PSI - Issue 41

Victor Rizov et al. / Procedia Structural Integrity 41 (2022) 103–114 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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T n T nT  (here, 0 1   n ) the temperature increases linearly. The temperature is 1 T

n i i t t t T    where

At

T n T mT  , 0 1   m . At

i n i t T t t T      1 where m

1      i m i t t t T the temperature decreases 1

at

linearly (Fig. 3).

Fig. 3. Periodic variation of temperature with time.

The effect of temperature on * E is treated by using the approach presented in (Narisawa (1987)). In order to apply this approach, the temperature has to be expressed as a function of time. For this purpose, the temperature is expanded in series of Fourier              1 1 0 sin cos j j j j j t j t q p T p   , T T   2  , (36) where   T t dt T p T T T   0 0 1 , (37)     j t dt T t T p T T T j   0 cos 2  , (38)     j t dt T t T q T T T j   0 sin 2  . (39) After performing of some mathematical operations, one obtains   p T n m 3 2 2 1 0    . (40)