Mechanical part fuzzy reliability calculation method based on random finite element of super-relaxation iteration method

[0026] (1) Mean and variance of stress and strength

[0027] The geometric parameters, material parameters, and loads of mechanical parts are regarded as n normal random variables a 1 ,a 2 ,...,a i ,...,a n . produce N 1 Set geometric parameters, material parameters, and load values ​​of mechanical parts.

[0028] The finite element governing equation under static load can be written as

[0029] [K]{δ}={F}

[0030] where U = displacement vector, F = load, K = overall stiffness matrix

[0031] The super-relaxed iterative method is used to solve the above equation, as follows

[0032]

[0033]

[0034] (i=1,2,...,n; k=0,1)

[0035] The stress of element d is

[0036] {σ}=[D][B]U

[0037] [D] is the elasticity matrix, [B] is the strain matrix, and U is the node displacement array.

[0038] The average stress is

[0039]

[0040] The stress variance is

[0041]

[0042] If the numerical range of material strength is given in the design manual (σ xmin , σ...