Fonksiyonel Dereceli Kirişin Birleşim Metodu Kullanılarak Büyük Sehim Analizi

Year 2024, Volume: 5 Issue: 1, 87 - 105, 26.06.2024

Ersin Demir , Prof. Dr. Hasan Çallıoğlu , Zekeriya Girgin

https://doi.org/10.55546/jmm.1451429

Abstract

Bu çalışmada dairesel kesitli bir kirişin büyük sehim davranışı Birleşim Metodu (BM) kullanılarak incelenmiştir. BM, Matlab-Simulink programındaki blok diyagramları ve Diferansiyel Quadrature Metodundaki (DQM) ağırlık katsayılarını kullanan sayısal bir çözüm yöntemidir. Dikkate alınan kiriş malzemesi Fonksiyonel Derecelendirilmiş Malzemedir (FDM). Kirişin sınır koşulları ankastre-serbest (A-S) olarak alınmış ve kirişin serbest ucundan tekil bir yükün uygulandığı varsayılmıştır. Kirişin büyük sehim denklemleri hesaplanırken ve sayısal analiz yapılırken geometrik doğrusal olmayan analiz yapılır. Kirişe uygulanan kuvvetin arttırılması, kiriş kesitinin boyuna yönde değiştirilmesi ve FDM'nin malzeme indisinin değiştirilmesinin kirişin aşırı sehim davranışı üzerindeki etkileri incelenmiştir. Karşılaştırma amacıyla BM'den elde edilen sonuçlar hem SolidWorks-Simulation hem de Ansys-Workbench programlarından elde edilen sonuçlarla karşılaştırılmıştır.

Keywords

Büyük Sehim, Kiriş, Birleşim Metodu, Sonlu Elemanlar Metodu, Fonksiyonel Derecelendirilmiş Malzeme

Large Deflection Analysis of Functionally Graded Beam by Using Combining Method

Abstract

In this study, the large deflection behavior of a circular cross-section beam is examined using the Combining Method (CM). The CM is a numerical solution method that uses block diagrams in the Matlab-Simulink program and weighting coefficients in the Differential Quadrature Method (DQM). The beam material considered is Functionally Graded Material (FGM). Boundary conditions of the beam are taken as clamped-free (C-F) and a singular load is assumed to be applied from the free end of the beam. Geometric nonlinear analysis is performed while calculating the large deflection equations of the beam and performing numerical analysis. The effects of increasing the force applied to the beam, changing the beam cross-section in the longitudinal direction, and changing the material index of the FGM on the extreme deflection behavior of the beam were examined. For comparison purposes, the results obtained from CM are compared with the results obtained from both SolidWorks-Simulation and Ansys-Workbench programs. As a result of the analysis, increasing the applied force causes the x and y coordinates of the end point of the beam to decrease. The change in geometry and material index greatly affects the large deflection occurring in the beam.

Keywords

Large Deflection, Beam, Combining Method, Finite Element Method, Functionally Grade Material

References

• Belendez T., Neipp C., Belendez A., Large and small deflections of a cantilever beam. European Journal of Physics 23, 371-379, 2002.
• Brojan M., Cebron M., Kosel F., Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end. Acta Mechanica Sinica 28(3), 863-869, 2012.
• Dado M., Al-Sadder S., A new technique for large deflection analysis of non-prismatic cantilever beams. Mechanics Research Communications 32, 692-703, 2005.
• Davoodinik A.R., Rahimi G.H., Large deflection of flexible tapered functionally graded beam. Acta Mechanica Sinica 27(5), 767-777, 2011.
• Demir E, A numerical study on the large displacement in a functionally graded beam under thermal effect. Journal of Materials and Mechatronics: A 4(2), 492-503, 2023.
• Girgin Z., Aysal F.E., Bayrakçeken H., Large deflection analysis of prismatic cantilever beam comparatively by using Combing method and iterative DQM. Journal of Polytechnic 23 (1), 111-120, 2020.
• Girgin Z., Combining differential quadrature method with simulation technique to solve non-linear differential equations. International Journal for Numerical Methods in Engineering 75, 722-734, 2008.
• Girgin Z., Combining modified integral quadrature method with simulation technique to solve nonlinear initial and boundary value problems. International Journal of Nonlinear Sciences & Numerical Simulation 10(4), 475-482, 2009.
• Girgin Z., Yilmaz Y., Demir E., A Combining method for solution of nonlinear boundary value problems. Applied Mathematics and Computation 232, 1037-1045, 2014.
• Horibe T., Mori K., Large deflections of tapered cantilever beams made of axially functionally graded material. Bulletin of the JSME Mechanical Engineering Journal 5(1), 1-10, 2018.
• Hu Y.J., Liu M., Zhu W., Jiang C., An adaptive differential quadrature element method for large deformation contact problems involving curved beams with a finite number of contact points. International Journal of Solids and Structures 115–116, 200-207, 2017.
• Kang Y.A., Li X.F., Large deflections of a non-linear cantilever functionally graded beam. Journal of Reinforced Plastics and Composites 29(12), 1761-1774, 2010.
• Kien N.D., Large displacement response of tapered cantilever beams made of axially functionally graded material. Composites Part B 55, 298-305, 2013.
• Koizumi M., The concept of FGM. Ceramic Transactions, Functionally Gradient Materials 34, 3-10, 1993.
• Kurtaran H., Large displacement static and transient analysis of functionally graded deep curved beams with generalized differential quadrature method. Composite Structures 131, 821-831, 2015.
• Li Z., Huang D., Yan K., Xu Y., Large deformation analysis of functionally graded beam with variable cross-section by using peridynamic differential operator. Composite Structures 279, 1-13, 2022.
• Lin X., Huang Y., Zhao Y., Wang, T., Large deformation analysis of a cantilever beam made of axially functionally graded material by homotopy analysis method. Applied Mathematics and Mechanics (English Edition) 40(10), 1375-1386, 2019.
• Nguyen D.K., Bui T.T.H., Tran T.T.H., Alexandrov, S., Large deflections of functionally graded sandwich beams with influence of homogenization schemes. Archive of Applied Mechanics 92, 1757-1775, 2022a.
• Nguyen V.X., Nguyen K.T., Thai S., Large deflection analysis of functionally graded beams based on geometrically exact three-dimensional beam theory and isogeometric analysis. International Journal of Non-Linear Mechanics 146, 1-16, 2022b.
• Saraçoğlu M.H., Güçlü G., Uslu F., Deflection analysis of functionally graded equal strength beams. European Mechanical Science 6(2), 119 - 128, 2022.
• Saraçoğlu M.H., Güçlü G., Uslu F., Static Analysis of Orthotropic Euler-Bernoulli and Timoshenko Beams with Respect to Various Parameters 8(2), 628 - 641, 2019.
• Sitar M., Kosel F., Brojan M., Large deflections of nonlinearly elastic functionally graded composite beams. Archives of Civil and Mechanical Engineering 14, 700-709, 2014.
• Soleimani A., Large deflection of various functionally graded beam using Shooting Method. Applied Mechanics and Materials 110-116, 4705-4711, 2012.