The nanoplates have been used extensively in electronic devices, during the working process they can be affected by external forces. To enhance the working performance of mechanical systems, flexoelectric effects are usually added, therefore, it is necessary to study the mechanical behavior of these material structures under the effect of these effects. This is the first research to examine the vibration response and static buckling of variable flexoelectric nanoplates using the FEM and novel shear deformation theory type hyperbolic sine functions, where the thickness is adjusted by linear and nonlinear rules. This is a simple theory, which does not need any shear correction factors, while the mechanical responses of the structures are still described exactly. The numerical results of this work are compared with those of the analytical approach and other methods. Then, the influences of geometrical and material parameters on the free vibration and static bucking of the structure are explored. The data shows that the flexoelectric effect has a strong effect on the free vibration and static bucking behavior as well as the vibration mode shapes of the nanoplates. The working performance is increased when taking into account the effect of flexoelectricity. This work also shows that for each changing rule of plate thickness, the flexoelectric effect also significantly changes the mechanical response of the plate. This is an important suggestion in the design and use of plate structures in engineering practice.

This work is the first exploration of the static bending and dynamic response analyses of piezoelectric bidirectional functionally graded plates by combining the third‐order shear deformation theory of Reddy and the finite element approach, which can numerically model mechanical relations of the structure. The present approach and mechanical model are confirmed through the verification examples. The geometrical and material study is conducted to evaluate the effects of the feedback coefficients, volume fraction parameter, and constraint conditions on the static and dynamic behaviors of piezoelectric bidirectional functionally graded structures, and this work presents a wide variety of static and dynamic behaviors of the plate with many interesting results. There are many meanings that have not been mentioned by any work, especially the working performance of the structure is better than that when the feedback parameter of the piezoelectric component is added, that is, the piezoelectric layer increases the working efficiency. Numerical investigations are the important basis for calculating and designing related materials and structures in technical practice.

This paper carries out the static bending analysis of symmetric three-layer functionally graded sandwich beams, in which each layer is made from different functionally graded materials, and they are connected by shear connectors due to sliding movement. The finite element formulations are based on Timoshenko’s first-order shear deformation beam theory (FSDT) and the finite element method to establish the equilibrium equation of beams. The calculation program is coded in the MATLAB environment, and then verification examples are given out to compare the numerical data of present work with those of exact open sources. The impact of several geometrical and material parameters on the mechanical response of the structure, such as the height-to-length ratio, boundary conditions, volume fraction index, and especially the shear coefficient of connectors, is being explored. When designing and using these types of structures in engineering practice, the computed results can be utilized as a valid reference.

This article presents a finite element method (FEM) integrated with the nonlocal theory for analysis of the static bending and free vibration of the sandwich functionally graded (FG) nanoplates resting on the elastic foundation (EF). Material properties of nanoplates are assumed to vary through thickness following two types (Type A with homogeneous core and FG material for upper and lower layers and Type B with FG material core and homogeneous materials for upper and lower layers). In this study, the formulation of the four-node quadrilateral element based on the mixed interpolation of tensorial components (MITC4) is used to avoid “the shear-locking” problem. On the basis of Hamilton’s principle and the nonlocal theory, the governing equations for the sandwich FG nanoplates are derived. The results of the proposed model are compared with published works to verify the accuracy and reliability. Furthermore, the effects of geometric parameters and material properties on the static and free vibration behaviors of nanoplates are investigated in detail.