Journal of Solid Mechanics
Volume:4 Issue: 3, Summer 2012

In this research, residual strength and stress concentration factor of laminated composites with a circular open hole are studied analytically, numerically and experimentally. The numerical study was carried out using the finite element method. Moreover an analytical study was carried out with developing of point stress criterion. Mechanical testing was performed to determine the un-notched tensile properties and notched strength of composite laminates and characteristic length to reinforcement of the notched strength of composite laminates are determined. Results show that the influence of specimen dimension, notch size, lay ups and material properties are important on residual strength and stress concentration factor of laminated composite materials.

Using the infinitesimal theory of elasticity and analytical formulation, displacements and stresses based on the high-order shear deformation theory (HSDT) is presented for axisymmetric thick-walled cylinders made of functionally graded materials under internal and/or external uniform pressure. The material is assumed to be isotropic heterogeneous with constant Poisson’s ratio and radially varying elastic modulus continuously along the thickness with a power function. At first, general governing equations of the FGM thick cylinders are derived by assumptions of the high-order shear deformation theory. Following that, the set of non-homogenous linear differential equations with constant coefficients, for the cylinder under the generalized clamped-clamped conditions have been solved analytically and the effect of loading and inhomogeneity on the stresses and displacements have been investigated. The results are compared with the findings of both first-order shear deformation theory (FSDT) and finite element method (FEM). Finally, the effects of higher order approximations on the stresses and displacements have been studied.

The effect of magnetic field on torsional waves propagating in non-homogeneous viscoelastic cylindrically aeolotropic material is discussed. The elastic constants and non-homogeneity in viscoelastic medium in terms of density and elastic constant is taken. The frequency equations have been derived in the form of a determinant involving Bessel functions. Dispersion equation in each case has been derived and the graphs have been plotted showing the effect of variation of elastic constants and the presence of magnetic field. The obtained dispersion equations are in agreement with the classical result. The numerical calculations have been presented graphically by using MATLAB.

Using harmonic differential quadrature (HDQ) method, nonlinear vibrations and instability of a smart composite cylindrical shell made from piezoelectric polymer of polyvinylidene fluoride (PVDF) reinforced with boron nitride nanotubes (BNNTs) are investigated while clamped at both ends and subjected to combined electro-thermo-mechanical loads and conveying a viscous-fluid. The mathematical modeling of the cylindrical shell and the resulting nonlinear coupling governing equations between mechanical and electrical fields are derived using Hamilton’s principle based on the first-order shear deformation theory (FSDT) in conjunction with the Donnell's non-linear shallow shell theory. The governing equations are discretized via HDQ method, and solved to obtain the resonant frequencies and critical flow velocities associated with divergence and flutter instabilities as well as re-stabilization of the system. Results indicate that the internal moving fluid plays an important role in the instability of the cylindrical shell. Application of a smart material such as PVDF improves significantly the stability and vibration of the system.

In this paper, dynamic behavior of a functionally graded cantilever micro-beam and its pull-in instability, subjected to simultaneous effects of a thermal moment and nonlinear electrostatic pressure, has been studied. It has been assumed that the top surface is made of pure metal and the bottom surface from a metal–ceramic mixture. The ceramic constituent percent of the bottom surface ranges from 0% to 100%. Along with the Volume Fractional Rule of material, an exponential function has been applied to represent the continuous gradation of the material properties through the micro-beam thickness. Attentions being paid to the ceramic constituent percent of the bottom surface, five different types of FGM micro-beams have been studied. Nonlinear integro-differential thermo-electro-mechanical equation based on Euler–Bernoulli beam theory has been derived. The governing equation in the static case has been solved using Step-by-Step Linearization Method and Finite Difference Method. Fixed points or equilibrium positions and singular points of the FGM micro-beam have been determined and shown in the state control space. In order to study stability of the fixed points, beam motion trajectories have been drawn, with different initial conditions, in the phase plane. In order to find the response of the micro-beam to a step DC voltage, the nonlinear equation of motion has been solved using Galerkin-based reduced-order model and time histories and phase portrait for different applied voltages and various primal temperatures have been illustrated. The effects of temperature change and electrostatic pressure on the deflection and stability of FGM micro-beams having various amounts of the ceramic constituent have been studied.

Using principle of minimum total potential energy approach in conjunction with Rayleigh-Ritz method, the electro-thermo-mechanical axial buckling behavior of piezoelectric polymeric cylindrical shell reinforced with double-walled boron-nitride nanotube (DWBNNT) is investigated. Coupling between electrical and mechanical fields are considered according to a representative volume element (RVE)-based micromechanical model. This study indicates how buckling resistance of composite cylindrical shell may vary by applying thermal and electrical loads. Applying the reverse voltage or decreasing the temperature, also, increases the critical axial buckling load. This work showed that the piezoelectric BNNT generally enhances the buckling resistance of the composite cylindrical shell.

In this paper, transverse vibrations of thin circular plates with guided edge and resting on Winkler foundation have been studied on the basis of Classical Plate Theory. Parametric investigations on the vibration of circular plates resting on elastic foundation have been carried out with respect to various foundation stiffness parameters. Twelve vibration modes are presented. The location of the stepped region with respect to foundation stiffness parameter is presented.

In the present paper, time dependent creep behavior of hollow circular rotating cylinders made of exponentially graded material (EGM) is investigated. Loading is composed of an internal pressure, a distributed temperature field due to steady state heat conduction with convective boundary condition and a centrifugal body force. All the material properties are assumed to be exponentially graded along radius. A semi analytical solution followed by the method of successive approximation has been developed to obtain history of stresses and deformations during creep evolution of the EGM rotating cylinder. The material creep constitutive model is defined by the Bailey-Norton time-dependent creep law. A comprehensive comparison has been made between creep response of homogenous and non-homogenous cylinder. It has been found that the material in-homogeneity exponent has a significant effect on creep response of the EGM cylinder. It has been concluded that using exponentially graded material significantly decreases creep strains, stresses and deformations of the EGM rotating cylinder.