Steel structure stability problem of the reliability of the Research Review

(A) The steel structure system stability Research
The past two to three decades, the use of high-strength steel, the development of construction technology and computer applications make the steel system development and wide range of applications possible. The steel system stability has been the research areas of concern to scholars at home and abroad. After decades of research, has made a lot of research.
So far, the study of the basic building blocks of steel structure theory more and more mature stability analysis based on a variety of numerical analysis [1]. Member overall stability and local stability of the interaction of theory and design applications has yet to be carried out in-depth research. Reticulated shells damage due to structural instability, reticulated shell stability is a very important issue, correct latticed shell structure the monolayer shells structure stability analysis and design is to ensure that network shell the security of the key. Since the sixties, the the reticulated shell nonlinear stability analysis has been the focus of attention of scholars at home and abroad. Britain, the United States, Germany, Italy, Australia, Romania, Poland and other countries, researchers conducted a wide range of theoretical analysis and study of the theoretical aspects.Various methods such as the Newton - Raphson iteration method and arc-length method, generalized inverse method, artificial spring method, automatic solution technology, energy balancing technology to track the yield problem the whole process, the structure of the descent stage curves become possible [2] . Domestic scholars have undertaken extensive research about the stability of reticulated shells. [3] on the basis of the foreign research, through accurate theories expression, reasonable path to balance tracking technology and iterative strategies geometric nonlinear analysis of complex structural systems and regularity results. Random defect mode method and consistent defects modal method while taking advantage of the two methods, the reticulated shell structures of various initial defect study to describe the actual structure carrying. Some scholars to conduct experimental research [4] - [6], the validity and accuracy of different analytical methods were described. [7] the power of reticulated shell instability mechanism, stability criteria, dynamic postbuckling research. Like dynamic stability study of of reticulated shells sensitive structures such defects in the role of the strong winds and earthquakes, as it involves the theory of stability and vibration theory, it is difficult, the research is still very limited. [8] studied the dynamic stability of the spatial structure.
Large span truss arch structure as a new large-span structure, its stability, very little research. [9] using nonlinear finite element theory to the entire process of tracking the stability of large-span truss arch structure, and to draw some conclusions with practical application value. The cable-stayed space grid structure is a new type of hybrid space structure, the depth and breadth of its research is still very limited. [10] pointed out the need to further study the stability of the cable-stayed monolayer shells. Studies have grid structure the pillars supporting role and the grid structure of the cable-stayed plane in the grid structure constraints simplify the equivalent spring pillar stability, draw some useful conclusions 11]. Pre-tensioning structural system is currently more and more, a new type of structural system [12] - [16]. The system theoretical studies of this system largely lags behind the actual application, in particular, the study did not pay sufficient attention to the pre-tensioning structural system stability, the research is still very limited. [12] [13], the stability of the initial equilibrium state of the pre-tensioning structural system must attract enough attention, instability and failure may also occur under load prestressed cable structure system in working condition, and the actual The design calculations proposed two methods - direct algorithm with stability design method, nature and structural stability of the structure of the system to determine the method, and provide some theoretical guidance for further research.
In addition, scholars from the perspective of the overall stability of the stability of the steel frame structure, draw some useful conclusions [17] - [19].
(B) of the steel structure system stability study
Steel structure system stability studies made some progress, but there are also some problems can not be ignored:
1) the study of the stability of reticulated shells, beam - column element theory has become a major research tool. Beam - column element if true reflection of the stress state of the structure of the network shell is hard to say, although some scholars have been fixed beam - column unit [3]. The main problem is how to reflect the coupled effect of axial forces and bending moments.
2) the overall stability in the large span structure design, with locally stable relationship is a question worth exploring, take a unified stability safety factor in the design of large-span structures do not reflect the overall stability and local stability associated.
3) pre-tensioning structural system stable design theory is far from perfect, yet do not have a complete theoretical system to analyze the stability of the pre-tensioning structural system.
4) Study on the stability of the steel structure system, there are many random factors, the the structure random effects most of the analysis process is limited to determining the structure parameters, random load input range of such a pattern, and in the actual project, due to structural parameters uncertainty will cause the structural response of a significant difference. So we should focus on considering the structure of the random parameters extremum instability, interference-type buckling jumping instability problem in [20] [21] had to consider the stability problem of the random parameters dome network shell beneficial.
Steel structure system reliability stability problems
The actual structure due to the presence of a variety of random defects ideal structural differences. For the sensitivity of the structure of the defect, the defect may cause a sharp decline in the structural stability, it is necessary to consider the impact of random parameters, the introduction of the reliability of analytical methods, stability reliability.Due to the large-span steel structure system reliability study involved more knowledge of mechanics and mathematics, there is a certain degree of difficulty, the limited success of current research in this area. [2] had the reliability of the analysis and design of the stability of reticulated shell exhaustive research, rich theoretical and computational methods of structural reliability, and applied to engineering analysis and design of the structure, showing good prospects.
