A Numerical Method to Analyze some Simple Planar Frames Subjected to Concentrated Loads with Elastic Large Deflection

Abstract:

In this paper a general numerical method to analyze some simple planar frames subjected to concentrated loads with elastic large deflection is presented. In the method some reactions or displacements at the ends of the frames with three or below redundant constraints are considered as unknown, and a numerical method based on a more-fold method of bisection is presented to solve for the unknown reactions or displacments under known boundary conditions. In the examples in the paper,the flow graphs of solving for unknown reactions or displacements are demonstrated and some analysical results are given by the aid of some graphics.These examples show that some simple frame structures with three or below redundant constraints can all be analyzed easily and quickly with the numerical method presented in the paper.

• Periodical: Advanced Materials Research (Volume 413)
• Pages: 277-282
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.413.277
• Online since: December 2011
• Authors: Tian Jie Cao
• Keywords: Concentrated Load, Large Deflection, Numerical Method, Simple Planar Frame

References

[1] Bisshopp K.E., Drucker D.C., Large deflection of cantilever beams. Quarterly of Applied Mathematics, 1945, 3：272～275.

DOI: 10.1090/qam/13360

[2] Barten H.J., On the deflection of a cantilever beam. Quarterly of Applied Mathematics, 1944, 2：168～171.

[3] Barten H.J., On the deflection of a cantilever beam. Quarterly of Applied Mathematics, 1945, 3：275～276(in Chinese).

[4] Rohde F.V. Large deflection of a cantilever beam with uniformly distributed load. Quarterly of Applied Mathematics, 1953, 11, 337～338.

DOI: 10.1090/qam/56438

[5] Chien Wei-zang. Second Order Approximation Solution of Nonlinear Large Deflection Problems of Yongjiang Railway Bridge in Ningbo. Applied Mathematics and Mechanics(English Edition) , 2002, 23(5), 493～506.

DOI: 10.1007/bf02437768

[6] He Xiao-ting, Chen Shan-lin. Biparametric Perturbation Solutions of Large Deflection Problem of Cantilever Beams. Applied Mathematics and Mechanics(English Edition) , 2006, 27(4), 453～460.

DOI: 10.1007/s10483-006-0404-z

[7] Jenkins J.A., Seitz J.B., Przomieniecki J.S., Large deflection of diamond-shaped frames. Int.J. Solids Struct., 1966, 2：591～603.

DOI: 10.1016/0020-7683(66)90041-2

[8] Kerr C.N., Large deflection of square frame. Quart. J. Mech. Math., 1964, 17：23～38.

[9] Wu Xiaoqiang, Yu Tongxi. Analysis of the Entire Process of Large deflection of an Elastic-plastic Cantilever. Acta Mechanica Sinica, 1986, 18(6)：516～525(in Chinese).

DOI: 10.1007/bf02488476

[10] Luan Feng, Yu Tong-xi. An Analysis of the Large Deflection of an Elastic-Plastic Cantilever Subjected to an Inclined Concentrated Force. Applied Mathematics and Mechanics, 1991, 12(6), 515～522(in Chinese).

DOI: 10.1007/bf02015568