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- MakaleYayıncıda açık erişim2018Scopus SJRQ2Finite difference method for bitsadze-samarskii type overdetermined elliptic problem with dirichlet conditions
Ashyralyyev, Charyyar; Akyuz, Gulzipa
In this paper, we apply finite difference method to Bitsadze-Samarskii type overdetermined elliptic problem with Dirichlet conditions. Stability, coercive stability inequalities for solution of the first and second order of accuracy difference schemes (ADSs) are proved. Then, established abstract results are applied to get stable difference schemes for Bitsadze-Samarskii type overdetermined elliptic multidimensional differential problems with multipoint nonlocal boundary conditions. Finally, numerical results with explanation on the realization in two dimensional and three dimensional cases are presented.
AtıfScopus10WoS7OpenAlex11
İncele - MakaleAçık Erişim2017Scopus SJRQ3A fourth order approximation of the neumann type overdetermined elliptic problem
Ashyralyyev, Charyyar
In this paper, we consider an inverse elliptic problem with Neumann type overdetermination and construct a fourth order of accuracy difference scheme for its solution. Stability, almost coercive stability and coercive stability estimates for the solution of difference problem are proved. Later, we construct a fourth order difference scheme for an inverse problem for multidimensional elliptic equation with Neumann type overdetermination and Dirichlet boundary condition. Finally, we illustrate numerical example with descriptions of numeric realization in a two-dimensional case.
AtıfScopus19WoS12OpenAlex17İncele - MakaleYalnız künye2010Scopus SJRQ3Optimum design of planar beams based on sensitivity analysis
Uysal, H.; Asci Demiröz, N.; Uzman, U.
In this study, the size optimization problem of a beam, in which the beam heights are determined along the beam axis, is considered as a shape optimization problem of a plate in plane elasticity. To achieve the shape optimization, different principles such as structural analysis, sensitivity analysis and mathematical programming are interrelated. The ANSYS that is a reliable finite element package programme is used only for the static analysis. The objective of this optimization problem is to minimize the volume of the beam under the constraints that the maximum value of the von Mises stress in each node do not exceed a predefined value and the beam axis is to remain straight. Design variables are the vertical coordinates of the corner nodal points of design elements. The design sensitivities are calculated through the finite, difference method and linear programming technique is used for obtaining the final shape of a beam. Several examples are solved under different loadings and boundary conditions. The obtained optimum beam volumes and the design variables are given in tables and the optimum beam shapes are plotted. One of the results given is compared with the literature.