Thermo-elastic/plastic semi-analytical solution of incompressible functionally graded spherical pressure vessel under thermo-mechanical loading

In this paper, numerical solutions to assess partially plastic and fully plastic deformation behavior of a functionally graded spherical pressure vessel are presented. The modulus of elasticity of the material is assumed to vary nonlinearly in the radial direction and axisymmetric displacements and stresses in the functionally graded spherical vessel subjected to thermal loading and uniform internal pressure are determined using plasticity theory. Tresca??s yield criterion and its associated flow rule are used to formulate different plastic regions for an ideal FG material. In this way, the material property varies by Young??s modulus that may be an arbitrary function of the radial coordinate. Therefore, the material is assumed to be functionally graded in the radial direction. Hence, the general analytical solutions of such equations are not available, the numerical method (semi-analytical) is applied and a new collection of equilibrium equations with small deflections is presented. Accordingly, the radial domain is divided into some virtual sub-domains in which the power-law distribution is used for the thermomechanical properties of the elemental components. By considering the necessary continuity conditions between adjacent sub-domains, jointly with the global boundary conditions, a set of linear differential equations is obtained. Solution of the linear differential equations yields the thermoelastic responses for each sub-domain as exponential functions of the radial coordinate. Subsequently, attributed to centrifugal force, results for the stress, strain, and displacement components along the radius in elastic and plastic area are presented.     

Stability analysis of an electrostatically actuated out of plane MEMS structure

In the present research, stability and static analyses of microelectromechanical systems microstructure were investigated by presenting an out-of-plane structure for a lumped mass. The presented model consists of two stationary electrodes in the same plane along with a flexible electrode above and in the middle of the two electrodes. The nonlinear electrostatic force was valuated via numerical methods implemented in COMSOL software where three-dimensional simulations were performed for different gaps. The obtained numerical results were compared to those of previous research works, indicating a good agreement. Continuing with the research, curves of electrostatic and spring forces were demonstrated for different scenarios, with the intersection points (i.e., equilibrium points) further plotted. Also drawn were plots of deflection versus voltage for different cases and phase and time history curves for different values of applied voltage followed by introducing and explaining pull-in and pull-out snap-through voltages in the system for a specific design. It is worth noting that, at voltages between the pull-in and pull-out snap-through voltages, the system was in bi-stable state. Based on the obtained results, it was observed that the gap between the two electrodes and the applied voltage play significant roles in the number and type of the equilibrium points of the system.