5.5 Component level reliability investigation of a statically indeterminate 10-bar truss
5.5.7 Conclusions on the methodologies
In previous sections, the reliability evaluation of a statically indeterminate ten-bar truss was performed using three methods of reliability calculation. Two different cases were considered for the structure. In Case I, load effect follows an Extreme Type I distribution and the resistance (yield stress) has a lognormal distribution. In case II, both of the random variables are normally distributed. In both of the cases, all of the basic random variables were uncorrelated.
The following conclusions are presented regarding a component level reliability analysis: • Computer programs were developed for all of the aforementioned methodologies. It was
shown that all the methods can be properly used for a computerised component level reliability analysis. For all of the above-mentioned methods, it is essential that proper interaction between the reliability evaluation modules and the deterministic finite element analysis be established. In the case of simulation methods, the results of the deterministic FEM analysis are used for the simulation and computation of failures during the simula- tion. For response surface method, FEM analysis is needed to obtain the required values for the regression and formation of the explicit limit states, and for the First Order Re- liability Methods (FORM) the FEM analysis is exploited for the calculation of the limit
perturbation where alterations to the finite element coding are necessary. As a result, failure to establish a proper link to the finite element module will lead to an incorrect and inaccurate reliability evaluation of the components.
• Among all the simulation methods, the updated Latin Hypercube seems to be the most efficient one. This fact is supported by the data presented in Table 5.33. The only problem with the updated Latin Hypercube sampling is the fact that the updating process and re- arrangement of the permutation matrix can make the process more time-consuming. Thus, if applying the updated Latin Hypercube sampling is not possible, the Latin Hypercube sampling can be a proper replacement. The Latin Hypercube sampling can take less time compared to the updated Latin Hypercube sampling, and it is more efficient compared to the direct Monte Carlo simulation. However, direct Monte Carlo method can also be useful for reliability computation.
• The response surface method was also used for the reliability assessment. With respect to component level reliability evaluation, response surface methods might not be as efficient as the other two methods since it is not as straightforward to program, and it has to be used together with either a simulation method or a first order reliability method anyway. However, when linear elastic analysis is performed and strength limit states of the compon- ents are being investigated, the regression part of the method can be eliminated. This is due to the fact that the relationship between the load and displacements is linear and only by applying an external force vector of unit forces, such as FI (refer to step 5 of FSFEM method in Section 5.5.5.2), the relationship between the external and internal component forces can be established. In other terms, the factor m shown in Section 5.5.5.3 can be obtained this way. This method can specifically be efficient in calculation of the system reliability. This will be discussed in Chapter 7 comprehensively.
• For the case of FORM methods, a fully stochastic finite element formulation seems more efficient compared to the application of a commercial FEM package such as Strand7. The fully stochastic finite element method only takes less than 5 seconds to compute the component reliability whereas the proposed FD-SFEM methodology takes about 1200 seconds for case I and about 500 seconds for Case II. However, both methods prove to yield reasonably accurate results.
• In general, it is recommended that a finite element code be provided instead of using a commercial FEM package. This is due to two reasons: first, the efficiency of using a commercial FEM package is significantly less than a developed FEM code, and, Moreover, due to the lack of speed using a commercial FEM package is not a viable option for simulation methods; therefore, a finite element code has to be provided for simulation methods anyway (a FEM code that is developed in the same programming language as the reliability analysis modules). Second, The coding of an application programming interface (API) that is used as a link between the commercial FEM package and the reliability analysis modules appears no less complex than developing a FEM code. Therefore, a
method such as FD-SFEM is only recommended when the finite element formulation is rather complex.
• In reliability evaluation of compression members the value of χ, which further reduces the member resistance, is recommended to be considered as a random variable. This will lead to a more realistic evaluation of the reliability index where it was shown that the effect in some cases can be significant.
• In conclusion, it can be inferred that for a comprehensive component level reliability eval- uation all the three methods are useful and access to all the developed methods should be provided in an integrated reliability analysis environment. A more sophisticated method such as FSFEM can be used for the preliminary evaluation which offers a faster way of reli- ability computation, and a simulation method can then be used for the confirmation of the FSFEM results. The response surface methods, should also be included in an integrated reliability environment where its usefulness is employed in system reliability calculation.