Year 2020, Volume 23 , Issue 1, Pages 111 - 120 2020-03-01

Large Deflection Analysis of Prismatic Cantilever Beam Comparatively by Using Combing Method and Iterative DQM
Large Deflection Analysis of Prismatic Cantilever Beam Comparatively by Using Combing Method and Iterative DQM

Zekeriya GİRGİN [1] , Faruk Emre AYSAL [2] , Hüseyin BAYRAKÇEKEN [3]


There is no exactly analytical solution for the large deflection problem of prismatic cantilever beams under general loading conditions. In the case of considering a non-prismatic cantilever beam, the difficulty of the larger deflection problem is increased. In this study, the comparison of the Iterative Differential Quadrature Method (I-DQM) and the Combining Method (CM) was performed. Numerical solution of the large deflection problem was separately performed with both the I-DQM and the CM for prismatic cantilever beams. The obtaining results show that both of these methods gave more accurate solutions compared with a reliable semi-analytic method which was introduced by Dado and Sadder (2005). Besides, it was demonstrated that the I-DQM provided a more wide-range solution than the CM.

There is no exactly analytical solution for the large deflection problem of prismatic cantilever beams under general loading conditions. In the case of considering a non-prismatic cantilever beam, the difficulty of the larger deflection problem is increased. In this study, the comparison of the Iterative Differential Quadrature Method (I-DQM) and the Combining Method (CM) was performed. Numerical solution of the large deflection problem was separately performed with both the I-DQM and the CM for prismatic cantilever beams. The obtaining results show that both of these methods gave more accurate solutions compared with a reliable semi-analytic method which was introduced by Dado and Sadder (2005). Besides, it was demonstrated that the I-DQM provided a more wide-range solution than the CM.

