plates are examined in this study: one with FGM face sheets and a homogeneous core and the other with an FGM core and homogeneous face sheets. The governing equations of motion are derived based on Hamilton's principle and then solved using the Navier method. The results of natural frequencies of simply supported FGM sandwich plates are compared with the available solutions in the literature. The effects of volume fraction distribution, geometrical parameters, and temperature increments on the free vibration characteristics are discussed in detail.

Dynamic analysis of functionally graded sandwich beams using a semi-analytic method named scaled boundary finite element method

Vibration of post-buckled sandwich plates with FGM face sheets in a thermal environment

2 - Sandwich Structures

Vibro-acoustic characteristics of eccentrically stiffened functionally graded material sandwich cylindrical shell under external mean fluid

This paper presents an analytical solution for the thermomechanical buckling of functionally graded material (FGM) sandwich plates. The solution is obtained using a four-variable equivalent-single-layer (ESL) plate theory. Two types of sandwich plates are included: one with FGM facesheets and homogeneous core, and vice versa for the other. The governing equations are derived based on the principle of minimum total potential energy. For simply supported boundary conditions, these equations are solved via the Navier method. The results on critical buckling load and temperature increment of simply supported FGM sandwich plates are compared with the available solutions in the literature. Several results are presented considering various material and geometrical parameters as well as their effect on the thermomechanical buckling response of FGM sandwich plates. The relationship between the mechanical load and the temperature increment for uniform/linear temperature rise of FGM sandwich plates under combined mechanical and thermal loads is studied.

Transient response of rotating laminated functionally graded cylindrical shells in thermal environment

Thermoelastic analysis of stiffened sandwich doubly curved plate with FGM core under low velocity impact

This work presents a finite element formulation for the vibration analysis of functionally graded material (FGM) plates containing microstructural defects operating in thermal environments. The material properties are assumed to be temperature-dependent and are modeled as higher-order functions of temperature. The volume fractions of the constituent materials are varied through the plate thickness according to a power-law distribution. The effective material properties of the FGM are evaluated using both the Mori–Tanaka homogenization scheme and the rule of mixtures. The kinematics of the FGM plates are described using an efficient layerwise theory. The governing equations of motion, constitutive relations, and boundary conditions are derived using on Hamilton’s principle. The stiffness coefficients of the plates are computed using a sub-laminate mechanics approach, wherein the plate thickness is discretized into several thin sublayers, each assumed to possess uniform material properties. This approach is particularly effective for micromechanical models where exact analytical integration of stiffness coefficients is difficult due to the complex polynomial variation of properties across the thickness. A four-noded quadrilateral finite element, previously developed for laminated and FGM shells, is extended in this study to analyze the dynamic behavior of FGM plates with microstructural defects and temperature dependent material properties. The natural frequencies are obtained using a subspace iteration technique, while the transient responses under step and impulse excitations are computed using the state-space form of the governing dynamic equations. The proposed finite element model is validated against three-dimensional elasticity and Ritz-based semi-analytical solutions, demonstrating excellent accuracy and reliability across varying thermal environments. A detailed parametric study is also carried out to investigate the effects of temperature, inhomogeneity index, porosity concentration, boundary conditions, and geometric parameters on the natural frequencies and transient responses of porous FGM plates.

Temperature-dependent shear correction factor with heat transfer based on micromechanical properties for FGM plates

The nonlinear vibration behavior of the spiral stiffened multilayer functionally graded (SSMFG) cylindrical shells with initial imperfection exposed to axial parametric and external excitation in the thermal environment is presented in this paper using a semi-analytical method. The distribution of temperature and material constitutive of the stiffeners along the direction of thickness is assumed. The cylindrical shell consists of three layers, the interior and exterior layer is respectively rich metal and ceramic, and the middle layer is functionally graded material (FGM). Using the smeared stiffeners technique, von Kármán equations, and the Galerkin method, the nonlinear vibration problem has been solved. Then, utilizing the multiple scales method, the nonlinear vibration behavior of the system is examined. The resonant case, including internal parametric resonance among three modes and subharmonic resonance of order one-half, is considered. The results show that although the trend of all figures is approximately like together, but the maximum amplitude vibration of the internal SSMFG cylindrical shell with the angle of stiffeners and the external SSMFG cylindrical shell with the angle of stiffeners is more than others.

This study focuses on free vibration analysis of functionally graded material (FGM) plates supported by Winkler–Pasternak elastic foundation in thermal environment using element-free Galerkin (EFG) meshless method. Plate kinematics depend on first-order shear deformation theory. Uniform, linear, and nonlinear temperature variations through the thickness direction are considered, along with the temperature-dependent material properties. The numerical outcomes obtained from EFG method are compared with those available in the published literature to validate the proposed method’s accuracy. An artificial neural network (ANN) model that can easily predict the natural frequencies of the plate is constructed from the EFG method outcomes. Further, the effect of foundation parameters, power law index, thickness ratio, temperature variations, and different boundary conditions are investigated; results show that these significantly influence the vibration response of FGM plates supported by the elastic foundation. Increasing the temperature of FGM plates supported by the Winkler–Pasternack foundation causes a decrease in the dimensionless fundamental natural frequency, and the uniform temperature influence is greater than that of linear and nonlinear temperature variation. The proposed EFG-ANN prediction model saves approximately 98.80% computation time when predicting the natural frequency with an accuracy of approximately 98.76% compared to that by EFG meshless method alone.

Detailed formulation and coding of exact finite element is carried out to study the static behavior of a layered beam structure. The beam element is modelled based on the first-order shear deformation theory and it is assumed to be composed of three layers whereas the middle layer is made of functionally graded material (FGM), i.e. with variable elastic properties in the thickness direction. The shape of the FGM mechanical properties variation in the thickness direction takes the form of exponential or power-law. The governing equations and boundary conditions are derived by applying the virtual work principle. Variations of displacements along the beam and stresses across the depth due to mechanical loadings are investigated. Comparative examples are carried out to highlight the static behavior difference between FGM layered beams and pure metal-ceramic beams.

Three-dimensional Analyses of Functionally Graded Multi-layered Systems