An Approximate Linear Analysis of Structures Using Incremental Loading of Force Method

Authors

DOI:

https://doi.org/10.25079/ukhjse.v4n1y2020.pp37-44

Keywords:

Force Method, Dynamic Relaxation, Geometrically Non-linear Structures, Cable Structures, Prestressed Structures

Abstract

A relatively simple technique has been introduced in this paper. The approach is based on the Linear Force Method (FM) with discretion of the applied loads to the subsequence steps and updating coordinates in each iteration to have new geometrical property. The accuracy of the technique depends on the size of the discretion which depends on the number of iterations. A small change in the configuration could hugely affect the displacement and internal forces in geometrically nonlinear structures, that’s why the current approach is vital. The proposed technique is validated with other techniques of nonlinear analysis of the structures with a very good agreement in both terms of external nodal displacements and internal bar forces.

Downloads

Download data is not yet available.

Author Biographies

  • Ahmed Aulla Manguri, Civil Engineering Department, University of Raparin, Rania, Sulaymaniyah, Kurdistan Region-F.R. Iraq

    MSc. In Structural Engineering from Cardiff University-UK, Year 2015

  • Najmadeen Mohammed Saeed, Civil Engineering Department, University of Raparin, Rania, Sulaymaniyah, Kurdistan Region-F.R. Iraq

    Asst. Prof. Dr. Najmadeen Mohammed Saeed

    PhD Civil Engineering\ Structures School of Engineering United Kingdom 2015-04-22 Master Building Construction Engineering\ Structures College of Engineering/ Building Construction Department Kurdistan Region/ Iraq 2010-04-20 Bachelor Building Construction Engineering College of Engineering/ Building Construction Department Kurdistan Region/ Iraq 2002-07-04

References

Abad, M. S. A., Shooshtari, A., Esmaeili, V., & Riabi, A. N. (2013). Nonlinear analysis of cable structures under general loadings. Finite Elements in Analysis and Design, 73, 11-19. doi:https://doi.org/10.1016/j.finel.2013.05.002

Buchholdt, H. A. (1969). A non-linear deformation theory applied to two dimensional pretensioned cable assemblies. Proceedings of the Institution of Civil Engineers, 42(1), 129-141. doi:https://doi.org/10.1680/iicep.1969.7547

Buchholdt, H. A., Poskitt, T. J., & Brown, C. W. (1969). Discussion. A non-linear deformation theory applied to two dimensional pretensioned cable assemblies. Proceedings of the Institution of Civil Engineers, 43(4), 665-674. doi:DOI:10.1680/iicep.1969.7320

Coyette, J. P., & Guisset, P. (1988). Cable network analysis by a nonlinear programming technique. Engineering Structures, 10(1), 41-46. doi:https://doi.org/10.1016/0141-0296(88)90015-6

Kwan, A. S. K. (1991). A pantographic deployable mast. (PhD Thesis), University of Cambridge. Retrieved from URL: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.386086

Kwan, A. S. K. (1998). A new approach to geometric nonlinearity of cable structures. Computers & Structures, 67(4), 243-252. doi:https://doi.org/10.1016/S0045-7949(98)00052-2

Kwan, A. S. K. (2000). A simple technique for calculating natural frequencies of geometrically nonlinear prestressed cable structures. Computers & Structures, 74(1), 41-50. doi:https://doi.org/10.1016/S0045-7949(98)00318-6

Lewis, W. J., Jones, M. S., & Rushton, K. R. (1984). Dynamic relaxation analysis of the non-linear static response of pretensioned cable roofs. Computers & Structures, 18(6), 989-997. doi:https://doi.org/10.1016/0045-7949(84)90142-1

Luo, Y., & Lu, J. (2006). Geometrically non-linear force method for assemblies with infinitesimal mechanisms. Computers & Structures, 84(31-32), 2194-2199. doi:https://doi.org/10.1016/j.compstruc.2006.08.063

Naghavi Riabi, A. R., & Shooshtari, A. (2015). A numerical method to material and geometric nonlinear analysis of cable structures. Mechanics Based Design of Structures and Machines, 43(4), 407-423. doi:https://doi.org/10.1080/15397734.2015.1012295

Pellegrino, S. (1990). Analysis of prestressed mechanisms. International Journal of Solids and Structures, 26(12), 1329-1350. doi:https://doi.org/10.1016/0020-7683(90)90082-7

Pellegrino, S. (1993). Structural computations with the singular value decomposition of the equilibrium matrix. International Journal of Solids and Structures, 30(21), 3025-3035. doi:https://doi.org/10.1016/0020-7683(93)90210-X

Pellegrino, S., Kwan, A. S. K., & Van Heerden, T. F. (1992). Reduction of equilibrium, compatibility and flexibility matrices, in the force method. International journal for numerical methods in engineering, 35(6), 1219-1236. doi:DOI: http://dx.doi.org/10.1002/nme.1620350605

Raju, N. R. B. K., & Nagabhushanam, J. (2000). Nonlinear structural analysis using integrated force method. Sadhana, 25(4), 353-365. doi:https://link.springer.com/article/10.1007/BF03029720

Saeed, N. M. (2014). Prestress and deformation control in flexible structures. (PhD Thesis), Cardiff University. Retrieved from URL: http://orca.cf.ac.uk/69777/

Saeed, N. M., & Kwan, A. S. K. (2016a). Simultaneous displacement and internal force prescription in shape control of pin-jointed assemblies. AIAA journal, 54(8), 2499-2506. doi:DOI: http://dx.doi.org/10.2514/1.J054811

Saeed, N. M., & Kwan, A. S. K. (2016b). Displacement and force control of complex element structures by Matrix Condensation. Structural Engineering and Mechanics, 59(6), 973-992. doi:DOI: http://dx.doi.org/10.12989/sem.2016.59.6.973

Stefanou, G. D., Moossavi, E., Bishop, S., & Koliopoulos, P. (1993). Conjugate gradients method for calculating the response of large cable nets to static loads. Computers & Structures, 49(5), 843-848. doi:https://doi.org/10.1016/0045-7949(93)90031-8

Thai, H.-T., & Kim, S.-E. (2011). Nonlinear static and dynamic analysis of cable structures. Finite Elements in Analysis and Design, 47(3), 237-246. doi:https://doi.org/10.1016/j.finel.2010.10.005

Published

2020-06-30

Issue

Section

Research Articles

How to Cite

An Approximate Linear Analysis of Structures Using Incremental Loading of Force Method. (2020). UKH Journal of Science and Engineering, 4(1), 37-44. https://doi.org/10.25079/ukhjse.v4n1y2020.pp37-44

Most read articles by the same author(s)