Abstract
Tail equivalent linearization method is based on first order reliability method, which obtains an equivalent linear system for the considered nonlinear problem with equal tail probability related to a specified threshold and time. This method has been applied only to nonlinear non-degrading single- and multi-degrees of freedom shear beam two-dimensional models and three-dimensional one-story rigid diaphragm supported by frames with in-plane uni-axial stiffness which is subjected to independent random excitation along the structural axes. To use TELM for more practical problems it is required to extend this method to cover more realistic material and excitation characteristics. In this paper, some of these developments have been presented. Application of TELM for bi-directional excitation with bi-axial material subjected to different incidence angles of excitation and using TELM for degrading material which has been presented in the previous works of the authors have been reviewed briefly. In addition a new method for defining rotational dependent component of earthquake excitation in terms of independent translational components in the standard normal random variable space is proposed, and TELM has been used for this kind of excitation. Three examples related to these extensions have been presented; the comparison of the TELM results with Mote-Carlo simulation results shows good agreement.
Highlights
Most structures under extreme dynamic loads resulting from natural hazards with low probability exhibit nonlinear behavior
Tail equivalent linearization method is based on first order reliability method, which obtains an equivalent linear system for the considered nonlinear problem with equal tail probability related to a specified threshold and time
Application of tail equivalent linearization method (TELM) for bi-directional excitation with bi-axial material subjected to different incidence angles of excitation and using TELM for degrading material which has been presented in the previous works of the authors have been reviewed briefly
Summary
Most structures under extreme dynamic loads resulting from natural hazards with low probability exhibit nonlinear behavior. Nonlinear random vibration methods are the best methods in the analysis of the structures under sever loads associated with natural hazards. Random vibration for linear structures uses the superposition principle This advantage is not applicable for nonlinear systems, but there are ways to transform a nonlinear system to an equivalent linear system that can benefit from this privilege. To overcome the shortcomings of the conventional ELM, Fujimura and Der Kiureghian (2007) presented tail equivalent linearization method (TELM) which uses the advantages of first order reliability method (FORM). In this method stochastic excitation is discretized and represented in terms of a finite set of standard normal random variables. Based on this representation of excitation, the limit state surface for
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