Dönen fonksiyonel dereceli polar ortotropik diskin gerilme analizi

Abstract

Bu çalışmada, zamana bağlı açısal hızla dönen bir fonksiyonel dereceli ortotropik değişken kalınlıklı diskin eksenel simetri varsayımı ve düzlem gerilme koşulları altında gerilme dağılımları sayısal olarak elde edilmiştir. Etkisi az olduğu düşünülen Poisson oranı dışındaki malzeme özelliklerinin yarıçap doğrultusunda üstel olarak değiştiği varsayılmıştır. Bu koşullar altında geleneksel yöntemlerle analitik olarak çözülmesi zor olan kısmi bir diferansiyel denklem elde edilir. Bu kısmi diferansiyel denklemin zaman bağımlılığı Laplace dönüşümü ile ortadan kaldırıldıktan sonra, radyal yöndeki çözüm pseudospektral Chebyshev yöntemi ile Laplace uzayında çözüldükten sonra, modifiye edilmiş ters Durbin yöntemi ile fiziksel uzaydaki sonuçlar elde edilmiştir. Değişken kesitli dönel diskin, farklı kesit alanları ve döndürme parametreleri için deplasman ve gerilmeleri radyal ve zaman yönünde incelenmiştir.

Keywords

• Elastik gerilmeler
• fonksiyonel dereceli ortotropik disk
• dönel disk
• pseudospektral Chebyshev yöntemi
• Laplace dönüşümü
• modifiye Durbin yötemi.

Stress analysis of a rotating functionally graded polar orthotropic disk

Abstract

In this study, the stress distributions of a functionally graded orthotropic variable-thickness disk rotating with time-dependent angular velocity are numerically obtained under axial symmetry and plane stress conditions. It is assumed that the material properties, except the Poisson's ratio, considered to have little effect, vary exponentially in the radius direction. Under these conditions, a partial differential equation, difficult to solve analytically using conventional methods, is obtained. After eliminating the time dependence of this partial differential equation with the Laplace transform, the radial solution is solved in Laplace space using the pseudospectral Chebyshev method, and the results in physical space are obtained using the modified inverse Durbin method. The displacements and stresses of the variable-cross-section rotating disk are investigated in the radial and time directions for different cross-sectional areas and rotation parameters.

Keywords

• Elastic stresses
• functionally graded orthotropic disk
• rotating disk
• pseudospectral Chebyshev method
• Laplace transforms
• modified Durbin method.

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