In this paper, a finite element method (FEM) and a new third-order shear deformation plate theory are proposed to investigate a static bending model of auxetic plates with negative Poisson’s ratio. The three – layer sandwich plate is consisted of auxetic honeycombs core layer with negative Poisson’s ratio integrated, isotropic homogeneous materials at the top and bottom of surfaces. A displacement-based finite element formulation associated with a novel third-order shear deformation plate theory without any requirement of shear correction factors is thus developed. The results show the effects of geometrical parameters, boundary conditions, uniform transverse pressure on the static bending of auxetic plates with negative Poisson’s ratio. Numerical examples are solved, then compared with the published literatures to validate the feasibility and accuracy of proposed analysis method. Keywords: Static bending; New third-order shear deformation plate theory; Auxetic material.

This paper carries out free and forced vibration analysis of piezoelectric FGM plates resting on two-parameter elastic foundations placed in thermal environments. By employing the third-order shear deformation theory and the finite element method, this work establishes free and forced vibration equations of piezoelectric FGM plates, where the materials are assumed to be varied in the thickness directions, and the mechanical properties depend on the temperature. Then, comparative examples are conducted to verify the proposed theory and mathematical model, and the results of this study and other methods meet a very good agreement. Then, effects of geometrical and material properties such as the feedback coefficient, voltage, volume fraction index, temperature as well as the parameters of elastic foundations on free and forced vibration of the plates are investigated, and the conclusions are given out to provide the effective direction for the design and practical use of these structures.

This work numerically simulates the natural vibration response of rotating piezoelectric functionally graded (FG) beams resting on two-parameter elastic mediums. This is a common kind of design seen in reality, such as marine engine gas turbine blades, rotating railway bridges, and helicopter rotors, where these components may be thought of as beam models rotating around a fixed axis. For the first time, this study uses the finite element method (FEM) in conjunction with Reddy’s theory of high-order shear deformation to model the vibration response of a beam rotating around one fixed axis. The present theory eliminates the necessity for shear correction factors while precisely describing the structure’s mechanical response. The piezoelectric layers are firmly connected to the top and bottom surfaces of the beam, while the core layer is composed of the FG material, whose material and physical characteristics are expected to gradually change along the thickness direction of the beam in accordance with a power law function as the thickness of the beam is increased. This study is conducted to determine the influences of the structure’s geometric and material characteristics on the beam’s free vibration behavior, including the rotational speed, distance between the fixed axis and beam endpoint, thickness of piezoelectric layers, and elastic foundation parameters, among other things. Due to the obvious calculation results, the free vibration response of this structure can be easily seen by readers, which serves as a foundation for its design and use in engineering practice.

In this article, a new sinusoidal shear deformation theory was developed for static bending analysis of functionally graded plates resting on elastic foundations. The proposed theory used an undefined integral term to reduce the number of the unknown to four without any shear correction factors. The high accuracy and efficiency of the proposed theory were proved thanks to the comparisons of the present results with other available solutions. And then, the proposed theory was successfully applied to investigate the bending behavior of the functionally graded plates resting on Winkler–Pasternak foundations. The governing equations of motion were established by using Hamilton’s principle, and the Navier’s solution technique was employed to solve these equations. The effects of some factors of the geometrics, the materials properties, and the elastic foundation parameters on the bending behaviors of the FGM plates were investigated intensely. Also, some novel results and special phenomenon were carried out.