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Flexoelectric effect is strengthened in dielectrics at nanoscale so that it could not be neglected. In this work, a laminated composite plate with flexoelectric core and two coverings of CNTRCs is modeled. The variational principles of the plate with generalized supporting conditions are derived considering both the flexoelectricity of the piezoelectric core and the reinforcement of the CNTRCs. According to it, the governing equation and boundary conditions with any supporting types are obtained. Then the analytical solutions to the displacements and resonant frequencies of the plate with two different boundary conditions for free vibration are given. The numerical results prove that the flexoelectric effect relies on the scale seriously. Moreover, the CNTRCs coverings can improve the bending stiffness of the whole plate. Therefore, the bending responses such as resonant frequency and bending deflection can be adjusted and optimized by changing the ratio of the CNTs to the matrix. It’s hopeful to provide the theoretical basis of numerical calculation of electronic devices with laminated structures at nanoscale.

The buckling of isotropic rings under external pressure has attracted the interest of researchers since late 1950s. The formula for critical fluid buckling pressure of thin rings is very well known. This formula was directly extended to account for homogeneous orthotropic rings as well. The buckling of orthotropic cylindrical shells was also a subject of interest since the 1960s. However, the formulations developed, to date, require numerical solutions to obtain the critical pressure. In this work, a generalized closed form analytical formula for the buckling of thin orthotropic multi-angle laminated rings/long cylinders is developed. Standard energy based formulation is used to express the kinematics and equilibrium equations. Classical lamination theory is implemented to introduce the constitutive equations of thin shells. These equations are statically condensed, in terms of the ring's boundary conditions, to produce effective axial, coupling and flexural rigidities for the cases of rings and long cylinders. The critical buckling pressure may be calculated by hand using the derived equation in terms of these effective elastic rigidities. Comparisons are made with some existing results. Parametric studies are conducted to compare the present results with those of the buckling equations implemented by design standards. Various fiber orientations and stacking sequences are considered.

In the present study, Gravitational Search Algorithm (GSA) is combined with Finite Element Method (FEM) for optimizing laminated composites vibration behavior. The fiber orientation angle of layers is considered as design variable. The 8-layerd and 12-layerd plates with both of square and rectangular shapes are investigated. Twenty distinct boundary conditions and $5^{\circ }$ of fiber angle increment are considered. The results of the proposed method are in good agreement with reference methods, and in some cases the GSA-FEM is more efficient. Moreover, the simple structure of GSA and its exploration and exploitation features avoids trapping in a local optimum.

This paper proposes several normalized and non-normalized displacement fields based on hybrid and trigonometric hyperbolic shear strain shape functions in order to solve the analytical thermoelastic problem of simply-supported laminated composite and sandwich plates using the Carrera unified formulation (CUF) as strategy. The equivalent single layer (ESL) governing equations for laminated composite plate are obtained by employing the principle of virtual displacement (PVD) and are solved using Navier’s method solution. Linear and nonlinear temperature distributions through the plate thickness are taken into account. A hybrid and trigonometric hyperbolic shear strain shape functions are introduced in normalized and non-normalized form in the mathematical model. The obtained results are compared with the classical polynomial ones for several order of expansion. Interesting approximations with 3D solution are shown for low and high order of expansion.

This research highlights dynamic displacements of laminated porous micro beams resting on elastic foundation under moving load. In the constituted equation of laminated micro scaled beam, the modified coupled stress theory is used in order to determine the size effect. Each layer is considered as identical and porosity distribution and assumed as uniform. Lagrange technique is applied in achieving governing equations, and Ritz method within algebraic polynomials is used for solution. For dynamic solution steps, Newmark average acceleration method is used within time domain. Influences of porosity coefficients, length scale parameter, foundation parameter, order of laminas, fiber orientation angles on dynamically deflections of laminated micro beam are investigated.