Beytullah Temel

Quasi-static and dynamic response of viscoelastic helical rods

In this study, the dynamic behaviour of cylindrical helical rods made of linear viscoelastic materials are investigated in the Laplace domain. The governing equations for naturally twisted and curved spatial rods obtained using the Timoshenko beam theory are rewritten for cylindrical helical rods. The curvature of the rod axis, effect of rotary inertia, and shear and axial deformations are considered in the formulation. The material of the rod is assumed to be homogeneous, isotropic and linear viscoelastic. In the viscoelastic material case, according to the correspondence principle, the material constants are replaced with their complex counterparts in the Laplace domain. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method to calculate the dynamic stiffness matrix of the problem. In the solutions, the Kelvin model is employed. The solutions obtained are transformed to the real space using the Durbins numerical inverse Laplace transform method. Numerical results for quasi-static and dynamic response of viscoelastic models are presented in the form of graphics.

An Efficient Unified Method for Thermoelastic Analysis of Functionally Graded Rotating Disks of Variable Thickness

Thermoelastic analysis of functionally-graded nonuniform rotating disks subjected to nonuniform change in temperature essentially requires solutions of two-point-boundary-value problems. Spatial variations of thermomechanical properties, thickness, and temperature change constitute governing differential equations with variable coefficients. Closed-form solutions to such equations can be obtained only for specific forms of grading functions. For general variations of the properties, numerical methods must be resorted to, and the complementary functions method (CFM) stands as a viable option. Infusion of CFM into the thermoelastic analysis of functionally-graded rotating disks of variable thickness is a unified novel approach; it can efficiently be used for both heat conduction problems and thermal stress analysis. Complementary functions method reduces the boundary-value problem to an initial-value problem, which can be solved accurately by one of many efficient methods, such as Runge-Kutta method. Material models available in the literature for ceramic-metal disks are used in the analysis. First, the proposed solution scheme is verified using simple closed-form solutions for a disk of uniform properties and then displacement and stresses are calculated for nonuniform heterogeneous disks. Use of CFM has given virtually exact results for few collocation points along the radius. Fifth-order Runge-Kutta method (RK5) has been employed as the numerical method.

Transient Response of FGM Pressure Vessels

The present study aims to investigate the transient behavior of thick-walled cylinders under dynamic internal pressure. Analytical solutions are possible only for simple time-dependent pressure functions. The solution procedure presented is general in the sense that the pressure applied may be an arbitrary continuous function of time, impulsive or given in a discrete form. The material considered is isotropic and heterogeneous with properties varying in the radial direction termed as Functionally Graded Material (FGM). Laplace transform method is used and the inversion into the time domain is performed using the modified Durbin’s method. Verification of the numerical procedure is performed by comparing the results with those of an analytical solution available in the literature for a simple exponentially-varying pressure. The inhomogeneity constant in the material property model is shown to have a significant effect on the transient response.