Journal of Solid Mechanics
Volume:2 Issue: 2, Spring 2010

In this paper, a comparison of weak-form Galerkin and least-squares finite element models of Timoshenko beam theory with the von Kármán strains is presented. Computational characteristics of the two models and the influence of the polynomial orders used on the relative accuracies of the two models are discussed. The degree of approximation functions used varied from linear to the 5th order. In the linear analysis, numerical results of beam bending under different types of boundary conditions are presented along with exact solutions to investigate the degree of shear locking in the newly developed mixed finite element models. In the nonlinear analysis, convergences of nonlinear finite element solutions of newly developed mixed finite element models are presented along with those of existing traditional model to compare the performance.

Time-dependent creep stress redistribution analysis of thick-walled FGM spheres subjected to an internal pressure and a uniform temperature field is investigated. The material creep and mechanical properties through the radial graded direction are assumed to obey the simple power-law variation throughout the thickness. Total strains are assumed to be the sum of elastic, thermal and creep strains. Creep strains are time temperature and stress dependent. Using equations of equilibrium, compatibility and stress-strain relations a differential equation, containing creep strains, for radial stress is obtained. Ignoring creep strains in this differential equation, a closed form solution for initial thermo-elastic stresses at zero time is presented. Initial thermo-elastic stresses are illustrated for different material properties. Using Prandtl-Reuss relation in conjunction with the above differential equation and the Norton’s law for the material uni-axial creep constitutive model, radial and tangential creep stress rates are obtained. These creep stress rates are containing integrals of effective stress and are evaluated numerically. Creep stress rates are plotted against dimensionless radius for different material properties. Using creep stress rates, stress redistributions are calculated iteratively using thermo-elastic stresses as initial values for stress redistributions. It has been found that radial stress redistributions are not significant for different material properties. However, major redistributions occur for tangential and effective stresses.

In this paper, the classic coupled poro-thermoelasticity model of hollow and solid cylinders under radial symmetric loading condition is considered. A full analytical method is used and an exact unique solution of the classic coupled equations is presented. The thermal and pressure boundary conditions, the body force, the heat source and the injected volume rate per unit volume of a distribute water source are considered in the most general forms and no limiting assumption is used. This generality allows simulation of several of the applicable problems.

In this paper, a radially piezoelectric functionally graded rotating disk is investigated by the analytical solution. The variation of material properties is assumed to follow a power law along the radial direction of the disk. Two resulting fully coupled differential equations in terms of the displacement and electric potential are solved directly. Numerical results for different profiles of inhomogeneity are also graphically displayed.

This paper investigates symmetrical buckling of orthotropic circular and annular plates of continuous variable thickness. Uniform compression loading is applied at the plate outer boundary. Thickness varies linearly along radial direction. Inner edge is free, while outer edge has different boundary conditions: clamped, simply and elastically restraint against rotation. The optimized Ritz method is applied for buckling analysis. In this method, a polynomial function that is based on static deformation of orthotropic circular plates in bending is used. Also, by employing an exponential parameter in deformation function, eigenvalue is minimized in respect to this parameter. The advantage of this procedure is simplicity, in comparison with other methods, while whole algorithm for solution can be coded for computer programming. The effects of variation of radius, thickness, different boundary conditions, ratio of radial Young modulus to circumferential one, and ratio of outer radius to inner one in annular plates on buckling load factor are investigated. The obtained results show that in plate with identical thickness, increasing of outer radius decreases the buckling load factor. Moreover, increase of thickness of the plates results in increase of buckling load factor.

In this article, the magneto-thermo-elastic problem of exponentially graded material (EGM) hollow rotating disk placed in uniform magnetic and temperature fields is considered. Exact solutions for stresses and perturbations of the magnetic field vector in EGM hollow rotating disk are determined using the infinitesimal theory of magneto-thermo-elasticity under plane stress. The material properties, except Poisson’s ratio, are assumed to depend on variable of the radius and they are expressed as exponential functions of radius. The direct method is used to solve the heat conduction and Hyper-geometric functions are employed to solve Navier equation.The temperature, displacement, and stress fields and the perturbationof the magnetic field vector are determined and compared with those of the homogeneous case. Hence, the effectof in-homogeneity on the stresses and the perturbation of magnetic field vector distribution are demonstrated. The results of this study are applicable for designing optimum EGM hollow rotating disk.© 2010IAU, Arak Branch. All rights reserved.

In this research, a functionally graded microbeam bonded with piezoelectric layers is analyzed under electric force. Static and dynamic instability due to the electric actuation is studied because of its importance in micro electro mechanical systems, especially in micro switches. In order to prevent pull-in instability, two piezoelectric layers are used as sensor and actuator. A current amplifier is used to supply input voltage of the actuator from the output of the sensor layer. Using Hamilton’s principle and Euler-Bernoulli theory, equation of motion of the system is obtained. It is shown that the load type (distributed or concentrated) applied to the micro beam from the piezoelectric layer, depends on the shape of the actuator layer (E.g. rectangle, triangular). Finite element method is implemented for evaluation of displacement field in the micro beam and dynamic response of the micro beam under electric force is calculated using finite difference method. Effect of squeeze film damping on pull-in voltage and time-response of the system is considered using nonlinear Reynolds equation. Effect of several parameters such as gain value between piezoelectric sensor and actuator layer, profile of functionally material, and geometry of the system is considered on dynamic behavior of the micro beam especially on pull-in instability. Results are verified for simple cases with previous related studies in the literature and good agreements were achieved. Results indicate that increasing gain value between sensor and actuator enhances stiffness of the system and will raise pull-in voltage. Also, dependency of dynamic properties of the system such as amplitude and frequency of vibration on functionally graded material profile is shown. The material distribution of the functionally graded material is designed in such a way that results in a specific pull-in voltage.

Embryogenesis, regeneration and cell differentiation in microbiological entities are influenced by mechanical forces. Therefore, development of mechanical properties of these materials is important. Neural network technique is a useful method which can be used to obtain cell deformation by the means of force-geometric deformation data or vice versa. Prior to insertion in the needle injection process, deformation and geometry of cell under external point-load is a key element to understand the interaction between cell and needle. In this paper, the goal is the prediction of cell membrane deformation under a certain force and to visually estimate the force of indentation on the membrane from membrane geometries. The neural network input and output parameters are associated to a three dimensional model without the assumption of the adherent affects. The neural network is modeled by applying error back propagation algorithm. In order to validate the strength of the developed neural network model, the results are compared with the experimental data on mouse oocyte and mouse embryos that are captured from literature. The results of the modeling match nicely the experimental findings.