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Öğe A shear deformable numerical approaches for the static analysis of bi-directional functionally graded beams(Techno-Press, 2025) Turan, Muhittin; Kahya, Volkan; Yaylaci, Ecren Uzun; Yaylaci, MuratThis paper introduces a highly accurate and computationally efficient shear deformable finite element model for the static analysis of bi-directional functionally graded beams (BD-FGBs) with various boundary conditions grounded in the first- order shear deformation theory (FSDT). The model, featuring ten degrees of freedom across five nodes, excels in capturing both axial and shear deformations with remarkable precision while maintaining a streamlined formulation. In a novel approach, Artificial Neural Network (ANN) methods are also employed alongside the finite element analysis, offering a dual-method investigation into the static behavior of BD-FGBs. This paper aims to further advance the understanding of BD-FGM beams by exploring their static behavior under diverse loading conditions and boundary constraints, employing advanced finite element methods and artificial neural network techniques. The material properties are modeled through power-law distributions, and the governing equations are derived from Lagrange's principle. Displacements and stresses were computed under different boundary conditions (BCs), slenderness ratios (L/h), and power-law indices (px, pz). Comparative analysis with existing literature reveals the superior suitability of the proposed finite element model for static analysis, while the ANN approach further reinforces its potential as a robust, complementary tool. The innovative combination of these methods promises to offer significant contributions to the field and provides new insights into the behavior of BD-FGBs under static loads.Öğe Fonksiyonel Derecelendirilmiş Kirişlerin Serbest Titreşim Analizi(Giresun Üniversitesi, 2018) Turan, Muhittin; Kahya, VolkanBu çalışmada, birinci mertebe kayma deformasyonu teorisine dayalı olarak fonksiyonel derecelendirilmiş kirişlerin serbest titreşim analizi Navier tipi çözüm yöntemi kullanılarak yapılmıştır. Hareket denklemleri Lagrange eşitlikleri ile türetilmiş, problemin çözümünde ise trigonometrik fonksiyonlar kullanılmıştır. Farklı sınır şartlarına, hacimsel oran fonksiyonunun farklı k değerlerine ve kirişin açıklığının yüksekliğine oranına bağlı olarak doğal frekanslar sayısal olarak hesaplanmıştır. Sayısal sonuçlar literatürle kıyaslanmış ve oldukça uyumlu oldukları görülmüştür.Öğe Free vibration and buckling analysis of functionally graded sandwich beams by Navier's method(Gazi Univ, Fac Engineering Architecture, 2021) Turan, Muhittin; Kahya, VolkanIn this study, free vibration and buckling analyses of functionally graded (FGM) sandwich beams is investigated by Navier's method. Displacement field is defined according to the first order shear deformation theory, and the equations of motion are derived by the Lagrange's principle. Volumetric ceramic ratio is defined by a power-law rule. In the analytical solution, different trigonometric series functions are used for each end conditions considered. Two cases of functionally graded sandwich beams are considered: a) Homogeneous ceramic core and FGM faces (Type A), and b) FGM core and homogeneous faces (Type B). Natural frequencies and buckling loads are obtained for different boundary conditions, power-law indices and slenderness. Numerical results are compared with the available literature, and a good agreement are obtained between the results.Öğe Use of trigonometric series functions in free vibration analysis of laminated composite beams(2020) Turan, Muhittin; Kahya, VolkanIn this study, free vibration analysis of layered composite beams is performed by using an analytical method based on trigonometric series. Based on the first-ordershear deformation beam theory, the governing equations are derived from the Lagrange’s equations. Appropriate trigonometric series functions are selected to satisfythe end conditions of the beam. Navier-type solution is used to obtain natural frequencies. Natural frequencies are calculated for different end conditions and laminastacking. It was seen that the slenderness, E11/E22 and fiber angle have a significanteffect on natural frequency. The results of the study are quite compatible with theliterature.












