Stress analysis of a functionally graded plate integrated with piezoelectric faces via a four-unknown shear deformation theory

Analysis for stress and deformation of a functionally graded plate integrated with faces made of piezoelectric materials is proposed in this paper. Four-unknown shear deformation plate theory is applied to express the displacement components. The electric potential distribution is composed of a linear function along the thickness direction and a cosine function along the planar coordinate. The plate is under mechanical load and the piezoelectric faces are subjected to an applied voltage. The governing equations and the boundary conditions are found by employing the virtual work principle. Navier’s solution is applied to solve the considered problem. The influence of applied voltage, material anisotropy, side-to-thickness ratio, aspect ratio and inhomogeneity parameter are discussed. The efficiency and exactness of the results are established by comparison with available once. Keywords: Piezoelectric faces, FG plate, Bending, Four-unknown plate theory, Navier’s metho

Analysis of wave propagation in a functionally graded nanobeam resting on visco-Pasternak’s foundation

Wave propagation analysis for a functionally graded nanobeam with rectangular cross-section resting on visco-Pasternak’s foundation is studied in this paper. Timoshenko’s beam model and nonlocal elasticity theory are employed for formulation of the problem. The equations of motion are derived using Hamilton’s principals by calculating kinetic energy, strain energy and work due to viscoelastic foundation. The effects of various parameters such as wavenumber, non-homogeneous index, nonlocal parameter and three parameters of foundation are performed on the phase velocity of the nanobeam. The obtained results indicate that some parameters such as non-homogeneous index, nonlocal parameter and wavenumber have significant effect on the response of the system

Static analyses of FGM beams by various theories and finite elements

The 1D Carrera Unified Formulation (CUF) is here used to perform static analyses of functionally graded (FG) structures. The hierarchical feature of CUF allows one to automatically generate an infinite number of displacement theories that may include any kind of functions of the cross-section coordinates (x, z), among which those used to describe the variation of the mechanical properties of FG materials. The governing equations are derived by means of the Principle of Virtual Displacements in a weak form and solved by means of the Finite Element method (FEM). The equations are written in terms of "fundamental nuclei", whose forms do not depend on the used expansions. Trigonometric, polynomial, exponential and miscellaneous expansions are here used and evaluated for various structural problems. Resulting theories are assessed by considering several aspect-ratios, gradation laws, loading and boundary conditions. The results are compared with 1-, 2- and 3-D solutions both in terms of displacements and stress distributions. The comparisons confirm that the 1D CUF elements are valuable tools for the study of FG structures