Formulation of a New Mixed Four-Node Quadrilateral Element for Static Bending Analysis of Variable Thickness Functionally Graded Material Plates

Abstract

A new mixed four-node quadrilateral element (MiQ4) is established in this paper to investigate functionally graded material (FGM) plates with variable thickness. The proposed element is developed based on the first-order shear deformation and mixed finite element technique, so the new element does not need any selective or reduced numerical integration. Numerous basic tests have been carried out to demonstrate the accuracy and convergence of the proposed element. Besides, the numerical examples show that the present element is free of shear locking and is insensitive to the mesh distortion, especially for the case of very thin plates. The present element can be applied to analyze plates with arbitrary geometries; it leads to reducing the computation cost. Several parameter studies are performed to show the roles of some parameters such as the power-law index, side-to-thickness ratio, boundary conditions (BCs), and variation of the plate thickness on the static bending behavior of the FGM plates.

A full numerical study of the strain based functionally graded rectangular plate finite element using the FSDT

“…The CCCC plate has the smallest maximum deflection, whereas the SSSS plate has the largest maximum deflection. In general, the current results closely align with the Four-Node Mixed Quadrilateral Element results (MiQ4) [19].…”

“…The factors for shear correction have been applied to determine the components of the transverse shear stresses and normal shear stress using the equilibrium equations. Van Vinh [19] presented a novel quadrilateral element (MiQ4),which was used to examine plates composed of functionally graded material that had different thicknesses.…”

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

“…Also adopting isogeometric analysis approach, Thai et al (2022a, b) recently investigated the nonlinear bending of MFGM plates with variable thickness. Phan (2021) proposed a new mixed four-node quadrilateral element to study the static bending response of variable-thickness FGM plates. The free vibration behavior of variable-thickness MFGM circular plates resting on elastic foundations was analyzed by Alipour et al (2010) and Hosseini-Hashemi et al (2010).…”

Natural Frequencies of a Viscoelastic Supported Axially Functionally Graded Bar With Tip Masses

“…Dynamic and static analyses of plates with unidirectional and bidirectional material changes have been carried out by finite element method using different order deformation theories. [1][2][3][4][5][6] There is less work on the analysis of FG beams and especially bars than on the FG plates and shells. Generally, material properties are considered as varying along the thickness direction in the studies on FGM beams.…”