Tamamlayıcı Fonksiyonlar Yöntemi ile Fonksiyonel Derecelenmiş Sandviç Dairesel Plakların Eğilme Analizi

Yıl 2022, Cilt: 37 Sayı: 3, 673 - 684, 17.10.2022

Ahmad Reshad Noorı

https://doi.org/10.21605/cukurovaumfd.1190287

Öz

Bu çalışmada, Fonksiyonel Derecelenmiş (FD) malzemeli sandviç dairesel plakların eğilme davranışı teorik olarak araştırılmıştır. Malzeme özellikleri kalınlığı boyunca değişen sandviç dairesel plakların, öz tabakası veya çekirdeği izotropik homojen yüzey tabakları ise FD malzemeli olarak kabul edilmiştir. Ele alınan plakların statik davranışını idare eden denklemler Kirchhoff–Love ve Mindlin–Reissner plak teorilerine göre minimum toplam enerji prensibi yardımıyla kanonik halde elde edilmiştir. Elde edilen bu denklemlerin sayısal çözümleri için Tamamlayıcı Fonksiyonlar Yöntemi (TFY) uygulanmıştır. Bu araştırmada, malzeme değişim katsayılarının, yarıçap-kalınlık oranlarının, kayma deformasyon etkisinin ve farklı sınır koşullarının FD sandviç dairesel plakların eğilme davranışı üzerindeki etkileri parametrik olarak incelenmiştir. TFY’nin bu tür problemlere etkin bir şekilde uygulanabilirliği ve yöntemin doğruluğu, elde edilen sonuçların mevcut literatür ile karşılaştırılarak gösterilmiştir.

Anahtar Kelimeler

Sandviç dairesel plak, Tamamlayıcı fonksiyonlar yöntemi, İki noktalı sınır değer problemi, Fonksiyonel derecelenmiş malzemeler

Bending Analysis of Functionally Graded Sandwich Circular Plates via the Complementary Functions Method

Öz

In this study, the flexural response of sandwich circular plates with Functionally Graded (FG) material is investigated theoretically. The core of the sandwich circular plates, whose material properties change throughout their thickness, is considered to be isotropic homogeneous and the face sheets are assumed to be FG. The governing equations of the static behavior of the considered plates are obtained in canonical form with the aid of the minimum total energy principle based on the Kirchhoff–Love and Mindlin–Reissner plate theories. For the numerical solutions of these equations, the Complementary Functions Method (CFM) is implemented. In this research, the effects of material gradient index, radius-thickness ratios, shear deformation effects and different boundary conditions on the bending behavior of FG sandwich circular plates are parametrically investigated. The efficient applicability of the CFM to this type of problem and the accuracy of the suggested method are demonstrated by comparing the results obtained with the existing literature.

Anahtar Kelimeler

Sandwich circular plate, Complementary functions method, Two-Point boundary value problem, Functionally graded materials

