Nonlinear dynamic response of functionally graded material plates using a high‐order implicit algorithm

Abstract

In this paper, the forced nonlinear dynamic behavior of functionally graded material (FGM) plate under external dynamic loads is analyzed by means of a high‐order implicit algorithm. The model is developed using the third‐order shear deformation plate kinematics (TSDT). Unlike previous works, in this contribution, the formulation is written without resorting to any homogenization technique neither rule of mixture nor considering FGM as a laminated composite. To handle integrals in the case of inhomogeneous FGMs, the stress vector is split to four parts and it is written in dimensionless form. The resulting equations of motion are established using the Hamilton principle. Finite element discretization is adopted using a four‐node quadrilateral element with seven degrees of freedom per node. The resolution of the nonlinear equations is made by a high‐order implicit algorithm based on the asymptotic numerical method (ANM) techniques. Numerical comparisons of vibration natural frequencies and dynamic response of FGM plates under external loading with literature and laminate composite modeling results are presented to validate the accuracy and the performance of the proposed model.

TSDT theory for free vibration of functionally graded plates with various material properties

“…In this study, the effect of different boundary conditions has been taken into account as shown in Fig. 5, material properties of FGM plate given in Table 1 are used, and the obtained numerical results are compared with those given in references [18] and [16] in particular case of P-FGM plates. In this part, we examine the influence of the exponent N of the volume fraction for P-FGM and S-FGM.…”

“…The plate is discretized by 5 × 5 elements. The eigen-frequencies have been calculated by the proposed approach for a square P-FGM plate and compared with the results of references [16] and [18] as shown in Table 2. Table 3 presents the calculated eigen-frequencies by the proposed approach for a square S-FGM.…”

“…[15] investigated analytical modeling of buckling behavior of porous FGM cylindrical shell embedded within an elastic foundation uisng Donnell shell theory. In the work of Bourihane et al (2020) [16], the free vibration and forced nonlinear dynamic behavior of plate material (P-FGM) are analyzed using TSDT. FGM plates operate as a laminated composite, and the power-law governs the variation of the material properties of FGM.…”

Nonlinear static and dynamic (deflection/stress) responses of porous functionally graded shell panel and experimental validation

“…24 Similarly, the HSDT/TSDT and VKNST kind of modelling approaches are adopted for the computation of dynamic deflections of FGM plates 25 considering the geometrical nonlinearity and porous FG plates. 26,27 A TSDT is utilised 28 to analyse the nonlinear dynamic behaviour of FG plates exposed to external dynamic load. FSDT and VKNST are employed in Nguyen et al 29 and Nazari et al 30 for the computation of nonlinear flexural deflection and/or dynamic responses of the FG plates.…”

Flexural analysis of I-section beams functionally graded materials

“…Consequently, the volume of research publications in this field has experienced exponential growth over the past decades, making FGMs progressively appealing in various engineering fabrication domains. Bourihane et al [7,8] proposed novel finite elements to explore the buckling and vibration behavior of rectangular plates made of Functionally Graded Materials (FGM) using an eigenvalues approach. Sitli and co-workers [9] analyzed the post-buckling behavior of rectangular plates by means of the ANM method.…”