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Structural Engineering and Mechanics Volume 36, Number 5, November30 2010 , pages 529-544 DOI: https://doi.org/10.12989/sem.2010.36.5.529 |
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Large strain analysis of two-dimensional frames by the normal flow algorithm |
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Tabatabaei, R. and Saffari, H.
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| Abstract | ||
| 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. | ||
| Key Words | ||
| equilibrium path; limit point; snap-through; snap-back; Davidenko | ||
| Address | ||
| Tabatabaei, R.: Islamic Azad University, Kerman Branch, Civil Engineering Department, PO Box 76175-6114, Kerman, Iran Saffari, H.: Shahid Bahonar University, Civil Engineering Department, Kerman, Iran | ||