Çiğdem Demir

Discrete singular convolution approach for buckling analysis of rectangular Kirchhoff plates subjected to compressive loads on two-opposite edges

Buckling analysis of rectangular plates subjected to various in-plane compressive loads using Kirchhoff plate theory is presented. The method of discrete singular convolution has adopted. Linearly varying, uniform and non-uniform distributed load conditions are considered on two-opposite edges for buckling. The results are obtained for different types of boundary conditions and aspect ratios. Comparisons are made with existing numerical and analytical solutions in the literature. The proposed method is suitable for the problem considered due to its simplicity, and potential for further development.

A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method

A size dependent finite element model is developed.Nonlocal elasticity theory is used.Finite element solution is presented for buckling of microtubules.The effect of elastic matrix surrounded by microtubules is modeled. A simple nonlocal beam model is proposed to study buckling response of protein microtubules. The size-effect for buckling model of microtubules is considered by using the nonlocal continuum theory. Finite element procedure is used for solution of nonlocal differential equation of microtubules for elastic stability. The influence of the small length scale on the buckling value is examined for different geometric parameters. The effect of elastic matrix surrounded of microtubules is also examined and some benchmark results are presented.

Vibration analysis of FG cylindrical shells with power-law index using discrete singular convolution technique

Abstract In the present manuscript, free vibration response of circular cylindrical shells with functionally graded material (FGM) is investigated. The method of discrete singular convolution (DSC) is used for numerical solution of the related governing equation of motion of FGM cylindrical shell. The constitutive relations are based on the Love’s first approximation shell theory. The material properties are graded in the thickness direction according to a volume fraction power law indexes. Frequency values are calculated for different types of boundary conditions, material and geometric parameters. In general, close agreement between the obtained results and those of other researchers has been found.

Free vibration analysis of annular sector plates via conical shell equations

Abstract In this paper, free vibration analysis of annular sector plates has been presented via conical shell equations. By using the first-order shear deformation theory (FSDT) equation of motion of conical shell is obtained. The method of discrete singular convolution (DSC) and method differential quadrature (DQ) are used for solution of the vibration problem of annular plates for some special value of semi-vertex angle via conical shell equation. The obtained numerical results based on the two numerical approaches for annular sector plates compare well with the results available in the literature. The effects of some geometric parameters, grid numbers and types of the grid distribution have been discussed for curved plates.