Kaynakça

• 1. Ma, L.S., Wang, T.J., 2003. Nonlinear Bending and Post-buckling of a Functionally Graded Circular Plate Under Mechanical and Thermal Loadings. International Journal of Solids and Structures, 40(13-14), 3311-3330.
• 2. Jalali, S.K., Naei, M.H., Poorsolhjouy, A., 2010. Thermal Stability Analysis of Circular Functionally Graded Sandwich Plates of Variable Thickness Using Pseudo-spectral Method. Materials & Design, 31(10), 4755-4763.
• 3. Jalali, S.K., Naei, M.H., Poorsolhjouy, A., 2011. Buckling of Circular Sandwich Plates of Variable Core Thickness and FGM Face Sheets. International Journal of Structural Stability and Dynamics, 11(02), 273-295.
• 4. Alipour, M.M., Shariyat, M., 2012. An Elasticity-equilibrium-based Zigzag Theory for Axisymmetric Bending and Stress Analysis of the Functionally Graded Circular Sandwich Plates, Using a Maclaurin-type Series Solution. European Journal of Mechanics-A/Solids, 34, 78-101.
• 5. Sburlati, R., 2012. An Axisymmetric Elastic Analysis for Circular Sandwich Panels with Functionally Graded Cores. Composites Part B: Engineering, 43(3), 1039-1044.
• 6. Nguyen, T.K., Vo, T.P., Thai, H.T., 2014. Vibration and Buckling Analysis of Functionally Graded Sandwich Plates with Improved Transverse Shear Stiffness Based on the First-order Shear Deformation Theory. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 228(12), 2110-2131.
• 7. Sburlati, R., Atashipour, S.R., Hosseini- Hashemi, S., 2013. Study on the Effect of Functionally Graded Coating Layers on Elastic Deformation of Thick Circular Plates: A Closed-Form Elasticity Solution. Composite Structures, 99, 131-140.
• 8. Shariyat, M., Alipour, M.M., 2013. Semi- analytical Consistent Zigzag-elasticity Formulations with Implicit Layerwise Shear Correction Factors for Dynamic Stress Analysis of Sandwich Circular Plates with FGM Layers. Composites Part B: Engineering, 49, 43-64.
• 9. Houari, M.S.A., Tounsi, A., Bég, O.A., 2013. Thermoelastic Bending Analysis of Functionally Graded Sandwich Plates Using a New Higher Order Shear and Normal Deformation Theory. International Journal of Mechanical Sciences, 76, 102-111.
• 10. Zenkour, A.M., 2013. Bending Analysis of Functionally Graded Sandwich Plates Using a Simple Four-unknown Shear and Normal Deformations Theory. Journal of Sandwich Structures & Materials, 15(6), 629-656.
• 11. Thai, C.H., Kulasegaram, S., Tran, L.V., Nguyen-Xuan, H., 2014. Generalized Shear Deformation Theory for Functionally Graded Isotropic and Sandwich Plates Based on Isogeometric Approach. Computers & Structures, 141, 94-112.
• 12. Thai, H.T., Nguyen, T.K., Vo, T.P., Lee, J., 2014. Analysis of Functionally Graded Sandwich Plates Using a New First-order Shear Deformation Theory. European Journal of Mechanics-A/Solids, 45, 211-225.
• 13. Alibeigloo, A., 2016. Thermo Elasticity Solution of Sandwich Circular Plate with Functionally Graded Core Using Generalized Differential Quadrature Method. Composite Structures, 136, 229-240.
• 14. Alipour, M.M., 2016. A Novel Economical Analytical Method for Bending and Stress Analysis of Functionally Graded Sandwich Circular Plates with General Elastic Edge Conditions, Subjected to Various Loads. Composites Part B: Engineering, 95, 48-63. 15. Mantari, J.L., Monge, J.C., 2016. Buckling, Free Vibration and Bending Analysis of Functionally Graded Sandwich Plates Based on an Optimized Hyperbolic Unified Formulation. International Journal of Mechanical Sciences, 119, 170-186.
• 16. Li, D., Deng, Z., Xiao, H., Jin, P., 2018. Bending Analysis of Sandwich Plates with Different Face Sheet Materials and Functionally Graded Soft Core. Thin-Walled Structures, 122, 8-16.
• 17. Beni, N.N., Dehkordi, M.B., 2018. An Extension of Carrera Unified Formulation in Polar Coordinate for Analysis of Circular Sandwich Plate with FGM Core Using GDQ Method. Composite Structures, 185, 421-434.
• 18. Farhatnia, F., Saadat, R., Oveissi, S., 2019. Functionally Graded Sandwich Circular Plate of Non-Uniform Varying Thickness with Homogenous Core Resting on Elastic Foundation: Investigation on Bending via Differential Quadrature Method. American Journal of Mechanical Engineering, 7(2), 68-78.
• 19. Chung, Y.L., Ou, Z.X., 2021. Exact Bending Solutions of Circular Sandwich Plates with Functionally Graded Material-undercoated Layer Subjected to Axisymmetric Distributed Loads. Journal of Sandwich Structures & Materials, 23(7), 2856-2881.
• 20. Duc, N. D., Vuong, P. M., 2022. Nonlinear Vibration Response of Shear Deformable FGM Sandwich Toroidal Shell Segments. Meccanica, 57, 1083–1103.
• 21. Shinde, B.M., Sayyad, A.S., 2022. A New Higher Order Shear and Normal Deformation Theory for FGM Sandwich Shells. Composite Structures, 280, 114865.
• 22. Sah, S.K., Ghosh, A., 2022. Influence of Porosity Distribution on Free Vibration and Buckling Analysis of Multi-directional Functionally Graded Sandwich Plates. Composite Structures, 279, 114795.
• 23. Dogan, A., 2022. Quasi-static and Dynamic Response of Functionally Graded Viscoelastic Plates. Composite Structures, 280, 114883.
• 24. Noori, A.R., Rasooli, H., Aslan, T.A., Temel, B., 2020. Fonksiyonel Derecelenmiş Sandviç Kirişlerin Tamamlayıcı Fonksiyonlar Yöntemi ile Statik Analizi. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, 35(4), 1091-1102.
• 25. Temel, B., Aslan, T. A., Noori, A. R., 2018. Dikdörtgen Kesitli Viskoelastik Sikloid Çubukların Zorlanmış Titreşimi. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, 33(1), 151-162.
• 26. Noori, A. R., Temel, B., 2020. On the Vibration Analysis of Laminated Composite Parabolic Arches with Variable Cross-Section of Various Ply Stacking Sequences. Mechanics of Advanced Materials and Structures, 27(19), 1658-1672.
• 27. Sivri, B., Temel, B., 2022. Değişken Kesitli Timoshenko Kolonlarının Tamamlayıcı Fonksiyonlar Yöntemiyle Burkulma Analizi. Niğde Ömer Halisdemir Üniversitesi, Mühendislik Bilimleri Dergisi, 11 (1) , 122- 128.
• 28. Eker, M., Yarımpabuç, D., Çelebi, K. 2018. Mechanical Behavior of Functionally Graded Pressure Vessels Under the Effect of Poisson’s Ratio . European Mechanical Science, 2(2), 52-59 .
• 29. Çalım, F.F., 2020. Vibration Analysis of Functionally Graded Timoshenko Beams on Winkler–pasternak Elastic Foundation. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 44(3), 901-920.
• 30. Yildirim, S., Tutuncu, N., 2018. Axisymmetric Plane Vibration Analysis of Polar-anisotropic Disks. Composite Structures, 194, 509-515.
• 31. Yıldırım, S., 2020. Effect of Boundary Conditions on Natural Frequencies of Orthotropic-cored Composite Sandwich Beams. Çukurova Üniversitesi, Mühendislik- Mimarlık Fakültesi Dergisi, 35(1), 221-226.
• 32. Noori, A.R., Temel, B., 2021. A Powerful Numerical Approach for the Axisymmetric Bending Response of Shear Deformable Two- directional Functionally Graded (2D-FG) Plates with Variable Thickness. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 235(22), 6370-6387.