Structural Engineering and Mechanics

  • 제36권5호
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  • Pages.529-544
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  • 2010
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Large strain analysis of two-dimensional frames by the normal flow algorithm

  • Tabatabaei, R. (Islamic Azad University, Kerman Branch, Civil Engineering Department) ;
  • Saffari, H. (Shahid Bahonar University, Civil Engineering Department)
  • 투고 : 2009.08.25
  • 심사 : 2010.07.16
  • 발행 : 2010.11.30
⟨ 이전 논문 다음 논문 ⟩

초록

Nonlinear equations of structures are generally solved numerically by the iterative solution of linear equations. However, this iterative procedure diverges when the tangent stiffness is ill-conditioned which occurs near limit points. In other words, a major challenge with simple iterative methods is failure caused by a singular or near singular Jacobian matrix. In this paper, using the Newton-Raphson algorithm based on Davidenko's equations, the iterations can traverse the limit point without difficulty. It is argued that the propose algorithm may be both more computationally efficient and more robust compared to the other algorithm when tracing path through severe nonlinearities such as those associated with structural collapse. Two frames are analyzed using the proposed algorithm and the results are compared with the previous methods. The ability of the proposed method, particularly for tracing the limit points, is demonstrated by those numerical examples.

키워드

참고문헌

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  3. Non-linear analysis of structures using two-point method vol.46, pp.6, 2011, https://doi.org/10.1016/j.ijnonlinmec.2011.03.008
  4. Efficient Numerical Method in Second-Order Inelastic Analysis of Space Trusses vol.27, pp.2, 2013, https://doi.org/10.1061/(ASCE)CP.1943-5487.0000193
  5. Application of cubic spline on large deformation analysis of structures vol.14, pp.1, 2014, https://doi.org/10.1007/s13296-014-1014-4
  6. A comparative study on application of Chebyshev and spline methods for geometrically non-linear analysis of truss structures vol.101-102, 2015, https://doi.org/10.1016/j.ijmecsci.2015.08.001
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  8. Geometrically nonlinear analysis of space trusses using new iterative techniques vol.21, pp.5, 2010, https://doi.org/10.1007/s42107-020-00239-x