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Structural Engineering and Mechanics   Volume 48, Number 6, December25 2013, pages 849-878
DOI: https://doi.org/10.12989/sem.2013.48.6.849
 
Comprehensive evaluation of structural geometrical nonlinear solution techniques Part I: Formulation and characteristics of the methods
M. Rezaiee-Pajand, M. Ghalishooyan and M. Salehi-Ahmadabad

 
Abstract     [Buy Article]
    This paper consists of two parts, which broadly examines solution techniques abilities for the structures with geometrical nonlinear behavior. In part I of the article, formulations of several well-known approaches will be presented. These solution strategies include different groups, such as: residual load minimization, normal plane, updated normal plane, cylindrical arc length, work control, residual displacement minimization, generalized displacement control, modified normal flow, and three-parameter ellipsoidal, hyperbolic, and polynomial schemes. For better understanding and easier application of the solution techniques, a consistent mathematical notation is employed in all formulations for correction and predictor steps. Moreover, other features of these approaches and their algorithms will be investigated. Common methods of determining the amount and sign of load factor increment in the predictor step and choosing the correct root in predictor and corrector step will be reviewed. The way that these features are determined is very important for tracing of the structural equilibrium path. In the second part of article, robustness and efficiency of the solution schemes will be comprehensively evaluated by performing numerical analyses.
 
Key Words
    nonlinear solution techniques; equilibrium path; condition equation
 
Address
M. Rezaiee-Pajand, M. Ghalishooyan and M. Salehi-Ahmadabad : Department of Civil Engineering, School of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
 

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