1、 1 1 英文原文 Reliability-based design optimization of adhesive bonded steel-Cconcret composite beams with probabilistic and non-probabilistic uncertainties ABSTRACT: It is meaningful to account for various uncertainties in the optimization design of the adhesive bonded steel-cconcrete composite beam.Ba
2、sed on the definition of the mixed reliability index for structural safety evaluation with probabilistic and non-probabilistic uncertainties,the reliability-based optimization incorporating such mixed reliability constraints are mathematically formulated as a nested problem.The performance measure a
3、pproach is employed to improve the convergence and the stability in solving the inner-loop.Moreover,the double-loop optimization problem is transformed into a series of approximate deterministic problems by incorporating the sequential approximate programming and the iteration scheme,which greatly r
4、educes the burdensome computation workloads in seeking the optimal design. The validity of the proposed formulation as well as the efficiency of the presented numerical techniques is demonstrated by a mathematical example.Finally,reliability-based optimization designs of a single span adhesive bonde
5、d steel-cconcrete composite beam with different loading cases are achieved throug integrating the present systematic method,the finite element analysis and the optimization package. 1. Introduction The steel-cconcrete composite beam,which integrates the high tensile strength of steel and the high co
6、mpressive strength of concrete,has been widely used in multi-storey buildings and bridges all over the world.At the beginning of the 1960s,an efficient adhesive bonding technique1,2was introduced to connect the Concrete slab and the steel girder by an adhesive joint,not by the conventional metallic
7、shear connectors.This so-called adhesive bonded steel-concrete composite beam is considered to be a very prospective alternate structure because it has the advantages of relieving stress concentration,avoiding site welding,and using the prefabricated concrete slab.Recently,an umber of studies on the
8、 experimental tests and numerical simulation of adhesive bonded steel-concrete composite beams have been presented in literatures3-5. With the ever increasing computational power,the past two decades have seen a 2 rapid development of structural optimization in both theories and engineering applicat
9、ions.In particular,the non-deterministic optimal design of steel or concrete beams incorporating stochastic uncertainties has been intensively studied by using the reliability-based design optimization (RBDO) method 6,7.Based on the classical probability theory,this conventional RBDO method describe
10、s uncertainties in structural systems as stochastic variables or random fields with certain probability distribution and thus provides an effective tool for determining the best design solution while explicitly considering the unavoidable effects of parameter variations8.As the most mature non-deter
11、ministic design approach,the RBDO has been successfully used in many real-life engineering applications9,10.However,the primary challenge to apply the conventional RBDO in practical applications is the availability of the precise statistical characteristics,which are crucial for a successful probabi
12、listic reliability analysis and design.Unfortunately,these accurate data usually cannot be obtained in some practical applications where only a limited number of samples are available. The early treatment 11,12 for insufficient uncertainties is to construction a closest uniform probabilistic distrib
13、ution by using the principle of maximum entropy.In 1990s,Elishakoff 13,14 explored that a small error in constructing the probabilistic density function for input uncertainties may lead to misleading assessment of the probabilistic reliability in particular cases.This conclusion illuminates that usi
14、ng the traditional probabilistic approach to deal with those problems involving in complete the information might be inconvincible. Consequently, an alternative category,namely the non-probabilistic approach 15,has been rapid developed for describing uncertainty with incomplete statistical informati
15、on by a fuzzy set or a convexset. In the fuzzy set method16,17 ,the fuzzy failure probability of structures is assessed based on membership function representation of the observed/measured inputs.In the convex set method18-20, all possible values of the uncertainties are bounded within a hyper-box o
16、r hyper-ellipsoid without assuming any inner probability distributions.Non-probabilistic models have been regarded as attractive supplements to the traditional probabilistic model in the reliability design of structural engineering.The interested readers are referred to research papers bye.g. Moens
17、and Vandepitte 21,Moller and Beer 22,Elishakoff and Ohsaki23. In a practical engineering problem of adhesive bonded steel-concrete composite beams,the uncertain scatter of structural parameters about their expected values is unavoidable.For example,the applied loads may fluctuate dramatically during
18、 its service life-cycle,and the parameters defining the structure,such as geometrical dimensions and 3 material properties,are also subject to inaccuracies or deviations.Among these concerned uncertainties,some can be characterized with precise-enough probability distributions,while others need to b
19、e treated as bounded ones due to a lack of sufficient sample data.A typical example of such bounded uncertainties is the load magnitude and the geometrical dimensions of a manufactured product,the variation ranges of which are controlled by specified tolerance bounds. From as early as 1993,attempts
20、have been made to assess and analyze the structural safety in the presence of both stochastic variables and uncertain-but-bounded variables by Elishakoff and Colombi 24. Recently ,many numerical methods,including the multi-point approximation technique25,the iterative rescaling method 26,the probabi
21、lity bounds (p-box) approach 27,and the interval truncation method 28,have been proposed for estimating the lower and upper bounds of failure probability of structures with a combination of stochastic and interval variables.Detailed surveys of both known and new algorithms for this safety assessment
22、 problem have also been made by Berleant etal.29 and Kreinovich etal.30.However,it is noted that a few studies have considered various uncertainties in the reliability-based design optimization problems.Duetal.31 extended the conventional RBDO method to structural design problems under the combinati
23、on of random and interval variables.In their study,a procedure for seeking the worst-case combination of the interval variables is embedded into the probabilistic reliability analysis. As the literature survey shows,the existing studies mainly focus on solving the combination of random/interval vari
24、ables. Basically,the interval set does not account for the dependencies among the bounded uncertainties,which can be regarded as the simplest instance of the set-value based convex model.Due to the unpredictability of structural parameters and the impossibility of the acquisition of sufficient uncer
25、tainty information,problems of structural optimization must be solved in the presence of various types of uncertainties,which remains a challenging problem in realistic systems 32.As a consequence,apractical and efficient reliability-based design optimization being capable of quantifying probabilist
26、ic and non-probabilistic uncertainties,as well as associated numerical techniques,should be fully developed and adopted in the professional practice of adhesive bonded steel-concrete composite beam design. In this paper,using the mathematical definition of structural reliability index based on probability and convexsetmixed model 33,a nested optimization formulation with constraints on such mixed reliability indices for the adhesive bonded steel-concrete
