Application of a few orthogonal polynomials to the assessment of the fracture failure probability of a spherical tank

This paper presents some methods to assess the fracture failure probability of a spherical tank. These methods convert the assessment of the fracture failure probability into the calculation of the moment of cracks and a one-dimensional integral. In the paper, we first derive series' formulae to calculation the moments of cracks on the occasion of the crack fatigue growth and the moments of crack opening displacements according to JWES-2805 code. We then use the first n moments of crack opening displacements and a few orthogonal polynomials to compose the probability density function of the crack opening displacement. Lastly, the fracture failure probability is obtained according to the interference theory. An example proves that these methods are simpler, quicker, and more accurate. At the same time, these methods avoid the disadvantage of Edgeworth's series method. (author)