Transient analysis of variable thickness multi-directional functionally graded plates using isogeometric analysis

Abstract

PurposeThe main objective of this study is to develop a numerical model based on Isogeometric Analysis to study the dynamic behavior of multi-directional functionally graded plates with variable thickness.Design/methodology/approachA numerical study was conducted on the dynamic behavior of multi-directional functionally graded plates. Rectangular and circular plates with variable thickness are taken into investigation. The third-order shear deformation plate theory of Reddy is used to describe the displacement field, while the equation of motion is developed based on the Hamilton's principle. Isogeometric Analysis approach is employed as a discretization tool to develop the system equation, where NURBS basis functions are used. The famous Newmark method is used to solve time-dependent problems.FindingsThe results obtained from this study indicated that the thickness gradation has a more considerable effect than in-plane variation of materials in MFGM plates. Additionally, the influence of the damping factor is observed to affect the vibration amplitude of the plate. The results obtained from this study could be used for future investigations, where the viscous elasticity and other dynamic factors are considered.Originality/valueAlthough there have been a number of studies in the literature devoted to analyzing the linear static bending and free vibration of FGM and MFGM plates with variable thickness, the study on dynamic response of FGM and MFGM plate is still limited. Therefore, this study is dedicated to the investigation of the dynamic behavior of multi-directional functionally graded plates.

A light gradient boosting machine-based method for predicting the dynamic response of functionally graded plates

“…where  stands for the plate's reference plane and   qt , which is the distributed load applied to the plate's upper surface, is dependent on the time t variable. For detailed information regarding the quantities specified in the preceding equation, we refer readers to [26].…”

“…where   qt denotes the load vector and M and K stand for the mass and stiffness matrices, respectively. The readers may find further details in [26]. In this analysis, only structural damping of the plate is considered.…”

“…The Newmark technique is applied to solve the timedependent problem as given in ( 24) [29]. The overall process for resolving the temporary issue is provided in [26].…”

Transient analysis of functionally graded plates using extreme gradient boosting

“…where Ω represents the reference plane of the plate; q (t) is the distributed load exerted on the upper surface of the plate and is dependent on the variable of time t. Readers can consult Ref. [5] for specific information about the quantities mentioned in the equation above.…”

“…Ootao et al [4] investigated the transient thermoelastic problem of a functionally graded plate with piecewise exponential law caused by a nonuniform heat supply. Tran and Thai [5] used isogeometric analysis to investigate transient analysis of multi-directional functionally graded plates. And several other studies as shown in [6,7].…”