Abstract
The reliability and limits of solutions for static structural analysis depend on the accuracy of the curvature and deflection calculations. Even if the material model is close to the actual material behavior, physically unrealistic deflections or divergence problems are unavoidable in the analysis if an appropriate fundamental kinematic theory is not chosen. Moreover, accurate deflection calculation plays an important role in ultimate strength analysis where in-plane stresses are considered. Therefore, a more powerful method is needed to achieve reliable deflection calculation and modeling. For this purpose, a new advanced step was developed by coupling the elasto-plastic material behavior with precise general planar kinematic analysis. The deflection is generated precisely without making geometric assumptions or using differential equations of the deflection curve. An analytical finite strain solution was derived for an elasto-plastic prismatic/non-prismatic rectangular cross-sectioned beam under a uniform moment distribution. A comparison of the analytical results with those from the Abaqus FEM software package reveals a coherent correlation.
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References
Chen W F and Duan L eds 2000 Bridge engineering handbook. Boca Raton: CRC Press
Tayyar GT 2011 Determination of ultimate strength of the ship girder (in Turkish). Ph.D. Istanbul Technical University, Istanbul. https://tez.yok.gov.tr/en. [Accessed 23.11.2012]
Fetis D G 2006 Nonlinear structural engineering with unique theories and methods to solve effectively complex nonlinear problems. Berlin: Springer
Bona F D and Zelenika S 1997 A generalized elastica-type approach to the analysis of large displacements of spring-strips. Proc. Instn. Mech. Eng. 221(C): 509–517
Lee K 2002 Large deflections of cantilever beams of non-linear elastic material under a combined loading. Int. J. Non linear Mech. 37: 439–443
Lewis G and Monasa F 1982 Large deflections of cantilever beams of non-linear materials of the ludwick type subjected to an end moment. Int. J. Nonlinear Mech. 17: 1–6
Prathap G and Varadan T K 1976 The inelastic large deformation of beams. J. Appl. Mech. 43: 689–690
Oden J T and Childs S B 1970 Finite deflections of a non-linearly elastic bar. J. Appl. Mech. 37: 48–52
Lo C C and Gupta S D 1978 Bending of a nonlinear rectangular beam in large deflection. J. Appl. Mech. 45: 213–215
Gao X 1994 Finite deformation elasto-plastic solution for the pure bending problem of wide plate of elastic linear-hardening material. Int. J. Solids Struct. 31(10): 1357–1376
Tayyar G T and Bayraktarkatal E 2012a Kinematic displacement theory of planar structures. Int. J. Ocean Syst. Eng. 2(2): 63–70
Hay G E 1942 The finite displacement of thin rods. Trans. Am. Math. Soc. 51: 65–102
Bolton K M 1975 Biarc curves. Comput. Aided Des. 7(29): 89–92
Meek D S 2002 Coaxing a planar curve to comply. J. Comput. Appl. Math. 140(1): 599–618
Tayyar G T 2012 A new analytical method with curvature based kinematic deflection curve theory. Int. J. Ocean Syst. Eng. 2(3): 195–199
Timoshenko S 1948 Strength of materials part I elementary theory and problems. New York: D. Van Nostrand Company
Tayyar G T and Bayraktarkatal E 2012b A new approximate method to evaluate the ultimate strength of ship hull girder. In: Rizzuto E and Soares C G (eds) Sustainable maritime transportation and exploitation of sea resources. London: Taylor & Francis Group. pp 323–329
Bayraktarkatal E and Tayyar G T 2014 Geometric solution in progressive collapse analysis of hull girder. J. Mar. Sci. Technol. 22(4): 417–423
Tayyar G T, Nam J and Choung J 2014 Prediction of hull girder moment-carrying capacity using kinematic displacement theory. Mar. Struct. 39: 157–173
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TAYYAR, G.T. A new approach for elasto-plastic finite strain analysis of cantilever beams subjected to uniform bending moment. Sādhanā 41, 451–458 (2016). https://doi.org/10.1007/s12046-016-0475-x
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DOI: https://doi.org/10.1007/s12046-016-0475-x