An improved first-order mixed plate element for static bending and free vibration analysis of functionally graded sandwich plates

For static bending and free vibration analysis of functionally graded (FG) sandwich plates, a novel, enhanced first-order mixed plate element (IMQ4) is developed in this work. The transverse shear stresses are enhanced by assuming parabolic distribution shear stresses which satisfies the free condition of the transverse shear stresses on the upper and lower surfaces of the plates. Also, the shear correction factor is not required to calculate the shear strain anergy. To develop the basic equations of the proposed element, the mixed finite element formulation is used in conjunction with first-order shear deformation theory. Without the use of the reduced or selective integrations, the current IMQ4 is free of shear-locking phenomenon. For static bending and free vibration analysis, a variety of FG sandwich plates including hardcore, softcore and FG core types are investigated. By comparing the current results to previously published solutions, the performance and dependability of the IMQ4 are analyzed. The proposed element can be useful for analysis, design and testing of FG structures. Finally, detailed parametric analyses are conducted to illustrate the impacts of many factors, such as the layup scheme, the power-law index, and the side-to-thickness ratio on the bending and free vibration of FG sandwich plates.

Automated summary

The paper develops a novel, enhanced first-order mixed plate element (IMQ4) for static bending and free vibration analysis of functionally graded (FG) sandwich plates. The transverse shear stresses are enhanced by assuming a parabolic distribution shear stress. The proposed element, IMQ4, is free of shear-locking phenomenon and can be useful for analysis, design, and testing of FG structures. Detailed parametric analyses on factors such as layup scheme, power-law index, and side-to-thickness ratio are conducted to illustrate their impacts on the bending and free vibration of FG sandwich plates.