A New Sinusoidal Shear Deformation Theory for Static Bending Analysis of Functionally Graded Plates Resting on Winkler–Pasternak Foundations

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.

Modeling on Actuation Behavior of Macro-Fiber Composite Laminated Structures Based on Sinusoidal Shear Deformation Theory

A new piezoelectric composite, macro fiber composite (MFC) is recombined with piezoceramic fibers, an epoxy resin basal body, and an interdigitated electrode. It has been widely applied in vibration reduction and deformation control of thin-walled structures, due to its great deformability and flexibility. Research on its actuation performance is mostly concentrated on the MFC actuating force calculation based on classical plate theory (CPT), and the overall modeling of MFC and its structure. However, they have some deficiencies in the tedious calculating process and neglect of shear deformation, respectively. To obtain a precise MFC actuating force, the sinusoidal shear deformation theory (SSDT) is adopted to deduce the MFC actuating force formula, and global–local displacement distribution functions are introduced to help the MFC laminated plate structure satisfy the deformation compatibility and stress balance. For instance, in the end displacement calculation of the MFC laminated beam structure. The experimental result of the MFC laminated beam is compared with those of the MFC actuating force based on SSDT and on CPT, which indicates that the MFC actuating force formula based on SSDT can reach higher computational accuracy.