All Set Theory in the Fuzzy-random Crack Structure

According to the all set theory, a fuzzy-random crack structural model is presented. To deal with the function, the following steps are taken. Firstly, when the structural geometry sizes are considered in the random numbers, the stress intensity factor (K1) equation of the mean value, variance and the interval of the random fracture function are transformed. Secondly, when the crack length is considered in a fuzzy variable, the K1 interval equation of the fracture structure is presented. Finally, the fuzzy-random K1 interval analysis to deal with the fracture structure is given, and the example shows application and effective in the fuzzy-random crack structures.