Functionally graded materials (FGM) belong to advanced composite materials class whose mechanical properties vary continuously from one surface to another at macro level. Thick walled annular structures are widely used in industry as nuclear reactors, long pipes used for carrying gases/oil, pressure vessels etc. Elastic analysis of FG thick walled cylindrical and spherical pressure vessels subjected only to internal pressure are studied. The material properties (Young' s modulus-Poisson' s ratio) are assumed to obey the power-law function through the wall thickness. Under these assumptions the governing equations of the FG vessels become a two-point boundary value problem. The analytical solution of such an equation can not be obtained except for simple grading functions. Complementary Functions Method is performed to solve governing equation in order to obtain displacement and stress distributions depending on inhomogeneity parameters.

In this paper, an elastic analysis of a thick-walled functionally graded cylinder subjected to internal pressure is examined. Material properties for the isotropic material are estimated to obey the Mori-Tanaka homogenization scheme through the thickness. The resulting two-point irregular boundary value problem is solved by the pseudospectral Chebyshev method that converts the boundary value problem to the system of equations, which can be solved by any appropriate decomposition method. Benchmark solutions are used to validate the method. The effect of the arbitrarily chosen volume fraction index is demonstrated for stress and displacement distributions. The effective stresses for different inner radius and volume fraction index are also discussed.

Purpose This paper aims to present thermal and mechanical stresses in solid and hollow thick-walled cylinders and spheres made of functionally graded materials (FGMs) under the effect of heat generation. Design/methodology/approach Constant internal temperature and convective external conditions in hollow bodies along with internal heat generation with a combination of outer convective conditions in solid bodies are investigated individually. The effect of the heat convection coefficient on solid bodies is additionally discussed. The variation of the FGM properties in the radial direction is adapted to the Mori–Tanaka homogenization schemes, which produces irregular and two-point linear boundary value problems that are numerically solved by the pseudospectral Chebyshev method. Findings It has been shown that the selection of the mixtures of FGMs has to be made correctly to keep the thermal and mechanical loads acting on objects at low levels. Originality/value In this study, both solid and hollow functionally graded cylinders and spheres for different boundary conditions that are as their engineering applications are examined with the proposed method. The results have demonstrated that the pseudospectral Chebyshev method has high accuracy, low calculation costs and ease of application and can be easily adapted to such engineering problems.

ÖzSürekli sistem olarak modellenen eksenel yüklenmiş heterojen bir çubuğun elastik davranış problemi analiz edilmiştir. Bu problemi modelleyen diferansiyel denklemlere Laplace dönüşümü uygulanarak zamandan bağımsız sınır değer problemi eksenel koordinatlarda elde edilmiş daha sonra bu problem tamamlayıcı fonksiyonlar metodu (TFM) tarafından çözülmüştür. Sayısal olarak çözülen denklemler Durbin'in sayısal ters dönüşümünü yardımıyla zaman uzayına dönüştürülmüştür. Her bir yükleme tipi ve inhomojenlik parametresi için elde edilen sayısal sonuçlar, analitik sonuçlar ve ANSYS sonuçları ile karşılaştırılmıştır. Bu birleşik yöntem, iyi yapılandırılmış, basit ve etkili bir yöntemdir.Anahtar Kelimeler: Heterojen çubuk, Zorlanmış titreşim, Laplace, Tamamlayıcı fonksiyonlar yöntemi Forced Vibration Analysis of A Heterogeneous Rod by Complementary Functions Method AbstractThe axial vibration problem formulation and solution of a heterogeneous rod modelled as a continuous system were analyzed. By applying Laplace transformation to the differential equations that model to this problem, time independent boundary value problems were obtained in the axial coordinates, then this problem is solved by the complementary functions method. The equations solved numerically is converted into time space with the help of Durbin's numerical inverse transformation. The numerical results that obtained for each load type and inhomogeneity parameter were compared with analytical and ANSYS results in the literature. This unified method is well-structured, simple and efficient.

Bu çalışmada, mekanik ve ısıl özelliklerinin radyal eksen boyunca üstel bir fonksiyonla değiştiği varsayılan, eksenel simetrik, ince, dikdörtgen profilli dairesel bir kanatçıktaki sıcaklık dağılımı ve sıcaklık farklarından dolayı oluşan ısıl gerilmeler, pseudospectral Chebysev ve sonlu elemanlar yöntemleri ile ele alınmıştır. Chebyshev yöntemin doğruluğu literatürde mevcut analitik çözümle karşılaştırılarak test edilmiştir. Kanatçık, ZrO_2/Ti-6Al-4V malzeme çifti ile derecelendirilmiş, uygulanan sınır koşulları altında sıcaklık dağılımı ve ısıl gerilmeler elde edilmiştir. Problem, pseudospektral Chebyshev ve sonlu elemanlar yöntemleri ile ayrı ayrı çözülmüş ve elde edilen sonuçlar grafiksel olarak karşılaştırılmıştır. Pseudospektral Chebyshev yönteminin sonlu elamanlar yöntemine göre daha az nokta sayısı ile yakın sonuçlar verdiği gözlemlenmiştir.