  • [1] AL-Sadder S. and AL-Rawi R. A. O., "Finite difference scheme for large-deflection analysis of non-prismatic cantilever beams subjected to different types of continuous and discontinuous loadings.", Arch Appl Mech, 75: 459-473, (2006).
  • [2] Dado M., and Al-Sadder S., "A new technique for large deflection analysis of non-prismatic cantilever beams.", Mechanics Research Communications, 32: 692-703, (2005).
  • [3] Barten H. J, "On the deflection of a cantilever beam". Quart. J. Appl. Math., 3: 275, (1945).
  • [4] Bisshop K. E. ve Drucker D. C. "Large deflections of cantilever beams.", Quart. J. Appl. Math., 3: 272-275, (1945).
  • [5] Freeman J. G. "Mathematical theory of deflection of beam", Philos. Mag, 37: 551, (1946).
  • [6] Conway H. D., "Large deflection of simply supported beams", Philos. Mag, 38: 905, (1947).
  • [7] Timoshenko S. P. and Gere J. M., "Theory of Elastic Stability." McGraw-Hill, New York, (1961).
  • [8] Holden J. T., "On the finite deflections of thin beams.", Int. J. Solids Struct, 8:1051-1055, (1972).
  • [9] Lau J. H., "Large deflections of beams with combined loads", ASCE J. Eng. Mech. Div,12:140, (1974).
  • [10] Wang,C. Y. And Watson L. T, "On large deformations of C-shaped springs.", Int. J. Mech. Sci, 22: 395-400, (1980).
  • [11] Chucheepsakul S., Buncharoen S. and Wang C. M, "Large deflection of beams under moment gradient.", ASCE J. Eng. Mech, 120: 1848, (1994).
  • [12] Bona F. and Zelenika S, "A generalized elastica-type approach to the analysis of large displacements of spring-strips.", Proc. Inst. Mech. Engrs. Part C, 21: 509-517, (1997).
  • [13] Wang X. W., and Gu H. Z., "Static Analysis of Frame Structures by The Differential Quadrature Element Method." International Journal for Numerical Method in Engineering, 40: 759-772, (1997).
  • [14] Chucheepsakul S., Wang C. M. and He X. Q., "Double curvature bending of variable-arc-length elastica.", J. Appl. Mech, 66: 87-94, (1999).
  • [15] Coffin D. W. and Bloom F., "Elastica solution for the hygrothermal buckling of a beam.", Int. J. Non-lin. Mech, 34: 935, (1999).
  • [16] Kang T.J., Kim J.G., Kim J.H. , Hwang K.C., Lee B.W., Baek C.W., Kim C.W., Kwon D., Lee H.Y. and Kim Y.H., "Deformation characteristics of electroplated MEMS cantilever beams released by plasma ashing.", Sensors and Actuators A: Physical, 148: 407-415, (2008).
  • [17] Tolou N. And Herder J. L., "A Semianalytical Approach to Large Deflections in Compliant Beams under Point Load.", Mathematical Problems in Engineering, 13 pages, (2009).
  • [18] Lin H. P. and Chang S. C., "Forced responses of cracked cantilever beams subjected to a concentrated moving load", International Journal of Mechanical Sciences, 48: 1456-1463, (2006).
  • [19] Batista M., "Analytical treatment of equilibrium configurations of cantilever under terminal loads using Jacobi elliptical functions", International Journal of Solids and Structures, 51: 2308-2326, (2014).
  • [20] Wang K.F. and Wang. B.L., "A general model for nano-cantilever switches with consideration of surface effects and nonlinear curvature.", Physica E, 66:197-208, (2015).
  • [21] Joseph R.P., Wang B.L. and Samali B., "Size effects on double cantilever beam fracture mechanics specimen based on strain gradient theory.", Engineering Fracture Mechanics, 169: 309-320, (2017).
  • [22] Abu-Alshaikh I. M., "Closed-Form Solution of Large Deflected Cantilever Beam against Follower Loading Using Complex Analysis", Modern Applied Science, 11(12): 12-21, (2017).
  • [23] Navaee, S. and Elling, R. E., "Equilibrium configurations of cantilever beam subjected to inclined end loads.", Trans. ASME, 59: 572-579, (1992).
  • [24] Faulkner M. G., Lipsett A. W. and Tam V., "On the use of a segmental shooting technique for multiple solutions of planar elastica problems.", Comp Meth Appl Mech Eng, 110: 221-236, (1993).
  • [25] Bellman R. and J. Casti J.. "Differential Quadrature and long term integration.", J. Math. Anal. Appl, 34 235-238, (1971).
  • [26] Bellman R., Kashef B.G. and Casti J., "Differential Quadrature: a technique for the rapid solution of non-linear partial differential equations.", J. Comput. Phys., 10: 40-52, (1972).
  • [27] Quan J. R., and Chang C. T., "New Insights in Solving Distributed System Equations by The Quadrature Methods I.", Computational Chemical Engineering, 13 779-788, (1989a).
  • [28] Quan J. R., and Chang C. T., "New Insights in Solving Distributed System Equations by The Quadrature Methods. II.", Computational Chemical Engineering, 13: 1017-1024, (1989b).
  • [29] Shu, C. and Richards B.E., "Application of generalized differential quadrature to solve two dimensional incompressible Navier Stokes equations.", Int. J. Numer. Methods Fluids, 15: 791-798, (1992).
  • [30] Jiwari R., Pandit S., and Mittal R. C., "Numerical simulation of two-dimensional Sine-Gordon solitons by differential quadrature method.", Computer Physics Communications, 183: 600-616, (2012).
  • [31] Ansari, R., Gholami R., Shojaei M. F., Mohammadi V. and Sahmani S., "Size-dependent bending, buckling and free vibration of functionally graded Timoshenko microbeams based on the most general strain gradient theory.", Composite Structures, 100: 385-397, (2013).
  • [32] Alinaghizadeh, F. and Shariati M., "Geometrically non-linear bending analysis of thick two-directional functionally graded annular sector and rectangular plates with variable thickness resting on non-linear elastic foundation.", Composites Part B, 86: 61-83, (2016).
  • [33] Yilmaz Y., Girgin Z., and Evran S. "Buckling Analyses of Axially Functionally Graded Nonuniform Columns with Elastic Restraint Using a Localized Differential Quadrature Method.", Mathematical Problems in Engineering, 12 pages, (2013).
  • [34] Sahmani S., Aghdam M. M. and Bahrami M., "On the free vibration characteristics of postbuckled third-order shear deformable FGM nanobeams including surface effects.", Composite Structures, 121: 377-385, (2015).
  • [35] Jang S. K., Bert C. W. and Striz A. G., "Application of Differential Quadrature to Static Analysis of Structural Components.", International Journal for Numerical Methods in Engineering, 28: 561-577, (1989).
  • [36] Wang, X., and Bert, C. W. "A New Approach in Applying Differential Quadrature to Static and Free Vibrational Analyses of Beams and Plates.", Journal of Sound and Vibration, 162(3): 566-572, (1993).
  • [37] Shu C., and Du H., "Implementation of Clamped and Simply Supported Boundary Conditions in The GDQ Free Vibration Analysis of Beams and Plates.", International Journal of Solids and Structures, 34(7): 819-835, (1997).
  • [38] Liu G. R., and Wu T. Y., "Numerical Solution for Differential Equations of Duffing-Type Non-Linearity Using The Generalized Differential Quadrature Rule.", Journal of Sound and Vibration, 237(5): 805-817, (2000).
  • [39] Tomasiello S., "Simulating Non-Linear Coupled Oscillators by An Iterative Differential Quadrature Method.", Journal of Sound and Vibration, 265: 507-525, (2003).
  • [40] Liu F. L., and Liew K. M., "Analysis of Vibrating Thick Rectangular Plates with Mixed Boundary Constrants Using Differential Quadrature Element Method.", Journal of Sound and Vibration, 222 (5) 915-934 (1999).
  • [41] Chen C. N., "Differential Quadrature Element Analysis Using Extended Differential Quadrature.", Computer and Mathematic with Application, 39: 65-79, (2000).
  • [42] Kol C., "Diferansiyel Kuadratür (Quadrature) Eleman Metodunun Plakalara Uygulanması.", Yüksek Lisans Tezi, Pamukkale Üniversitesi Fen Bilimleri Enstitüsü, (2003).
  • [43] Girgin Z., "Combining Differential Quadrature Method with simulation technique to solve nonlinear differential equations.", Int. J. Numer. Methods Eng., 75, (6): 723-733, (2008).
  • [44] Demir E., "Lineer Olmayan Titreşim Problemlerinin Çözümünde Birleşim (Diferansiyel Quadrature Ve Simülasyon) Metodu.", Doktora Tezi, Pamukkale Üniversitesi Fen Bilimleri Enstitüsü, (2009).
  • [45] Girgin Z., Yilmaz Y. and Demir E. "A Combining Method for solution of nonlinear boundary value problems.", Applied Mathematics and Computation, 232: 1037-1045, (2014).
Primary Language en
Subjects Engineering
Journal Section Research Article
Authors

