First- and second-order sensitivity analysis of finite element models using extended complex variables method

نویسندگانMojtaba Sheikhi-Mahdi Hassanzadeh
نشریهArchive of Applied Mechanics
نوع مقالهFull Paper
تاریخ انتشار2021
رتبه نشریهISI
نوع نشریهچاپی
کشور محل چاپایالات متحدهٔ امریکا

چکیده مقاله

This paper proposed a robust novel method that is called Extended Complex Variables
Method (ECVM) for the first and second-order sensitivity analysis. In the most previous
versions of complex variables method, only an imaginary step was used to analyze the
sensitivity. However, ECVM is employed both the real and imaginary parts to improve
the efficiency of it. The proposed method is applied for several problems with a closedform
solution, and the results are compared by past methods. It is illustrated that the
first-order sensitivity analysis is not influenced by the change of the step size for both
the traditional and extended complex variables methods. However, it is shown that,
unlike the complex variable’s method, the efficiency of ECVM is high and it is
independent of the step size for calculating the second-order sensitivity. The range of
accurate results for second-order sensitivity analysis by ECVM is between two until
four times more than CVM and FDM. Hence, this approach is suggested as an
appropriate technique for calculating simultaneously the first and second-order
sensitivities with high accuracy as well as low computational cost.

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