Vibration of completely free composite plates and cylindrical shell panels by a higher-order theory

This paper deals with the free vibration of open, laminated composite, circular cylindrical panels having a rectangular plan-form and all their edges free of external tractions. The material arrangement of the shell panels considered may vary from this of the single isotropic (or special orthotropic) layer to that of a general angle-ply lay-up. The analysis is based on the application of the Ritz approach on the energy functional of the Love-type version of a unified shear deformable shell theory. A through-thickness parabolic distribution of the transverse shear deformation is mainly assumed but, for comparison purposes, numerical results that are based on the assumptions of the classical Love-type shell theory are also presented. The Ritz method is a powerful analytical technique since, provided that a complete set of trial functions is employed, it can provide the exact solution of the problem considered in infinite series forms. The mathematical formulation is therefore presented in a general form, appropriate for any set of basis functions. The variational approach is, however, finally applied in conjunction with a complete functional basis made of the appropriate admissible orthonormal polynomials.     

Free vibration of laminated composite plates using two variable refined plate theory

Free vibration of laminated composite plates using two variable refined plate theory is presented in this paper. The theory accounts for parabolic distribution of the transverse shear strains through the plate thickness, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Equations of motion are derived from the Hamilton's principle. The Navier technique is employed to obtain the closed-form solutions of antisymmetric cross-ply and angle-ply laminates. Numerical results obtained using present theory are compared with three-dimensional elasticity solutions and those computed using the first-order and the other higher-order theories. It can be concluded that the proposed theory is not only accurate but also efficient in predicting the natural frequencies of laminated composite plates.     

Stiffness identification of laminated composite shafts

Distributions of bending stiffness along the spans of laminated composite shafts are determined via a non-destructive evaluation approach. The finite element method formulated on the assumption of uniform bending stiffness within each element is used in the deflection analysis of the shafts. Differences between measured and theoretically predicted deflections at any two points on a shaft are used to construct an error function for deflection. The identification of bending stiffness is formulated as a minimization problem in which the elemental bending stiffness are determined to make the error function a global minimum. A global minimization technique and a bounding method for establishing side constraints are presented to solve the above minimization problem. Experiments are performed to study the feasibility and applications of the proposed method.     

Dynamic stability of cross-ply laminated composite cylindrical shells

The dynamic stability of thin, laminated cylindrical shells under combined static and periodic axial forces is studied using Love’s classical theory of thin shells. A normal-mode expansion of the equations of motion yields a system of Mathieu–Hill equations. Bolotin’s method is then employed to obtain the dynamic instability regions. The present study examines the dynamic stability of antisymmetric cross-ply circular, cylindrical shells of different lamination schemes. The effect of the magnitude of the axial load on the instability regions is also examined.     

Vibration of functionally graded cylindrical shells

Functionally gradient materials (FGMs) have attracted much attention as advanced structural materials because of their heat-resistance properties. In this paper, a study on the vibration of cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of configurations of the constituent materials on the frequencies. The properties are graded in the thickness direction according to a volume fraction power-law distribution. The results show that the frequency characteristics are similar to that observed for homogeneous isotropic cylindrical shells and the frequencies are affected by the constituent volume fractions and the configurations of the constituent materials. The analysis is carried out with strains–displacement relations from Love’s shell theory and the eigenvalue governing equation is obtained using Rayleigh–Ritz method. The present analysis is validated by comparing results with those in the literature.     

Transverse vibration of a circular plate with arbitrary thickness variation

Rayleigh-Ritz method has been employed to obtain approximations to frequencies and mode shapes of circular plates with variable thickness. The boundary is either clamped, simply supported or completely free. The main distinguishing feature of the present investigations is that the thickness approximation is done by measuring thickness at a suitable set of sample points and then using interpolation to get the approximating polynomial. Thus, unlike other methods already available in literature where either linear or quadratic variation of thickness has been examined, here one can have a polynomial of arbitrary degree depending upon the number and locations of the sample points. The results have been tabulated in a large number of cases and three-dimensional mode shapes have been plotted for some selected cases. Comparison has been made with available results. A short tables are also given to depict the rate of convergence with the order of approximation.     

Analysis of annular Reissner/Mindlin plates using differential quadrature method

The axisymmetric flexure responses of moderately thick annular plates under static loading are investigated. The shear deformation is considered using the first-order Reissner/Mindlin plate theory and the solutions are obtained using the differential quadrature (DQ) method. In the solution process, the governing differential equations and boundary conditions for the problem are initially discretized by the DQ algorithm into a set of linear algebraic equations. The solutions of the problem are then determined by solving the set of algebraic equations. This study considers the plate subjected to various combinations of clamped, simply-supported, free and guided boundary conditions and different loading manners. The accuracy of the method is demonstrated through direct comparison of the present results with the corresponding exact solutions available in the literature.     

Forced axisymmetric response of an annular plate of parabolically varying thickness

Forced axisymmetric response of an annular plate of parabolically varying thickness, based on classical theory, is analyzed by the eigenfunction method. Plate subjected to constant and half-sine pulse loads uniformly distributed over an annular portion of the plate for various combination of boundary conditions are taken as example problems. Numerical results computed for the transverse deflection are plotted in graphs.     

Finite-element simulation of the lateral compression of aluminium tube between rigid plates

The lateral compression of aluminium and clad tubes owing to a large deformation is examined by an incremental elasto-plastic finite-element method based on an updated Lagrangian formulation in which a sliding-sticking friction mode is specially considered. It is mainly expected to predict the buckling process and load–deflection curves for energy dissipation capacity during the design stage, before trials. The high non-linearity of the process due to geometric changes, the inelastic constitutive behavior, and the deformation-dependent boundary conditions are taken into account in an incremental manner. A static explicit approach to the solution is applied, tangent stiffness matrix equation is solved without iteration and the r_min technique is employed to limit the step size to linear relation. The simulated load–deflection curve agrees with a published experimental result. The predicted geometries of the compressed tube clearly demonstrate the processes of the formation of buckling until unloading. The effects of various parameters of the process, such as elastic modulus, strain hardening exponent, tube thickness, friction coefficient and configurations of the clad tube, on the occurrence of buckling of tube are discussed and interpreted in simulation. The present work may be expected to improve the understanding of the buckling mechanism of lateral compression.