Abstract
Abstract Limit states of simple, spatial, non-linear models of structures with two degrees of freedom are considered. Geometric and material imperfections are taken in the form of random variables. The simulation of these random variables and the Monte Carlo technique are employed. Two possibilities in the assessment of the reliability of structures are presented: 1) Simulation of random imperfections and the Monte Carlo operation give as a result a histogram of the limit loads. Assuming that the probability distribution of the applied load is known, the structural reliability can be obtained according to the exact formula. 2) In order to obtain the histogram of the limit state of the structure, the values of the applied load are also simulated at every Monte Carlo step. The factor which amplifies the load responsible for the structure failure is derived. The set of all these factors leads to the model reliability calculation. The estimation of the limit state of an imperfect structures can be described a...
Highlights
Assessment of stability, reliability and safety of geometric and material imperfect structures belongs to the most complex problems in applied mechanics.Stability of one, and two-dimensional imperfect structure models has been the major concern of researchers [1,2,3,4]
2) In order to obtain the histogram of the limit state of the structure, the values of the applied load are simulated at every Monte Carlo step
The estimation of the limit state of an imperfect structures can be described as a transformation of random input data into random output results
Summary
Assessment of stability, reliability and safety of geometric and material imperfect structures belongs to the most complex problems in applied mechanics. The concept is based on simulation of random variables (describing loads and material properties) and on the Monte Carlo method (Marek, Gustar and Anagnos [11]). The calculation of the limit state of an imperfect non-linear model of structures is, from the mathematical point of view, a transformation of random input data (imperfections) into random output results. The first well-known concept takes into consideration the histogram of the structure limit loads N" To obtain this histogram, simulation of random imperfections and the Monte Carlo operation are applied. One of the characteristics of this histogram is the reliability To analyse these problems, a static response of spatial non-linear models of rigid bars supported by elastic and elastic-plastic springs is considered. On the basis of the simulated results the histograms of the critical load and the model reliabilities are derived. The known energy considerations (the second variation of potential energy is positively defined) lead to the conclusion that the stable and unstable regions are separated by the following surface (7)
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