Orcid: 0000-0001-5958-9735
Author: Zekeriya GİRGİN
Institution: PAMUKKALE UNIVERSITY,FACULTY OF ENGİNEERİNG
Country: Turkey


Orcid: 0000-0002-9514-1425
Author: Faruk Emre AYSAL (Primary Author)
Institution: AFYON KOCATEPE UNIVERSITY, FACULTY OF TECHNOLOGY
Country: Turkey


Orcid: 0000-0002-1572-4859
Author: Hüseyin BAYRAKÇEKEN
Institution: AFYON KOCATEPE UNIVERSITY, FACULTY OF TECHNOLOGY
Country: Turkey


Dates

Publication Date : March 1, 2020

Bibtex @research article { politeknik504480, journal = {Politeknik Dergisi}, issn = {}, eissn = {2147-9429}, address = {Gazi Üniversitesi Teknoloji Fakültesi 06500 Teknikokullar - ANKARA}, publisher = {Gazi University}, year = {2020}, volume = {23}, pages = {111 - 120}, doi = {10.2339/politeknik.504480}, title = {Large Deflection Analysis of Prismatic Cantilever Beam Comparatively by Using Combing Method and Iterative DQM}, key = {cite}, author = {GİRGİN, Zekeriya and AYSAL, Faruk Emre and BAYRAKÇEKEN, Hüseyin} }
APA GİRGİN, Z , AYSAL, F , BAYRAKÇEKEN, H . (2020). Large Deflection Analysis of Prismatic Cantilever Beam Comparatively by Using Combing Method and Iterative DQM. Politeknik Dergisi , 23 (1) , 111-120 . DOI: 10.2339/politeknik.504480
MLA GİRGİN, Z , AYSAL, F , BAYRAKÇEKEN, H . "Large Deflection Analysis of Prismatic Cantilever Beam Comparatively by Using Combing Method and Iterative DQM". Politeknik Dergisi 23 (2020 ): 111-120 <https://dergipark.org.tr/en/pub/politeknik/issue/51707/504480>
Chicago GİRGİN, Z , AYSAL, F , BAYRAKÇEKEN, H . "Large Deflection Analysis of Prismatic Cantilever Beam Comparatively by Using Combing Method and Iterative DQM". Politeknik Dergisi 23 (2020 ): 111-120
RIS TY - JOUR T1 - Large Deflection Analysis of Prismatic Cantilever Beam Comparatively by Using Combing Method and Iterative DQM AU - Zekeriya GİRGİN , Faruk Emre AYSAL , Hüseyin BAYRAKÇEKEN Y1 - 2020 PY - 2020 N1 - doi: 10.2339/politeknik.504480 DO - 10.2339/politeknik.504480 T2 - Politeknik Dergisi JF - Journal JO - JOR SP - 111 EP - 120 VL - 23 IS - 1 SN - -2147-9429 M3 - doi: 10.2339/politeknik.504480 UR - https://doi.org/10.2339/politeknik.504480 Y2 - 2019 ER -
EndNote %0 Politeknik Dergisi Large Deflection Analysis of Prismatic Cantilever Beam Comparatively by Using Combing Method and Iterative DQM %A Zekeriya GİRGİN , Faruk Emre AYSAL , Hüseyin BAYRAKÇEKEN %T Large Deflection Analysis of Prismatic Cantilever Beam Comparatively by Using Combing Method and Iterative DQM %D 2020 %J Politeknik Dergisi %P -2147-9429 %V 23 %N 1 %R doi: 10.2339/politeknik.504480 %U 10.2339/politeknik.504480
ISNAD GİRGİN, Zekeriya , AYSAL, Faruk Emre , BAYRAKÇEKEN, Hüseyin . "Large Deflection Analysis of Prismatic Cantilever Beam Comparatively by Using Combing Method and Iterative DQM". Politeknik Dergisi 23 / 1 (March 2020): 111-120 . https://doi.org/10.2339/politeknik.504480
AMA GİRGİN Z , AYSAL F , BAYRAKÇEKEN H . Large Deflection Analysis of Prismatic Cantilever Beam Comparatively by Using Combing Method and Iterative DQM. Politeknik Dergisi. 2020; 23(1): 111-120.
Vancouver GİRGİN Z , AYSAL F , BAYRAKÇEKEN H . Large Deflection Analysis of Prismatic Cantilever Beam Comparatively by Using Combing Method and Iterative DQM. Politeknik Dergisi. 2020; 23(1): 120-111.