The uncertainties sources of structural analysis of (a)
Affect just many of the basic variables of the structural stability of the system uncertainty is random, and is generally divided into three categories:
1) physical, geometrical uncertainty: such as material (elastic modulus, yield stress, Poisson's ratio, etc.), the size of the rod member, the cross-sectional area, the residual stress, initial deformation.
2) the statistical uncertainty: Statistics and relating to the stability of the physical quantities and Geometrical always based on limited samples to select the probability density function, so bring some empirical. This uncertainty called statistical uncertainty is caused by the lack of information.
3) the uncertainty of the model: In order to analyze the structure, the various factors mentioned assumptions, mathematical models, boundary conditions and the current level of technology is difficult to reflect in the calculation, the result of the theoretical values ​​with the actual carrying capacity differences attributed to the uncertainty of the model.
(B) the reliability of the study of the structure
Scholars of structural reliability theory has a more in-depth study, reliability analysis of the reliability calculation method and the complex structure made a lot of research [22] - [39].
The ultimate goal of any engineering analysis and design is to design structures to meet the different requirements of different features - security, usability, durability, due to the presence of uncertainty, you need these uncertainties added engineering design, whicha lot of reliability methods. In order to estimate the structural reliability, we must first solve the load and resistance parameters as well as the functional relationship between them, where this relationship (also called functions) denoted X1, X2, ..., Xn is a random variable. Limit state (or failure surface) is defined as Z0, reliability parameters describe the reliability index is defined as the minimum distance of the coordinate origin to the failure surface is calculated for reliability indicators are generally two methods: a reliability method (FORM ) and secondary Reliability of methods (SORM).
(C) Review of numerical methods of analysis for structural reliability
Performance function g (x) usually can not articulate the complex structure, usually by numerical methods (such as finite element) to calculate the response function, the structure of the input random variables. These numerical methods are generally divided into three categories: (1) Monte Carlo simulation (MonteCarloSimulation) [34] (including efficient sampling and variance reduction techniques); (2) in response to surface method (ResponseSurfaceMethod) [31] [32] ) based on the sensitivity analysis method (Sensitivity-basedApproach) [30].
1) Monte Carlo simulation (MonteCarloSimulation)
The basic idea of ​​the Monte Carlo simulation method for statistical analysis to calculate the reliability of the structure during every uncertainty analysis before randomly generated a set of input variables, a large number of repeat uncertainty analysis of structural response output parameter. Combine Monte Carlo simulation with finite element method, finite element method in Monte Carlo. Monte Carlo finite element method is usually calculated as the reliability of the relative exact solution, but to achieve high accuracy, a sufficient number of samples must be taken, the computational workload is quite vast.
2) Response surface methodology (ResponseSurfaceMethod)
The basic idea of ​​the response surface method implicit performance function g (X) (one or quadratic polynomial) is expressed by a polynomial approximation to construct a clear expression of the form, where X contains all load and resistance random variables a vector. In essence, the response surface method is a statistical method, considered this way to find the input variable values ​​variability or uncertainty after the response best value. The probability of failure by once or twice a reliability method. Response surface method for a problem with a large number of random variables, accurately construct an approximate polynomial deterministic analysis required is quite huge, so this method is very time-consuming. Even for a problem with a small number of random variables, response surface method of reliability estimation accuracy with the accuracy of the approximate polynomial functions. If implicit functions has strong nonlinear function approximation is very approximate reliability estimate is very approximate.
3) based on the sensitivity of the analytical method (Sensitivity-basedApproach)
Based on sensitivity analysis and a reliability method (FORM) / secondary reliability method (SORM) combined analysis of the reliability problems with implicit functions overcome the Monte Carlo simulation and response surface method shortcomings. This method in the process of looking for control point (also called a minimum distance point), the true value and the real gradient of the function of the information used in each iteration are functional, and using optimization method converges to the minimum distance point of the control point, with the Monte compared Carlo simulation and the response surface method, it is time-consuming small than the response surface method more accurately. In addition, based on the sensitivity analysis methods from the design point of view to know the sensitivity of the structural response of the basic random variables. Which may be based on the uncertainty of the random variable and their structural characteristics different design safety factor of different random variables. The method can also be based on the sensitivity analysis does not affect the calculation accuracy, ignore those little random variables on structural reliability, thereby saving computation time. Based on the sensitivity analysis method using an iterative the perturbation analysis technology have combined to produce a so-called stochastic finite element method (StochasticFiniteElementMethod) and the finite element method.Iterative perturbation technique stochastic finite element method can be used to carry out non-linear analysis of the structure.
4) steel structure system stability reliability research methods
Just the reliability of the study of the structural system stability, the stochastic finite element method provides a powerful means of analysis, stochastic finite element method can be expected due to the stochastic finite element to consider the actual structure of the presence of a variety of random factors, so [ 30] in this field of research will have a good prospect.