تجزیه و تحلیل حساسیت از مشکلات ثبات ساختار دیواره نازک

Analysing the system behaviour in relation to the input quantities it is often necessary to find out what quantities have the greatest effect on the studied output. The article shows the essential methods of applied sensitivity analysis. The objective of the paper is to analyse the influence of initial imperfections on the resistance of a member under axial compression. The analysis uses the Latin Hypercube Sampling simulation method (LHS) [Novák D, Teplý B, Shiraishi N. Sensitivity analysis of structures. In: Proc. of the fifth int. conference on civil and structural engineering computing. 1993. p. 201–07; Novák D, Lawanwisut W, Bucher C. Simulation of random fields based on orthogonal transformation of covariance matrix and Latin hypercube sampling. In: Proc. of int. conference on Monte Carlo simulation. 2000. p. 129–36] together with advanced models based on the nonlinear beam finite element method. The histograms of initial imperfections obtained by measurement [Melcher J, Kala Z, Holický M, Fajkus M, Rozlívka L. Design characteristics of structural steels based on statistical analysis of metallurgical products. Journal of Constructional Steel Research 2004;60:795–808] were considered.

Solving the problems of stability, we are usually, besides the final result (stress and deformation, load-carrying capacity, failure probability, etc.), interested in the fact of how much the input parameters affect the result, or in other words what is the sensitivity of the response to the change of the input parameter. The use of the sensitivity analysis enables us to determine the dominant quantities that must be paid special attention. The sensitivity analysis can be generally divided into two fields: The deterministic sensitivity analysis (or also the design sensitivity) is quite a well known and commonly used means for designing a structure. It is the component part of a design procedure, which uses a computational model enabling a successive change of values of one input quantity and uses parametric study to investigate the effect of the change on the output quantity. Even though these studies are very valuable and provide a quick overview on the model behaviour, they do not usually enable satisfactory conception of the whole spectrum of the possible cases that can occur on the real structure. In this connection we normally use a parametric study (sometimes called “what-if-study”). The stochastic sensitivity analysis provides more complex (and quantified!) information on the parameter’s influence. The procedure of determining the sensitivity is to a certain extent similar to the deterministic sensitivity analysis. We also change the value parameter and observe how it is reflected in the output quantity. The change of the input quantity respects also the frequency of the occurrence, i.e. the realizations of the input random quantities are simulated as if they were received by measuring. The simulation usually indicates a phase of experimental work using a representation of a computational model. The objective of the simulation is to analyse the behaviour of the system in dependence on the input quantities and values of parameters. In recent years, many various stochastic sensitivity analysis methods have been developed 12. and 13. and a number of possibilities for their practical applications has been presented 5. and 8.. Together with the development of new reliability analysis concepts (see, e.g., 6., 9. and 17.), these methods can contribute to qualitative improvement of structure reliability analysis methods.

It is evident from Fig. 2, Fig. 3 and Fig. 4 that the sensitivity coefficients vary in dependence on the member slenderness. Full-size image (40 K) Fig. 2. Results of sensitivity analysis of strut View the MathML sourceL=1.2m, View the MathML sourceλ¯=0.6. Figure options Full-size image (40 K) Fig. 3. Results of sensitivity analysis of strut View the MathML sourceL=2.0m, View the MathML sourceλ¯=1.0. Figure options Full-size image (40 K) Fig. 4. Results of sensitivity analysis of strut View the MathML sourceL=2.8m, View the MathML sourceλ¯=1.4. Figure options It is presented in Fig. 4 that the load-carrying capacity variability of a member with non-dimensional slenderness [18]View the MathML sourceλ¯=1.4 is highly sensitive to the variability of flange thickness t2t2 and further, to the variability of flange width bb and of Young’s modulus EE above all. The positive value of the correlation coefficient means that with increasing value of the given quantity, also the load-carrying capacity increases. The correlation coefficient value of Young’s modulus EE is comparable with the correlation coefficient of initial curvature e0e0; the value is, however, negative. The load-carrying capacity is sensitive to the Young modulus variability fyfy only very little. It is obvious from Fig. 2 that, for the member with non-dimensional slenderness View the MathML sourceλ¯=0.6 the yield strength considerably influences the increase in load-carrying capacity. The sensitivity coefficients kiki according to (2) refer to the dominant influence of yield strength on load-carrying capacity, as well. As both applied methods (1) and (2) are based on different assumptions the comparison of results is difficult. However, each method has the informative value of the other type. The flange thickness t2t2 and also the initial curvature e0e0 are further significant quantities. The variability influence of Young’s modulus EE on load-carrying capacity is practically negligible. For the member with non-dimensional slenderness View the MathML sourceλ¯=1.0 it can be seen from Fig. 3 that the influence of yield strength, flange thickness, and also of the other quantities is evidently overlapped by the variability influence of initial curvature e0e0. However, it is to be noticed that the differentiation of load-carrying capacity of compression members is derived from the effects of residual stresses above all which were neglected in the present study. The buckling curves aa, bb, cc, dd of [18] are the most differing and at the same time, they decrease most rapidly for the approximate value of View the MathML sourceλ¯≈1.0. The input random imperfections can be divided approximately into two basic groups—those the statistical characteristics of which can be favourably influenced by manufacturing (yield strength, geometrical characteristics), and those not satisfactorily sensitive to manufacturing technology changes (e.g., Young’s modulus EE variability). The first group of quantities can be subdivided into two subgroups: (i) quantities for which both mean value and standard deviation can be changed by improvement in quality of manufacturing–such a quantity is, e.g., yield strength; (ii) quantities the mean value of which cannot be changed more substantially as the mean value should equal the nominal value, e.g., geometrical characteristics of cross-section dimensions. According to Fig. 2, Fig. 3 and Fig. 4 the flange thickness t2t2 is the important quantity having always a relatively great influence on load-carrying capacity. Lowering the variability of this quantity can be reached by the manufacturing technology change. The variability decrease of yield strength fyfy can be recommended for members with lower non-dimensional slenderness above all.