Nonlinear vibration and dynamic stability analysis of composite plates

Buckling of FG-CNT reinforced composite thick skew plates resting on Pasternak foundations based on an element-free approach

This paper considers the free vibration behaviors of functionally graded carbon nanotube (FG-CNT) reinforced composite thick straight-sided quadrilateral plates resting on Pasternak foundations. The IMLS-Ritz method is used in this study. The FG-CNT reinforced composite plates considered are having the CNT reinforced uniaxially aligned in the axial direction with its material properties graded in the thickness direction. The first-order shear deformation theory (FSDT) is employed for formulation of the energy functional to incorporate the effects of transverse shear deformation and rotary inertia. Several example problems are considered with different boundary conditions. Convergence studies for the example problems are performed to demonstrate the numerical stability of the improved moving least-squares Ritz (IMLS-Ritz) method. Besides, the accuracy of the IMLS-Ritz results is examined by comparing with the published values. Close agreement is found from the comparison study. Parametric studies are conducted for various types of CNTs distributions, CNT ratios, aspect ratios, plate geometries and thickness-to-height ratios under different boundary conditions.

Vibration of FG-CNT reinforced composite thick quadrilateral plates resting on Pasternak foundations

The buckling behavior of nanocomposite plates of polygonal planform under in-plane loads is examined. The plate under consideration is reinforced by single-walled carbon nanotubes (CNTs). The governing eigenvalue equation to this problem is derived based on the first-order shear deformation plate theory (FSDT) with a set of element-free shape functions in approximating the two-dimensional displacement fields. To solve this eigenvalue equation, the element-free IMLS-Ritz method is employed to furnish the buckling solution. The convergence of the solution for the CNT-reinforced composite plates is examined. Comparison study is further carried out to validate the accuracy of the solution. A parametric study is performed by varying the CNT volume fraction, CNT distribution, plate thickness-to-apothem ratio and boundary conditions. This first known buckling solution may serve as benchmarks for future research.

An element-free based IMLS-Ritz method for buckling analysis of nanocomposite plates of polygonal planform

The present article deals with static and dynamic behavior of functionally graded skew plates based on the three-dimensional theory of elasticity. On the basis of the principle of minimum potential energy and the Rayleigh Ritz method, the equations of motion are derived in conjunction with the graded finite element approach. Solution of the resulted system of equations in time domain is carried out via Newmark's time integration method. Calculations are applied for fully clamped boundary condition. In the present paper, two different sets of distributions for material properties are considered. For the static analysis, material properties are considered to vary through the thickness direction according to an exponential law. In the case of dynamic analysis, variations of the volume fractions through the thickness are assumed to obey a power law function. Thus, the effective material properties at each point are determined by the Mori-Tanaka scheme. In case of dynamic analysis, the results are obtained for uniform step loadings. The effects of material gradient index and skew angle on displacement components and stress response are studied. Results of present formulations are verified by available results of a functionally graded rectangular plate for different boundary conditions and also compared with result of a homogenous skew plate by commercial FEM software.

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Y.S. Shih

Papers

Analysis of dynamic instability for arbitrarily laminated skew plates