Dao Huy Bich

Nonlinear thermal dynamic response of shear deformable FGM plates on elastic foundations

ABSTRACT This paper investigates the nonlinear dynamic response of thick functionally graded materials (FGM) plates using the third-order shear deformation plate theory and stress function. The FGM plate is assumed to rest on elastic foundations and subjected to thermal and damping loads. Numerical results for dynamic response of the FGM plate are obtained by Runge–Kutta method. The results show the influences of geometrical parameters, the material properties, the elastic foundations, and thermal loads on the nonlinear dynamic response of FGM plates.

Non-linear vibration of functionally graded shallow spherical shells

The present paper deals with the non-linear vibration of functionally graded shallow spherical shells. The properties of shell material are graded in the thickness direction according to the power law distribution in terms of volume fractions of the material constituents. In the derived governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. From the deformation compat- ibility equation and the motion equation a system of partial differential equations for stress function and deflection of shell is obtained. The Galerkin method and Runge- Kutta method are used for dynamical analysis of shells to give expressions of natural frequencies and non-linear dynamic responses. Numerical results show the essential in- fluence of characteristics of functionally graded materials and dimension ratios on the dynamical behaviors of shells.

Non-linear dynamical analysis of imperfect functionally graded material shallow shells

Dynamical behaviors of functionally graded material shallow shells with geometrical imperfections are studied in this paper. The material properties are graded in the thickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. The motion, stability and compatibility equations of these structures are derived using the classical shell theory. The non-linear equations are solved by the Newmarks numerical integration method. The non-linear transient responses of cylindrical and doubly-curved shallow shells subjected to excited external forces are obtained and the dynamic critical buckling loads are evaluated based on the displacement responses using the criterion suggested by Budiansky and Roth. Obtained results show the essential influence of characteristics of functionally graded materials on the dynamical behaviors of shells.

Nonlinear torsional buckling and post-buckling of eccentrically stiffened ceramic functionally graded material metal layer cylindrical shell surrounded by elastic foundation subjected to thermo-mechanical load

The nonlinear torsional buckling and post-buckling of ceramic functionally graded material (C-FGM-M) stiffened cylindrical shell surrounded by Pasternak elastic foundation in thermal environment are investigated in this paper. The C-FGM-M cylindrical shell is reinforced by ring and stringer stiffeners system in which the material properties of shell are assumed to be continuously graded in the thickness direction. Based on the classical shell theory, theoretical formulations are derived with the geometrical nonlinearity in von Karman sense and the smeared stiffeners technique. The three-term approximate solution of deflection is chosen more correctly and the explicit expression for finding critical load and post-buckling torsional load–deflection curves are given. The effects of geometrical parameters, temperature, stiffeners and elastic foundation are investigated.

On the linear stability of eccentrically stiffened functionally graded annular spherical shell on elastic foundations

The study deals with the formulation of governing equations of eccentrically stiffened functionally graded materials annular spherical shells resting on elastic foundations and based upon the classical shell theory and the smeared stiffeners technique taking into account geometrical nonlinearity in Von Karman-Donnell sense. The annular spherical shells are reinforced by eccentrically longitudinal and transversal stiffeners made of full metal or full ceramic depending on situation of stiffeners at metal-rich side or ceramic-rich side of the shell respectively. Approximate solutions are assumed to satisfy the simply supported boundary condition and Galerkin method is applied to obtain closed-form relations of bifurcation type of buckling loads. Numerical results are given to evaluate effects of inhomogeneous, dimensional parameters, outside stiffeners and elastic foundations to the buckling of structures.

Non-linear buckling analysis of functionally graded shallow spherical shells

In the present paper the non-linear buckling analysis of functionally graded spherical shells subjected to external pressure is investigated. The material properties are graded in the t hickness direction according to the power-law distribution in terms of volume fractions of the constituents of the material. In t he formulation of governing equations geometric non-linearity in all strain-displacement relations of the shell is considered. Using Bubnov-Galerkins method to solve the problem an approximated analytical expression of non-linear buckling loads of functionally graded spherical shells is obtained , that allows easily to investigate stability behaviors of the shell.

Nonlinear Post-Buckling of Thin FGM Annular Spherical Shells Under Mechanical Loads and Resting on Elastic Foundations

This paper presents an analytical approach to investigate the nonlinear buckling and post-buckling of thin annular spherical shells made of functionally graded materials (FGM) and subjected to mechanical load and resting on Winkler-Pasternak type elastic foundations. Material properties are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Equilibrium and compatibility equations for annular spherical shells are derived by using the classical thin shell theory in terms of the shell deflection and the stress function. Approximate analytical solutions are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain closed-form of load-deflection paths. An analysis is carried out to show the effects of material and geometrical properties and combination of loads on the stability of the annular spherical shells.

A coupling successive approximation method for solving Duffing equation and its application

The paper proposes an algorithm to solve a general Duffing equation, in which a process of transforming the initial equation to a resulting equation is proposed, and then the coupling successive approximation method is applied to solve the resulting equation. By using this algorithm a special physical factor and complex-valued solutions to the general Duffing equation are revealed. The proposed algorithm does not use any assumption of small parameters in the equation solving. The coupling successive procedure provides an analytic approximated solution in both real-valued or complex-valued solution. The procedure also reveals a formula to evaluate the vibration frequency, φ, of the non-linear equation. Since the first approximation solution is in a closed-form, the chaos index of the general Duffing equation and the chaotic characteristics of solutions can be predicted. Some examples are used to illustrate the proposed method. In the case of chaotic solution, the Pointcaré conjecture is used for solution verification.

Non-linear analysis on stability of corrugated cross-ply laminated composite plates

In the present paper the governing equations for corrugated cross-ply laminated composite plates in the form of a sine wave are developed based on the Kirchoff-Loves theory and the extension of Seydel s technique. By using Bubnov-Galerkin method approximated analytical solutions to the non-linear stability problem of corrugated laminated composite plates subjected to biaxial loads are investigated. The post buckling load-deflection curve of corrugated plates and analytical expressions of the upper and lower buckling loads are presented. The effectiveness of corrugated plates in enhancing the stability compared with corresponding fiat plates is given.

Parametric conditions and exact solution for the Duffing-Van der Pol class of equations

This paper presents a methodology to find the exact solution and respective parametric conditions to the Duffing-Van der Pol class of equations. The supposed method in this paper is different from the Prelle and Singer method and the Lie symmetry method. The main idea of the supposed method is implemented in finding the first integrals of the original equation and leading this equation to a solved equation of lower order to which the exact solution can be obtained. As results the parametric conditions and the exact solutions in parametric forms are indicated. The algorithm for determining integral constants and the investigation of solution characteristics are considered.